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NBA All-Star Game Most Valuable Player Award
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The National Basketball Association All-Star Game Most Valuable Player (MVP) is an annual National Basketball Association (NBA) award given to the player(s) voted best of the annual All-Star Game. The award was established in 1953 when NBA officials decided to designate an MVP for each year's game. The league also re-honored players from the previous two All-Star Games. Ed Macauley and Paul Arizin were selected as the 1951 and 1952 MVP winners respectively.[1] The voting is conducted by a panel of media members, who cast their vote after the conclusion of the game. The player(s) with the most votes or ties for the most votes wins the award.[2] No All-Star Game MVP was named in 1999 since the game was canceled due to the league's lockout.[3] As of 2018[update], the most recent recipient is Cleveland Cavaliers forward LeBron James.
Bob Pettit and Kobe Bryant are the only two players to win the All-Star Game MVP four times. Oscar Robertson, Michael Jordan, Shaquille O'Neal, and LeBron James have each won the award three times, while Bob Cousy, Julius Erving, Isiah Thomas, Magic Johnson, Karl Malone, Allen Iverson, and Russell Westbrook have all won the award twice. James' first All-Star MVP in 2006 made him the youngest to have ever won the award at the age of 21 years, 1 month. Kyrie Irving, winner of the 2014 All-Star Game MVP, is the second-youngest at 21 years, 10 months. They are notable as being the two youngest to win the award, both as Cleveland Cavaliers.[4][5] Four of the games had joint winners—Elgin Baylor and Pettit in 1959, John Stockton and Malone in 1993, O'Neal and Tim Duncan in 2000, and O'Neal and Bryant in 2009. O'Neal became the first player in All-Star history to share two MVP awards as well as the first player to win the award with multiple teams. The Los Angeles Lakers have had eleven winners while the Boston Celtics have had eight. Duncan of the U.S. Virgin Islands and Irving of Australia are the only winners not born in the United States. Both Duncan and Irving[a] are American citizens, but are considered "international" players by the NBA because they were not born in one of the fifty states or Washington, D.C.[6] No player trained entirely outside the U.S. has won the award; Irving lived in the U.S. since age two, and Duncan played U.S. college basketball at Wake Forest.
Bob Pettit (1958, 1959) and Russell Westbrook (2015, 2016) are the only players to win consecutive awards. Pettit (1956), Bob Cousy (1957), Wilt Chamberlain (1960), Bill Russell (1963), Oscar Robertson (1964), Willis Reed (1970), Dave Cowens (1973), Michael Jordan (1988, 1996, 1998), Magic Johnson (1990), Shaquille O'Neal (2000), and Allen Iverson (2001) all won the All-Star Game MVP and the NBA Most Valuable Player Award in the same season; Jordan is the only player to do this multiple times.[7] 14 players have won the award playing for the team that hosted the All-Star Game: Macauley (1951), Cousy (1957), Pettit (1958, 1962), Chamberlain (1960), Adrian Smith (1966), Rick Barry (1967), Jerry West (1972), Tom Chambers (1987), Jordan (1988), Karl Malone (1993), John Stockton (1993), O'Neal (2004, 2009), Bryant (2011) and Davis (2017); Pettit and O'Neal did this multiple times. Kareem Abdul-Jabbar has the distinction of playing in the most All-Star Games (18) without winning the All-Star Game MVP, while Adrian Smith won the MVP in his only All-Star Game.
Contents
[hide]
1 Winners
2 Multi-time winners
3 See also
4 Notes
5 References
Winners[edit]
Hall-of-Famer Bill Russell (left) won the award in the 1963 NBA All-Star Game. Hall-of-Famer Wilt Chamberlain (center) won the award in the 1960 NBA All-Star Game.
Hall-of-Famer Michael Jordan won the award three times in his career.
Hall-of-Famer Charles Barkley won the award in the 1991 NBA All-Star Game.
Hall-of-Famer Shaquille O'Neal has won the award three times in his career. He is also the oldest MVP ever, at 36 years and 346 days old.
Kobe Bryant has won the award a record four times in his career, a feat he shares with Bob Pettit.
LeBron James was the youngest player to ever win the award at 21 years and 51 days old and is the all-time leader in points scored in NBA All-Star Game history.[8]
Kyrie Irving won the award in his second All-Star game in 2014
^ Denotes player who is still active in the NBA
* Elected to the Naismith Memorial Basketball Hall of Fame
Player (X) Denotes the number of times the player has been awarded the MVP award
Team (X) Denotes the number of times a player from this team has won
Season
Player
Position
Nationality
Team
1951
Macauley, EdEd Macauley*
Center/Forward United States Boston Celtics
1952
Arizin, PaulPaul Arizin*
Forward/Guard United States Philadelphia Warriors
1953
Mikan, GeorgeGeorge Mikan*
Center United States Minneapolis Lakers
1954
Cousy, BobBob Cousy*
Guard United States Boston Celtics (2)
1955
Sharman, BillBill Sharman*
Guard United States Boston Celtics (3)
1956
Pettit, BobBob Pettit*
Forward/Center United States St. Louis Hawks
1957
Cousy, BobBob Cousy* (2)
Guard United States Boston Celtics (4)
1958
Pettit, BobBob Pettit* (2)
Forward/Center United States St. Louis Hawks (2)
1959[b]
Baylor, ElginElgin Baylor*
Forward United States Minneapolis Lakers (2)
Pettit, BobBob Pettit* (3)
Forward/Center United States St. Louis Hawks (3)
1960
Chamberlain, WiltWilt Chamberlain*
Center United States Philadelphia Warriors (2)
1961
Robertson, OscarOscar Robertson*
Guard United States Cincinnati Royals
1962
Pettit, BobBob Pettit* (4)
Forward/Center United States St. Louis Hawks (4)
1963
Russell, BillBill Russell*
Center United States Boston Celtics (5)
1964
Robertson, OscarOscar Robertson* (2)
Guard United States Cincinnati Royals (2)
1965
Lucas, JerryJerry Lucas*
Forward/Center United States Cincinnati Royals (3)
1966
Smith, AdrianAdrian Smith
Guard United States Cincinnati Royals (4)
1967
Barry, RickRick Barry*
Forward United States San Francisco Warriors (3)
1968
Greer, HalHal Greer*
Guard/Forward United States Philadelphia 76ers
1969
Robertson, OscarOscar Robertson* (3)
Guard United States Cincinnati Royals (5)
1970
Reed, WillisWillis Reed*
Center/Forward United States New York Knicks
1971
Wilkens, LennyLenny Wilkens*
Guard United States Seattle SuperSonics
1972
West, JerryJerry West*
Guard United States Los Angeles Lakers (3)
1973
Cowens, DaveDave Cowens*
Center/Forward United States Boston Celtics (6)
1974
Lanier, BobBob Lanier*
Center United States Detroit Pistons
1975
Frazier, WaltWalt Frazier*
Guard United States New York Knicks (2)
1976
Bing, DaveDave Bing*
Guard United States Washington Bullets
1977
Erving, JuliusJulius Erving*
Forward United States Philadelphia 76ers (2)
1978
Smith, RandyRandy Smith
Guard/Forward United States Buffalo Braves
1979
Thompson, DavidDavid Thompson*
Guard/Forward United States Denver Nuggets
1980
Gervin, GeorgeGeorge Gervin*
Guard/Forward United States San Antonio Spurs
1981
Archibald, NateNate Archibald*
Guard United States Boston Celtics (7)
1982
Bird, LarryLarry Bird*
Forward United States Boston Celtics (8)
1983
Erving, JuliusJulius Erving* (2)
Forward United States Philadelphia 76ers (3)
1984
Thomas, IsiahIsiah Thomas*
Guard United States Detroit Pistons (2)
1985
Sampson, RalphRalph Sampson*
Center/Forward United States Houston Rockets
1986
Thomas, IsiahIsiah Thomas* (2)
Guard United States Detroit Pistons (3)
1987
Chambers, TomTom Chambers
Forward/Center United States Seattle SuperSonics (2)
1988
Jordan, MichaelMichael Jordan*
Guard United States Chicago Bulls
1989
Malone, KarlKarl Malone*
Forward United States Utah Jazz
1990
Johnson, MagicMagic Johnson*
Guard United States Los Angeles Lakers (4)
1991
Barkley, CharlesCharles Barkley*
Forward United States Philadelphia 76ers (4)
1992
Johnson, MagicMagic Johnson* (2)
Guard United States Los Angeles Lakers (5)
1993[b]
Stockton, JohnJohn Stockton*
Guard United States Utah Jazz (2)
Malone, KarlKarl Malone* (2)
Forward United States Utah Jazz (3)
1994
Pippen, ScottieScottie Pippen*
Forward United States Chicago Bulls (2)
1995
Richmond, MitchMitch Richmond*
Guard United States Sacramento Kings (6)
1996
Jordan, MichaelMichael Jordan* (2)
Guard United States Chicago Bulls (3)
1997
Rice, GlenGlen Rice
Forward United States Charlotte Hornets
1998
Jordan, MichaelMichael Jordan* (3)
Guard United States Chicago Bulls (4)
1999
Not awarded as the game was canceled due to the league's lockout.[3]
2000[b]
O'Neal, ShaquilleShaquille O'Neal*
Center United States Los Angeles Lakers (6)
Duncan, TimTim Duncan Forward/Center United States[c] San Antonio Spurs (2)
2001
Iverson, AllenAllen Iverson*
Guard United States Philadelphia 76ers (5)
2002
Bryant, KobeKobe Bryant
Guard United States Los Angeles Lakers (7)
2003
Garnett, KevinKevin Garnett
Forward/Center United States Minnesota Timberwolves
2004
O'Neal, ShaquilleShaquille O'Neal* (2)
Center United States Los Angeles Lakers (8)
2005
Iverson, AllenAllen Iverson* (2)
Guard United States Philadelphia 76ers (6)
2006
James, LeBronLeBron James^ [d]
Forward United States Cleveland Cavaliers
2007
Bryant, KobeKobe Bryant (2)
Guard United States Los Angeles Lakers (9)
2008
James, LeBronLeBron James^ (2)
Forward United States Cleveland Cavaliers (2)
2009[b]
Bryant, KobeKobe Bryant (3)
Guard United States Los Angeles Lakers (10)
O'Neal, ShaquilleShaquille O'Neal* (3) [e]
Center United States Phoenix Suns
2010
Wade, DwyaneDwyane Wade^
Guard United States Miami Heat
2011
Bryant, KobeKobe Bryant (4)
Guard United States Los Angeles Lakers (11)
2012
Durant, KevinKevin Durant^
Forward United States Oklahoma City Thunder (3)
2013
Paul, ChrisChris Paul^
Guard United States Los Angeles Clippers (2)
2014
Irving, KyrieKyrie Irving^
Guard United States[a] Cleveland Cavaliers (3)
2015
Westbrook, RussellRussell Westbrook^
Guard United States Oklahoma City Thunder (4)
2016
Westbrook, RussellRussell Westbrook^ (2)
Guard United States Oklahoma City Thunder (5)
2017
Davis, AnthonyAnthony Davis^
Forward/Center United States New Orleans Pelicans
2018
James, LeBronLeBron James^ (3)
Forward United States Cleveland Cavaliers (4)
Multi-time winners[edit]
Player
Team
No.
Years
Pettit, BobBob Pettit St. Louis Hawks 4 1956, 1958, 1959, 1962
Bryant, KobeKobe Bryant Los Angeles Lakers 2002, 2007, 2009, 2011
Robertson, OscarOscar Robertson Cincinnati Royals 3 1961, 1964, 1969
Jordan, MichaelMichael Jordan Chicago Bulls 1988, 1996, 1998
O'Neal, ShaquilleShaquille O'Neal Los Angeles Lakers
Phoenix Suns 2000, 2004, 2009
James, LeBronLeBron James Cleveland Cavaliers 2006, 2008, 2018
Cousy, BobBob Cousy Boston Celtics 2 1954, 1957
Erving, JuliusJulius Erving Philadelphia 76ers 1977, 1983
Thomas, IsiahIsiah Thomas Detroit Pistons 1984, 1986
Malone, KarlKarl Malone Utah Jazz 1989, 1993
Johnson, MagicMagic Johnson Los Angeles Lakers 1990, 1992
Iverson, AllenAllen Iverson Philadelphia 76ers 2001, 2005
Westbrook, RussellRussell Westbrook Oklahoma City Thunder 2015, 2016
See also[edit]
National Basketball Association portal
NBA Most Valuable Player Award
Bill Russell NBA Finals Most Valuable Player Award
List of NBA All-Stars
Notes[edit]
^ Jump up to: a b Kyrie Irving was born in Australia to American parents who returned to the U.S. when he was two years old. He has dual U.S. and Australian citizenship, but has represented the United States internationally.[11]
^ Jump up to: a b c d Denotes All-Star Games in which joint winners were named
Jump up ^ Because Tim Duncan is a United States citizen by birth, as are all natives of the U.S. Virgin Islands,[9] he was able to play for the U.S. internationally.[10]
Jump up ^ James, at 21 years and 51 days old, is the youngest All-Star Game MVP in NBA history.
Jump up ^ O'Neal, at 36 years and 346 days old, is the oldest All-Star Game MVP in NBA history.
References[edit]
General
"All-Star Game: Year-by-Year Results". NBA.com. Turner Sports Interactive, Inc. Retrieved July 23, 2008.
Specific
Jump up ^ Steve Popper (February 5, 1998). "N.B.A. All-Star Weekend; Macauley's '51 All-Star Honors Came Late (but He's Not Complaining)". The New York Times. Retrieved July 23, 2008.
Jump up ^ Howard-Cooper, Scott (February 12, 1990). "East Stars Put It Together, but Magic Has Hardware Pro basketball: Laker guard earns MVP in losing effort as rest of his West teammates are shut down, 130-113". Los Angeles Times. Archived from the original on February 15, 2016.
^ Jump up to: a b Steele, David (December 9, 1998). "NBA Drops All-Stars – What's Left? February game in Philly latest casualty of lockout". San Francisco Chronicle. Retrieved December 17, 2008.
Jump up ^ "King-Sized Rally Propels East to Victory". NBA.com. Turner Sports Interactive, Inc. Retrieved April 25, 2009.
Jump up ^ Boyer, Mary (February 17, 2014). "Cleveland Cavaliers All-Star MVP Kyrie Irving has his moment – with advice from LeBron James". The Plain Dealer. Retrieved February 17, 2014.
Jump up ^ "Bargnani becomes first European top NBA draft pick". People's Daily Online. June 29, 2006. Retrieved June 16, 2008.
Jump up ^ "NBA & ABA Most Valuable Player Award Winners". Basketball-reference.com. Retrieved 2014-11-04.
Jump up ^ NBA All-Star Game Career Leaders | Basketball-Reference.com
Jump up ^ "Virgin Islands". CIA World Factbook. Retrieved August 12, 2008.
Jump up ^ "All-Time USA Basketball Men's Roster: D". USA Basketball. Archived from the original on August 28, 2009. Retrieved June 16, 2008.
Jump up ^ Ward, Roy (July 3, 2013). "Irving a must for Boomers in Rio: Bogut". The Sydney Morning Herald. Archived from the original on February 17, 2014.
[show]
v
t
e
NBA All-Star Game Most Valuable Player Award
1951: Macauley
1952: Arizin
1953: Mikan
1954: Cousy
1955: Sharman
1956: Pettit
1957: Cousy
1958: Pettit
1959: Baylor & Pettit
1960: Chamberlain
1961: Robertson
1962: Pettit
1963: Russell
1964: Robertson
1965: Lucas
1966: A. Smith
1967: Barry
1968: Greer
1969: Robertson
1970: Reed
1971: Wilkens
1972: West
1973: Cowens
1974: Lanier
1975: Frazier
1976: Bing
1977: Erving
1978: R. Smith
1979: Thompson
1980: Gervin
1981: Archibald
1982: Bird
1983: Erving
1984: Thomas
1985: Sampson
1986: Thomas
1987: Chambers
1988: Jordan
1989: Malone
1990: Johnson
1991: Barkley
1992: Johnson
1993: Stockton & Malone
1994: Pippen
1995: Richmond
1996: Jordan
1997: Rice
1998: Jordan
1999: No game played
2000: O'Neal & Duncan
2001: Iverson
2002: Bryant
2003: Garnett
2004: O'Neal
2005: Iverson
2006: James
2007: Bryant
2008: James
2009: Bryant & O'Neal
2010: Wade
2011: Bryant
2012: Durant
2013: Paul
2014: Irving
2015: Westbrook
2016: Westbrook
2017: Davis
[show]
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Who Wants to Be a Millionaire? New Zealand
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Who Wants to Be a Millionaire? New Zealand
Logo of Who Wants to Be a Millionaire? New Zealand
Also known as
'Millionaire'
Genre
Game show
Created by
David Briggs
Directed by
Peter Ots
Presented by
Mike Hosking
Composer(s)
Keith Strachan
Matthew Strachan
Country of origin
New Zealand
Original language(s)
English
No. of seasons
1
No. of episodes
10
Production
Location(s)
Richmond, Victoria, Australia
Running time
60 minutes (with commercials)
Production company(s)
2waytraffic
Release
Original network
TV ONE
Picture format
576i (SDTV)
1080i (HDTV)
Audio format
Stereo
Original release
9 September – 11 November 2008
Who Wants to Be a Millionaire? New Zealand was a New Zealand game show based on the original British format of Who Wants to Be a Millionaire?. The show was hosted by Mike Hosking. The main goal of the game was to win one million New Zealand dollars by answering 15 multiple-choice questions correctly. There were four "lifelines". It was broadcast on the TVNZ station TV ONE. The show was taped in Melbourne, Australia on the set of the Australian version of the show.
One contestant, Kristin Castle, made New Zealand television history after walking away with NZ$250,000, the highest amount of money ever given to a single person on New Zealand television. The show received wide media coverage after the first ever contestant on the show, Courtney Washington, walked away with nothing after incorrectly answering the question about BMW supplying New Zealand's new fleet of ministerial limousines.[1]
Rules[edit]
As in the syndicated United States' version, contestants were selected for the show through a qualifying test instead of the traditional "Fastest Finger First" as seen on the British version. Contestants sit in the "Hot Seat" and are asked increasingly difficult general knowledge questions by the host. Questions are multiple choice and contestants choose between a possible four answers, sometimes with the aid of lifelines. On answering a question correctly the contestant plays for a bigger sum of money, getting ever closer to the maximum amount of one million dollars.
The traditional 15-question money tree was used and there was no clock.
The complete sequence of prizes is as follows. Guaranteed safe levels, where the contestant is guaranteed this amount of money to take home, regardless of any subsequent questions they may get wrong, are in bold.
Prize levels
$100
$200
$300
$500
$1,000
$2,000
$4,000
$8,000
$16,000
$32,000
$64,000
$125,000
$250,000
$500,000
$1,000,000
The contestants' run ends when they either answer a question incorrectly, decide to not answer a question and walk away with their prize money, or if they answer all 15 questions correctly (winning $1 million).
Lifelines[edit]
If at any point the contestants are unsure of the answer to a question, they use one or more "lifelines". After using lifelines, contestants can either answer the question, use another lifeline, or walk away and keep the money (except for the Switch lifeline).
50/50: The contestant asks the host to have the computer randomly eliminate two of the incorrect answer choices, leaving the contestant with a choice between the correct answer and one incorrect one.
Phone a Friend: Contestants may call one of up to three prearranged friends. The contestant must provide the three friends' names and phone numbers in advance. The contestant has thirty seconds to read the four choices to the friend, who must select an answer before the time runs out. Phone-a-friends often express their certainty as a percentage (I am 80% sure it's C).
Ask the Audience: The contestant polls the studio audience to ask them which answer they believe is correct. Members of the studio audience indicate their choices using an audience response system. The results are immediately displayed on the contestant's and host's screens. This is a popular lifeline, known for its near-perfect accuracy.
Switch the Question: This lifeline becomes available only after the contestant has correctly answered the $32,000 question. If the contestant has not chosen a final answer on the revealed question, this lifeline entitles the contestant to switch out the original question for another question of the same value. Once the contestant elects to use this lifeline, he or she cannot return to the original question, and thus the correct answer is revealed for the record. In addition, any lifelines used by the contestant while attempting to answer the original revealed question prior to the question switch will not be reinstated.
References[edit]
Jump up ^ Milne, Rebecca (5 October 2008). "The bitter millionaire contestant". The New Zealand Herald. Retrieved 3 December 2011.
Retrieved from "https://en.wikipedia.org/w/index.php?title=Who_Wants_to_Be_a_Millionaire%3F_New_Zealand&oldid=742185609"
Categories:
Who Wants to Be a Millionaire?
New Zealand game shows
TVNZ 1 programmes
2000s New Zealand television series
2008 New Zealand television series debuts
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Television shows set in Victoria (Australia)
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Brock
From Wikipedia, the free encyclopedia
Jump to: navigation, search
Brock may refer to:
Look up brock in Wiktionary, the free dictionary.
Contents
[hide]
1 Businesses
2 Fictional characters
3 People
4 Places
5 Schools
6 Ships
7 Other uses
8 See also
Businesses[edit]
Brock Motors, a short-lived automotive company founded in 1921 in Amherstberg, Ontario
Crowne Plaza Niagara Falls – Fallsview also known as the Brock Hotel, a hotel in Niagara Falls, Ontario
Brock Hotel Corporation, founded by Robert L. Brock
Fictional characters[edit]
Brock (Pokémon), a character in the fictional world of Pokémon
The Brocks, a family on the American television show Picket Fences
Eddie Brock, the longtime host of the Marvel alien symbiote Venom
John Brock, a fictional British undercover agent created by Desmond Skirrow
Matthew Brock, a news reporter on the American sitcom NewsRadio
Brock Lovett, a character in the 1997 film Titanic
Tommy Brock the badger from The Tale of Mr. Tod by Beatrix Potter
Brock Cantillo, on Breaking Bad the son of character Andrea Cantillo
Brock Samson, a character in the animated television series The Venture Bros.
People[edit]
Brock (surname), various people with this surname
Brock (given name), various people with this given name
Places[edit]
In Canada
Brock, Ontario, a township
Brock, Saskatchewan, a village
Brock No. 64, Saskatchewan. a rural municipality
Brock Island, a Canadian arctic island in the Northwest Territories
Brock River (Chibougamau River), a tributary of the Chibougamau River, in Eeyou Istchee Baie-James, Nord-du-Québec, Quebec
Brock River West, a tributary of Brock River, Quebec
Brock River North, a tributary of Brock River, Quebec
In England
Brock, a small village in Lancashire, England
River Brock, a river in Lancashire, England
In the United States:
Brock, Missouri, an unincorporated community
Brock, Nebraska, a village
Brock, Ohio, an unincorporated community
Brock, Texas, an unincorporated community
Schools[edit]
Brock University, a comprehensive university located in St. Catharines, Ontario, Canada
Brock High School (Ontario), a high school in Brock, Ontario
Brock High School (Texas), a high school in Brock, Texas
Ships[edit]
HMS Sir Isaac Brock, a British naval vessel destroyed at the Battle of York prior to being completed
USS Brock (APD-93), a United States Navy high-speed transport in commission from 1945 to 1947
Other uses[edit]
Brock, a traditional name for a badger
Team Brock (disambiguation), a series of Australian motor racing teams
Brock (miniseries), an Australian mini-series based on the life of motor racing driver Peter Brock
See also[edit]
Broc (disambiguation)
Brok (disambiguation)
This disambiguation page lists articles associated with the title Brock.
If an internal link led you here, you may wish to change the link to point directly to the intended article.
Retrieved from "https://en.wikipedia.org/w/index.php?title=Brock&oldid=816396496"
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This page was last edited on 21 December 2017, at 02:19.
Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. By using this site, you agree to the Terms of Use and Privacy Policy. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization.
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text:
pH
From Wikipedia, the free encyclopedia
Jump to: navigation, search
For other uses, see PH (disambiguation).
pH values of some common substances
Acids and bases
pH
Reaction
Titration
Extraction
Dissociation constant (acid)
Acid strength
Acidity function
Buffer solutions
Proton affinity
Self-ionization of water
Amphoterism
Acid types
Brønsted
Lewis
Mineral
Organic
Strong
Superacids
Weak
Monobasic acid
Dibasic acid
Tribasic acid
Solid
Base types
Brønsted
Lewis
Organic
Strong
Superbases
Non-nucleophilic
Weak
v
t
e
In chemistry, pH (/piːˈ(h)eɪtʃ/) (potential of hydrogen) is a numeric scale used to specify the acidity or basicity of an aqueous solution. It is approximately the negative of the base 10 logarithm of the molar concentration, measured in units of moles per liter, of hydrogen ions. More precisely it is the negative of the base 10 logarithm of the activity of the hydrogen ion.[1] Solutions with a pH less than 7 are acidic and solutions with a pH greater than 7 are basic. Pure water is neutral, at pH 7 (25 °C), being neither an acid nor a base. Contrary to popular belief, the pH value can be less than 0 or greater than 14 for very strong acids and bases respectively.[2]
Measurements of pH are important in agronomy, medicine, biology, chemistry, agriculture, forestry, food science, environmental science, oceanography, civil engineering, chemical engineering, nutrition, water treatment and water purification, and many other applications.
The pH scale is traceable to a set of standard solutions whose pH is established by international agreement.[3] Primary pH standard values are determined using a concentration cell with transference, by measuring the potential difference between a hydrogen electrode and a standard electrode such as the silver chloride electrode. The pH of aqueous solutions can be measured with a glass electrode and a pH meter, or an indicator.
Contents
[hide]
1 History
2 Definition and measurement
2.1 pH
2.2 p[H]
2.3 pH indicators
2.4 pOH
2.5 Extremes of pH
2.6 Non-aqueous solutions
3 Applications
3.1 pH in soil
3.1.1 Classification of soil pH ranges
3.2 pH in nature
3.3 Seawater
3.4 Living systems
4 Calculations of pH
4.1 Strong acids and bases
4.2 Weak acids and bases
4.3 General method
5 See also
6 References
7 External links
History
The concept of pH was first introduced by the Danish chemist Søren Peder Lauritz Sørensen at the Carlsberg Laboratory in 1909[4] and revised to the modern pH in 1924 to accommodate definitions and measurements in terms of electrochemical cells. In the first papers, the notation had the "H" as a subscript to the lowercase "p", as so: pH.
The exact meaning of the "p" in "pH" is disputed, but according to the Carlsberg Foundation, pH stands for "power of hydrogen".[5] It has also been suggested that the "p" stands for the German Potenz[not in citation given] (meaning "power"), others refer to French puissance (also meaning "power", based on the fact that the Carlsberg Laboratory was French-speaking). Another suggestion is that the "p" stands for the Latin terms pondus hydrogenii (quantity of hydrogen), potentia hydrogenii (capacity of hydrogen), or potential hydrogen. It is also suggested that Sørensen used the letters "p" and "q" (commonly paired letters in mathematics) simply to label the test solution (p) and the reference solution (q).[6] Currently in chemistry, the p stands for "decimal cologarithm of", and is also used in the term pKa, used for acid dissociation constants.[7]
Definition and measurement
pH
pH is defined as the decimal logarithm of the reciprocal of the hydrogen ion activity, aH+, in a solution.[3]
p H = − log 10  ( a H + ) = log 10  ( 1 a H + ) {\displaystyle \mathrm {pH} =-\log _{10}(a_{{\textrm {H}}^{+}})=\log _{10}\left({\frac {1}{a_{{\textrm {H}}^{+}}}}\right)}
For example, a solution with a hydrogen ion activity of 5×10−6 = 1/(2×105) (at that level essentially the number of moles of hydrogen ions per liter of solution) has a pH of log10(2×105) = 5.3. For a commonplace example based on the facts that the masses of a mole of water, a mole of hydrogen ions, and a mole of hydroxide ions are respectively 18 g, 1 g, and 17 g, a quantity of 107 moles of pure (pH 7) water, or 180 tonnes (18×107 g), contains close to 1 g of dissociated hydrogen ions (or rather 19 g of H3O+ hydronium ions) and 17 g of hydroxide ions.
Note that pH depends on temperature. For instance at 0 °C the pH of pure water is 7.47. At 25 °C it's 7.00, and at 100 °C it's 6.14.
This definition was adopted because ion-selective electrodes, which are used to measure pH, respond to activity. Ideally, electrode potential, E, follows the Nernst equation, which, for the hydrogen ion can be written as
E = E 0 + R T F ln  ( a H + ) = E 0 − 2.303 R T F p H {\displaystyle E=E^{0}+{\frac {RT}{F}}\ln(a_{{\textrm {H}}^{+}})=E^{0}-{\frac {2.303RT}{F}}\mathrm {pH} }
where E is a measured potential, E0 is the standard electrode potential, R is the gas constant, T is the temperature in kelvins, F is the Faraday constant. For H+ number of electrons transferred is one. It follows that electrode potential is proportional to pH when pH is defined in terms of activity. Precise measurement of pH is presented in International Standard ISO 31-8 as follows:[8] A galvanic cell is set up to measure the electromotive force (e.m.f.) between a reference electrode and an electrode sensitive to the hydrogen ion activity when they are both immersed in the same aqueous solution. The reference electrode may be a silver chloride electrode or a calomel electrode. The hydrogen-ion selective electrode is a standard hydrogen electrode.
Reference electrode | concentrated solution of KCl || test solution | H2 | Pt[clarification needed]
Firstly, the cell is filled with a solution of known hydrogen ion activity and the emf, ES, is measured. Then the emf, EX, of the same cell containing the solution of unknown pH is measured.
pH(X) = pH(S) + E S − E X z {\displaystyle {\text{pH(X)}}={\text{pH(S)}}+{\frac {E_{\text{S}}-E_{\text{X}}}{z}}}
The difference between the two measured emf values is proportional to pH. This method of calibration avoids the need to know the standard electrode potential. The proportionality constant, 1/z is ideally equal to 1 2.303 R T / F {\displaystyle {\frac {1}{2.303RT/F}}\ } the "Nernstian slope".
To apply this process in practice, a glass electrode is used rather than the cumbersome hydrogen electrode. A combined glass electrode has an in-built reference electrode. It is calibrated against buffer solutions of known hydrogen ion activity. IUPAC has proposed the use of a set of buffer solutions of known H+ activity.[3] Two or more buffer solutions are used in order to accommodate the fact that the "slope" may differ slightly from ideal. To implement this approach to calibration, the electrode is first immersed in a standard solution and the reading on a pH meter is adjusted to be equal to the standard buffer's value. The reading from a second standard buffer solution is then adjusted, using the "slope" control, to be equal to the pH for that solution. Further details, are given in the IUPAC recommendations.[3] When more than two buffer solutions are used the electrode is calibrated by fitting observed pH values to a straight line with respect to standard buffer values. Commercial standard buffer solutions usually come with information on the value at 25 °C and a correction factor to be applied for other temperatures.
The pH scale is logarithmic and therefore pH is a dimensionless quantity.
p[H]
This was the original definition of Sørensen,[5] which was superseded in favor of pH in 1909. However, it is possible to measure the concentration of hydrogen ions directly, if the electrode is calibrated in terms of hydrogen ion concentrations. One way to do this, which has been used extensively, is to titrate a solution of known concentration of a strong acid with a solution of known concentration of strong alkaline in the presence of a relatively high concentration of background electrolyte. Since the concentrations of acid and alkaline are known, it is easy to calculate the concentration of hydrogen ions so that the measured potential can be correlated with concentrations. The calibration is usually carried out using a Gran plot.[9] The calibration yields a value for the standard electrode potential, E0, and a slope factor, f, so that the Nernst equation in the form
E = E 0 + f 2.303 R T F log  [ H + ] {\displaystyle E=E^{0}+f{\frac {2.303RT}{F}}\log[{\mbox{H}}^{+}]}
can be used to derive hydrogen ion concentrations from experimental measurements of E. The slope factor, f, is usually slightly less than one. A slope factor of less than 0.95 indicates that the electrode is not functioning correctly. The presence of background electrolyte ensures that the hydrogen ion activity coefficient is effectively constant during the titration. As it is constant, its value can be set to one by defining the standard state as being the solution containing the background electrolyte. Thus, the effect of using this procedure is to make activity equal to the numerical value of concentration.
The glass electrode (and other ion selective electrodes) should be calibrated in a medium similar to the one being investigated. For instance, if one wishes to measure the pH of a seawater sample, the electrode should be calibrated in a solution resembling seawater in its chemical composition, as detailed below.
The difference between p[H] and pH is quite small. It has been stated[10] that pH = p[H] + 0.04. It is common practice to use the term "pH" for both types of measurement.
pH indicators
Main article: pH indicator
Chart showing the variation of color of universal indicator paper with pH
Indicators may be used to measure pH, by making use of the fact that their color changes with pH. Visual comparison of the color of a test solution with a standard color chart provides a means to measure pH accurate to the nearest whole number. More precise measurements are possible if the color is measured spectrophotometrically, using a colorimeter or spectrophotometer. Universal indicator consists of a mixture of indicators such that there is a continuous color change from about pH 2 to pH 10. Universal indicator paper is made from absorbent paper that has been impregnated with universal indicator. Another method of measuring pH is using an electronic pH meter.
pOH
Relation between p[OH] and p[H] (red = acidic region, blue = basic region)
pOH is sometimes used as a measure of the concentration of hydroxide ions. OH−. pOH values are derived from pH measurements. The concentration of hydroxide ions in water is related to the concentration of hydrogen ions by
[ O H − ] = K W [ H + ] {\displaystyle [\mathrm {OH} ^{-}]={\frac {K_{W}}{[\mathrm {H} ^{+}]}}}
where KW is the self-ionisation constant of water. Taking logarithms
p O H = p K W − p H {\displaystyle \mathrm {pOH} =\mathrm {pK_{W}} -\mathrm {pH} }
So, at room temperature, pOH ≈ 14 − pH. However this relationship is not strictly valid in other circumstances, such as in measurements of soil alkalinity.
Extremes of pH
Measurement of pH below about 2.5 (ca. 0.003 mol dm−3 acid) and above about 10.5 (ca. 0.0003 mol dm−3 alkaline) requires special procedures because, when using the glass electrode, the Nernst law breaks down under those conditions. Various factors contribute to this. It cannot be assumed that liquid junction potentials are independent of pH.[11] Also, extreme pH implies that the solution is concentrated, so electrode potentials are affected by ionic strength variation. At high pH the glass electrode may be affected by "alkaline error", because the electrode becomes sensitive to the concentration of cations such as Na+ and K+ in the solution.[12] Specially constructed electrodes are available which partly overcome these problems.
Runoff from mines or mine tailings can produce some very low pH values.[13]
Non-aqueous solutions
Hydrogen ion concentrations (activities) can be measured in non-aqueous solvents. pH values based on these measurements belong to a different scale from aqueous pH values, because activities relate to different standard states. Hydrogen ion activity, aH+, can be defined[14][15] as:
a H + = exp  ( μ H + − μ H + ⊖ R T ) {\displaystyle a_{H^{+}}=\exp \left({\frac {\mu _{H^{+}}-\mu _{H^{+}}^{\ominus }}{RT}}\right)}
where μH+ is the chemical potential of the hydrogen ion, μoH+ is its chemical potential in the chosen standard state, R is the gas constant and T is the thermodynamic temperature. Therefore, pH values on the different scales cannot be compared directly due to different solvated proton ions such as lyonium ions, requiring an intersolvent scale which involves the transfer activity coefficient of hydronium/lyonium ion.
pH is an example of an acidity function. Other acidity functions can be defined. For example, the Hammett acidity function, H0, has been developed in connection with superacids.
The concept of "Unified pH scale" has been developed on the basis of the absolute chemical potential of the proton. This scale applies to liquids, gases and even solids.[16]
Applications
Pure water is neutral. When an acid is dissolved in water, the pH will be less than 7 (25 °C). When a base, or alkali, is dissolved in water, the pH will be greater than 7. A solution of a strong acid, such as hydrochloric acid, at concentration 1 mol dm−3 has a pH of 0. A solution of a strong alkali, such as sodium hydroxide, at concentration 1 mol dm−3, has a pH of 14. Thus, measured pH values will lie mostly in the range 0 to 14, though negative pH values and values above 14 are entirely possible. Since pH is a logarithmic scale, a difference of one pH unit is equivalent to a tenfold difference in hydrogen ion concentration.
The pH of neutrality is not exactly 7 (25 °C), although this is a good approximation in most cases. Neutrality is defined as the condition where [H+] = [OH−] (or the activities are equal). Since self-ionization of water holds the product of these concentration [H+]×[OH−] = Kw, it can be seen that at neutrality [H+] = [OH−] =√(Kw), or pH = pKw/2. pKw is approximately 14 but depends on ionic strength and temperature, and so the pH of neutrality does also. Pure water and a solution of NaCl in pure water are both neutral, since dissociation of water produces equal numbers of both ions. However the pH of the neutral NaCl solution will be slightly different from that of neutral pure water because the hydrogen and hydroxide ions' activity is dependent on ionic strength, so Kw varies with ionic strength.
If pure water is exposed to air it becomes mildly acidic. This is because water absorbs carbon dioxide from the air, which is then slowly converted into bicarbonate and hydrogen ions (essentially creating carbonic acid).
CO 2 + H 2 O ↽ − − ⇀ HCO 3 − + H + {\displaystyle {\ce {{CO2}+{H2O}<=>{HCO3^{-}}+{H+}}}}
pH in soil
Classification of soil pH ranges
The United States Department of Agriculture Natural Resources Conservation Service, formerly Soil Conservation Service classifies soil pH ranges as follows: [17]
Denomination
pH range
Ultra acidic < 3.5
Extremely acidic 3.5–4.4
Very strongly acidic 4.5–5.0
Strongly acidic 5.1–5.5
Moderately acidic 5.6–6.0
Slightly acidic 6.1–6.5
Neutral 6.6–7.3
Slightly alkaline 7.4–7.8
Moderately alkaline 7.9–8.4
Strongly alkaline 8.5–9.0
Very strongly alkaline > 9.0
pH in nature
Lemon juice tastes sour because it contains 5% to 6% citric acid and has a pH of 2.2. (high acidity)
pH-dependent plant pigments that can be used as pH indicators occur in many plants, including hibiscus, red cabbage (anthocyanin) and red wine. The juice of citrus fruits is acidic mainly because it contains citric acid. Other carboxylic acids occur in many living systems. For example, lactic acid is produced by muscle activity. The state of protonation of phosphate derivatives, such as ATP, is pH-dependent. The functioning of the oxygen-transport enzyme hemoglobin is affected by pH in a process known as the Root effect.
Seawater
See also: Ocean acidification
The pH of seawater is typically limited to a range between 7.5 and 8.4.[18] It plays an important role in the ocean's carbon cycle, and there is evidence of ongoing ocean acidification caused by carbon dioxide emissions.[19] However, pH measurement is complicated by the chemical properties of seawater, and several distinct pH scales exist in chemical oceanography.[20]
As part of its operational definition of the pH scale, the IUPAC defines a series of buffer solutions across a range of pH values (often denoted with NBS or NIST designation). These solutions have a relatively low ionic strength (≈0.1) compared to that of seawater (≈0.7), and, as a consequence, are not recommended for use in characterizing the pH of seawater, since the ionic strength differences cause changes in electrode potential. To resolve this problem, an alternative series of buffers based on artificial seawater was developed.[21] This new series resolves the problem of ionic strength differences between samples and the buffers, and the new pH scale is referred to as the 'total scale', often denoted as pHT. The total scale was defined using a medium containing sulfate ions. These ions experience protonation, H+ + SO2−
4 ⇌ HSO−
4, such that the total scale includes the effect of both protons (free hydrogen ions) and hydrogen sulfate ions:
[H+]T = [H+]F + [HSO−
4]
An alternative scale, the 'free scale', often denoted 'pHF', omits this consideration and focuses solely on [H+]F, in principle making it a simpler representation of hydrogen ion concentration. Only [H+]T can be determined,[22] therefore [H+]F must be estimated using the [SO2−
4] and the stability constant of HSO−
4, K*
S:
[H+]F = [H+]T − [HSO−
4] = [H+]T ( 1 + [SO2−
4] / K*
S )−1
However, it is difficult to estimate K*
S in seawater, limiting the utility of the otherwise more straightforward free scale.
Another scale, known as the 'seawater scale', often denoted 'pHSWS', takes account of a further protonation relationship between hydrogen ions and fluoride ions, H+ + F− ⇌ HF. Resulting in the following expression for [H+]SWS:
[H+]SWS = [H+]F + [HSO−
4] + [HF]
However, the advantage of considering this additional complexity is dependent upon the abundance of fluoride in the medium. In seawater, for instance, sulfate ions occur at much greater concentrations (>400 times) than those of fluoride. As a consequence, for most practical purposes, the difference between the total and seawater scales is very small.
The following three equations summarise the three scales of pH:
pHF = − log [H+]F
pHT = − log ( [H+]F + [HSO−
4] ) = − log [H+]T
pHSWS = − log ( [H+]F + [HSO−
4] + [HF] ) = − log [H+]SWS
In practical terms, the three seawater pH scales differ in their values by up to 0.12 pH units, differences that are much larger than the accuracy of pH measurements typically required, in particular, in relation to the ocean's carbonate system.[20] Since it omits consideration of sulfate and fluoride ions, the free scale is significantly different from both the total and seawater scales. Because of the relative unimportance of the fluoride ion, the total and seawater scales differ only very slightly.
Living systems
pH in living systems[23]
Compartment
pH
Gastric acid 1.5-3.5[24]
Lysosomes 4.5
Human skin 4.7[25]
Granules of chromaffin cells 5.5
Urine 6.0
Cytosol 7.2
Blood (natural pH) 7.34–7.45
Cerebrospinal fluid (CSF) 7.5
Mitochondrial matrix 7.5
Pancreas secretions 8.1
The pH of different cellular compartments, body fluids, and organs is usually tightly regulated in a process called acid-base homeostasis. The most common disorder in acid-base homeostasis is acidosis, which means an acid overload in the body, generally defined by pH falling below 7.35. Alkalosis is the opposite condition, with blood pH being excessively high.
The pH of blood is usually slightly basic with a value of pH 7.365. This value is often referred to as physiological pH in biology and medicine. Plaque can create a local acidic environment that can result in tooth decay by demineralization. Enzymes and other proteins have an optimum pH range and can become inactivated or denatured outside this range.
Calculations of pH
The calculation of the pH of a solution containing acids and/or bases is an example of a chemical speciation calculation, that is, a mathematical procedure for calculating the concentrations of all chemical species that are present in the solution. The complexity of the procedure depends on the nature of the solution. For strong acids and bases no calculations are necessary except in extreme situations. The pH of a solution containing a weak acid requires the solution of a quadratic equation. The pH of a solution containing a weak base may require the solution of a cubic equation. The general case requires the solution of a set of non-linear simultaneous equations.
A complicating factor is that water itself is a weak acid and a weak base (see amphoterism). It dissociates according to the equilibrium
2 H 2 O ↽ − − ⇀ H 3 O + ( aq ) + OH − ( aq ) {\displaystyle {\ce {2H2O<=>{H3O+(aq)}+{OH^{-}(aq)}}}}
with a dissociation constant, Kw defined as
K w = [ H + ] [ OH − ] {\displaystyle K_{w}={\ce {[H+][OH^-]}}}
where [H+] stands for the concentration of the aqueous hydronium ion and [OH−] represents the concentration of the hydroxide ion. This equilibrium needs to be taken into account at high pH and when the solute concentration is extremely low.
Strong acids and bases
Strong acids and bases are compounds that, for practical purposes, are completely dissociated in water. Under normal circumstances this means that the concentration of hydrogen ions in acidic solution can be taken to be equal to the concentration of the acid. The pH is then equal to minus the logarithm of the concentration value. Hydrochloric acid (HCl) is an example of a strong acid. The pH of a 0.01M solution of HCl is equal to −log10(0.01), that is, pH = 2. Sodium hydroxide, NaOH, is an example of a strong base. The p[OH] value of a 0.01M solution of NaOH is equal to −log10(0.01), that is, p[OH] = 2. From the definition of p[OH] above, this means that the pH is equal to about 12. For solutions of sodium hydroxide at higher concentrations the self-ionization equilibrium must be taken into account.
Self-ionization must also be considered when concentrations are extremely low. Consider, for example, a solution of hydrochloric acid at a concentration of 5×10−8M. The simple procedure given above would suggest that it has a pH of 7.3. This is clearly wrong as an acid solution should have a pH of less than 7. Treating the system as a mixture of hydrochloric acid and the amphoteric substance water, a pH of 6.89 results.[26]
Weak acids and bases
A weak acid or the conjugate acid of a weak base can be treated using the same formalism.
Acid: HA ↽ − − ⇀ H + + A − {\displaystyle {\ce {HA<=>{H+}+{A^{-}}}}}
Base: HA + ↽ − − ⇀ H + + A {\displaystyle {\ce {HA+ <=> {H+}+ A}}}
First, an acid dissociation constant is defined as follows. Electrical charges are omitted from subsequent equations for the sake of generality
K a = [ H ] [ A ] [ HA ] {\displaystyle K_{a}={\frac {{\ce {[H] [A]}}}{{\ce {[HA]}}}}}
and its value is assumed to have been determined by experiment. This being so, there are three unknown concentrations, [HA], [H+] and [A−] to determine by calculation. Two additional equations are needed. One way to provide them is to apply the law of mass conservation in terms of the two "reagents" H and A.
C A = [ A ] + [ HA ] {\displaystyle C_{{\ce {A}}}={\ce {[A]}}+{\ce {[HA]}}}
C H = [ H ] + [ HA ] {\displaystyle C_{{\ce {H}}}={\ce {[H]}}+{\ce {[HA]}}}
C stands for analytical concentration. In some texts one mass balance equation is replaced by an equation of charge balance. This is satisfactory for simple cases like this one, but is more difficult to apply to more complicated cases as those below. Together with the equation defining Ka, there are now three equations in three unknowns. When an acid is dissolved in water CA = CH = Ca, the concentration of the acid, so [A] = [H]. After some further algebraic manipulation an equation in the hydrogen ion concentration may be obtained.
[ H ] 2 + K a [ H ] − K a C a = 0 {\displaystyle [{\ce {H}}]^{2}+K_{a}[{\ce {H}}]-K_{a}C_{a}=0}
Solution of this quadratic equation gives the hydrogen ion concentration and hence p[H] or, more loosely, pH. This procedure is illustrated in an ICE table which can also be used to calculate the pH when some additional (strong) acid or alkaline has been added to the system, that is, when CA ≠ CH.
For example, what is the pH of a 0.01M solution of benzoic acid, pKa = 4.19?
Step 1: K a = 10 − 4.19 = 6.46 × 10 − 5 {\displaystyle K_{a}=10^{-4.19}=6.46\times 10^{-5}}
Step 2: Set up the quadratic equation. [ H ] 2 + 6 ⋅ 46 × 10 − 5 [ H ] − 6 ⋅ 46 × 10 − 7 = 0 {\displaystyle {\ce {{[H]^{2}}+{6.46\times 10^{-5}[H]}-6.46\times 10^{-7}=0}}}
Step 3: Solve the quadratic equation. [ H + ] = 7 ⋅ 74 × 10 − 4 {\displaystyle {\ce {{[H+]}=7.74\times 10^{-4}}}} ; pH = 3.11
For alkaline solutions an additional term is added to the mass-balance equation for hydrogen. Since addition of hydroxide reduces the hydrogen ion concentration, and the hydroxide ion concentration is constrained by the self-ionization equilibrium to be equal to K w [ H + ] {\displaystyle {\frac {K_{w}}{{\ce {[H+]}}}}}
C H = [ H ] + [ HA ] − K w [ H ] {\displaystyle C_{\ce {H}}={\frac {[{\ce {H}}]+[{\ce {HA}}]-K_{w}}{\ce {[H]}}}}
In this case the resulting equation in [H] is a cubic equation.
General method
Some systems, such as with polyprotic acids, are amenable to spreadsheet calculations.[27] With three or more reagents or when many complexes are formed with general formulae such as ApBqHr the following general method can be used to calculate the pH of a solution. For example, with three reagents, each equilibrium is characterized by an equilibrium constant, β.
[ A p B q H r ] = β p q r [ A ] p [ B ] q [ H ] r {\displaystyle [{\ce {A}}_{p}{\ce {B}}_{q}{\ce {H}}_{r}]=\beta _{pqr}[{\ce {A}}]^{p}[{\ce {B}}]^{q}[{\ce {H}}]^{r}}
Next, write down the mass-balance equations for each reagent:
C A = [ A ] + Σ p β p q r [ A ] p [ B ] q [ H ] r C B = [ B ] + Σ q β p q r [ A ] p [ B ] q [ H ] r C H = [ H ] + Σ r β p q r [ A ] p [ B ] q [ H ] r − K w [ H ] − 1 {\displaystyle {\begin{aligned}C_{\ce {A}}&=[{\ce {A}}]+\Sigma p\beta _{pqr}[{\ce {A}}]^{p}[{\ce {B}}]^{q}[{\ce {H}}]^{r}\\C_{\ce {B}}&=[{\ce {B}}]+\Sigma q\beta _{pqr}[{\ce {A}}]^{p}[{\ce {B}}]^{q}[{\ce {H}}]^{r}\\C_{\ce {H}}&=[{\ce {H}}]+\Sigma r\beta _{pqr}[{\ce {A}}]^{p}[{\ce {B}}]^{q}[{\ce {H}}]^{r}-K_{w}[{\ce {H}}]^{-1}\end{aligned}}}
Note that there are no approximations involved in these equations, except that each stability constant is defined as a quotient of concentrations, not activities. Much more complicated expressions are required if activities are to be used.
There are 3 non-linear simultaneous equations in the three unknowns, [A], [B] and [H]. Because the equations are non-linear, and because concentrations may range over many powers of 10, the solution of these equations is not straightforward. However, many computer programs are available which can be used to perform these calculations. There may be more than three reagents. The calculation of hydrogen ion concentrations, using this formalism, is a key element in the determination of equilibrium constants by potentiometric titration.
See also
Alkaline diet
Arterial blood gas
Bel
Chemical equilibrium
pCO2
References
Jump up ^ Bates, Roger G. Determination of pH: theory and practice. Wiley, 1973.
Jump up ^ Lim, Kieran F. (2006). "Negative pH Does Exist". Journal of Chemical Education. 83 (10): 1465. Bibcode:2006JChEd..83.1465L. doi:10.1021/ed083p1465.
^ Jump up to: a b c d Covington, A. K.; Bates, R. G.; Durst, R. A. (1985). "Definitions of pH scales, standard reference values, measurement of pH, and related terminology" (PDF). Pure Appl. Chem. 57 (3): 531–542. doi:10.1351/pac198557030531. Archived (PDF) from the original on 24 September 2007.
Jump up ^ Sorensen, S. P. L. (1909). "Über die Messung und die Bedeutung der Wasserstoffionenkonzentration bei enzymatischen Prozessen". Biochem. Zeitschr. 21: 131–304. Two other publications appeared in 1909 one in French and one in Danish
^ Jump up to: a b "Carlsberg Group Company History Page". Carlsberggroup.com. Archived from the original on 18 January 2014. Retrieved 7 May 2013.
Jump up ^ Myers, Rollie J. (2010). "One-Hundred Years of pH". Journal of Chemical Education. 87: 30–32. Bibcode:2010JChEd..87...30M. doi:10.1021/ed800002c.
Jump up ^ Nørby, Jens (2000). "The origin and the meaning of the little p in pH". Trends in Biochemical Sciences. 25 (1): 36–37. doi:10.1016/S0968-0004(99)01517-0. PMID 10637613.
Jump up ^ Quantities and units – Part 8: Physical chemistry and molecular physics, Annex C (normative): pH. International Organization for Standardization, 1992.
Jump up ^ Rossotti, F.J.C.; Rossotti, H. (1965). "Potentiometric titrations using Gran plots: A textbook omission". J. Chem. Educ. 42 (7): 375–378. Bibcode:1965JChEd..42..375R. doi:10.1021/ed042p375.
Jump up ^ Mendham, J.; Denney, R. C.; Barnes, J. D.; Thomas, M. J. K. (2000), Vogel's Quantitative Chemical Analysis (6th ed.), New York: Prentice Hall, ISBN 0-582-22628-7 , Section 13.23, "Determination of pH"
Jump up ^ Feldman, Isaac (1956). "Use and Abuse of pH measurements". Analytical Chemistry. 28 (12): 1859–1866. doi:10.1021/ac60120a014.
Jump up ^ Mendham, J.; Denney, R. C.; Barnes, J. D.; Thomas, M. J. K. (2000), Vogel's Quantitative Chemical Analysis (6th ed.), New York: Prentice Hall, ISBN 0-582-22628-7 , Section 13.19 The glass electrode
Jump up ^ Nordstrom, D. Kirk; Alpers, Charles N. (March 1999). "Negative pH, efflorescent mineralogy, and consequences for environmental restoration at the Iron Mountain Superfund site, California". Proceedings of the National Academy of Sciences of the United States of America. PNAS. 96 (7): 3455–62. Bibcode:1999PNAS...96.3455N. doi:10.1073/pnas.96.7.3455. PMC 34288  . PMID 10097057.
Jump up ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "activity (relative activity), a".
Jump up ^ International Union of Pure and Applied Chemistry (1993). Quantities, Units and Symbols in Physical Chemistry, 2nd edition, Oxford: Blackwell Science. ISBN 0-632-03583-8. pp. 49–50. Electronic version.
Jump up ^ Himmel, D.; Goll, S. K.; Leito, I.; Krossing, I. (2010). "A Unified pH Scale for all Phases". Angew. Chem. Int. Ed. 49 (38): 6885–6888. doi:10.1002/anie.201000252.
Jump up ^ Soil Survey Division Staff. "Soil survey manual.1993. Chapter 3, selected chemical properties". Soil Conservation Service. U.S. Department of Agriculture Handbook 18. Archived from the original on 14 May 2011. Retrieved 12 March 2011.
Jump up ^ Chester, Jickells, Roy, Tim (2012). Marine Geochemistry. Blackwell Publishing. ISBN 978-1-118-34907-6.
Jump up ^ Royal Society (2005). Ocean acidification due to increasing atmospheric carbon dioxide (PDF). ISBN 0-85403-617-2. Archived (PDF) from the original on 16 July 2010.
^ Jump up to: a b Zeebe, R. E. and Wolf-Gladrow, D. (2001) CO2 in seawater: equilibrium, kinetics, isotopes, Elsevier Science B.V., Amsterdam, Netherlands ISBN 0-444-50946-1
Jump up ^ Hansson, I. (1973). "A new set of pH-scales and standard buffers for seawater". Deep-Sea Research. 20 (5): 479–491. Bibcode:1973DSROA..20..479H. doi:10.1016/0011-7471(73)90101-0.
Jump up ^ Dickson, A. G. (1984). "pH scales and proton-transfer reactions in saline media such as sea water". Geochim. Cosmochim. Acta. 48 (11): 2299–2308. Bibcode:1984GeCoA..48.2299D. doi:10.1016/0016-7037(84)90225-4.
Jump up ^ Boron, Walter, F.; Boulpaep, E.L. (2004). Medical Physiology: A Cellular And Molecular Approach. Elsevier/Saunders. ISBN 1-4160-2328-3.
Jump up ^ Marieb EN, Hoehn K (2010). Human anatomy & physiology. San Francisco: Benjamin Cummings. ISBN 0-8053-9591-1.
Jump up ^ Lambers, H.; Piessens, S.; Bloem, A.; Pronk, H.; Finkel, P. (2006-10-01). "Natural skin surface pH is on average below 5, which is beneficial for its resident flora". International Journal of Cosmetic Science. 28 (5): 359–370. doi:10.1111/j.1467-2494.2006.00344.x. ISSN 1468-2494. PMID 18489300.
Jump up ^ Maloney, Chris. "pH calculation of a very small concentration of a strong acid". Archived from the original on 8 July 2011. Retrieved 13 March 2011.
Jump up ^ Billo, E.J. (2011). EXCEL for Chemists (3rd ed.). Wiley-VCH. ISBN 978-0-470-38123-6.
External links
Wikimedia Commons has media related to pH.
The pH Scale
Chem1 Virtual Textbook, Acid-base Equilibria and Calculations
Red Cabbage pH Indicator
Food and Foodstuff – pH Values
Online pH Calculator for about 100 inorganic Acids, Bases, and Salts
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Strong acid

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Dibasic acid

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Activity (chemistry)

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Basic (chemistry)

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Hydrogen electrode

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Hydroxide ion

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Ion-selective electrode

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values: {\displaystyle {\frac {1}{2.303RT/F}}\ }

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values: {\displaystyle [\mathrm {OH} ^{-}]={\frac {K_{W}}{[\mathrm {H} ^{+}]}}}

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values: {\displaystyle \mathrm {pOH} =\mathrm {pK_{W}} -\mathrm {pH} }

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values: \mathrm {pOH} =\mathrm {pK_{W}} -\mathrm {pH}

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Alkaline soils

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Acid-base homeostasis

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Cubic equation

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Simultaneous equation

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Hydronium ion

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Strong base

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Mass conservation

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Analytical concentration

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values: {\displaystyle {\frac {K_{w}}{{\ce {[H+]}}}}}

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API oil-water separator

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values:
https://af.wikipedia.org/wiki/PH
PH – Afrikaans
af
af
interlanguage-link-target

values:
https://als.wikipedia.org/wiki/PH-Wert
PH-Wert – Alemannisch
als
als
interlanguage-link-target

values: أس هيدروجيني – Arabic

values: Вадародны паказчык – Belarusian

values: Водороден показател – Bulgarian

values:
https://bs.wikipedia.org/wiki/PH
PH – Bosnian
bs
bs
interlanguage-link-target

values:
https://ca.wikipedia.org/wiki/PH
PH – Catalan
ca
ca
interlanguage-link-target

values:
https://cs.wikipedia.org/wiki/PH
PH – Czech
cs
cs
interlanguage-link-target

values:
https://cy.wikipedia.org/wiki/PH
PH – Welsh
cy
cy
interlanguage-link-target

values:
https://da.wikipedia.org/wiki/PH
PH – Danish
da
da
interlanguage-link-target

values:
https://se.wikipedia.org/wiki/PH
PH – Northern Sami
se
se
interlanguage-link-target

values:
https://de.wikipedia.org/wiki/PH-Wert
PH-Wert – German
de
de
interlanguage-link-target

values:
https://el.wikipedia.org/wiki/PH
PH – Greek
el
el
interlanguage-link-target

values:
https://es.wikipedia.org/wiki/PH
PH – Spanish
es
es
interlanguage-link-target

values:
https://eu.wikipedia.org/wiki/PH
PH – Basque
eu
eu
interlanguage-link-target

values:
https://ga.wikipedia.org/wiki/PH
PH – Irish
ga
ga
interlanguage-link-target

values:
https://gl.wikipedia.org/wiki/PH
PH – Galician
gl
gl
interlanguage-link-target

values:
https://hak.wikipedia.org/wiki/PH
PH – Hakka Chinese
hak
hak
interlanguage-link-target

values: 수소 이온 농도 – Korean

values: Ջրածնային ցուցիչ – Armenian

values:
https://hi.wikipedia.org/wiki/PH
PH – Hindi
hi
hi
interlanguage-link-target

values:
https://hr.wikipedia.org/wiki/PH
PH – Croatian
hr
hr
interlanguage-link-target

values:
https://io.wikipedia.org/wiki/PH
PH – Ido
io
io
interlanguage-link-target

values:
https://id.wikipedia.org/wiki/PH
PH – Indonesian
id
id
interlanguage-link-target

values:
https://it.wikipedia.org/wiki/PH
PH – Italian
it
it
interlanguage-link-target

values:
https://he.wikipedia.org/wiki/PH
PH – Hebrew
he
he
interlanguage-link-target

values: ಪಿ ಹೆಚ್ – Kannada

values:
https://pam.wikipedia.org/wiki/PH
PH – Pampanga
pam
pam
interlanguage-link-target

values:
https://kk.wikipedia.org/wiki/PH
PH – Kazakh
kk
kk
interlanguage-link-target

values:
https://ht.wikipedia.org/wiki/PH
PH – Haitian Creole
ht
ht
interlanguage-link-target

values:
https://ku.wikipedia.org/wiki/Nirxa_pH
Nirxa pH – Kurdish
ku
ku
interlanguage-link-target

values:
https://lv.wikipedia.org/wiki/PH
PH – Latvian
lv
lv
interlanguage-link-target

values:
https://hu.wikipedia.org/wiki/PH
PH – Hungarian
hu
hu
interlanguage-link-target

values: Водороден показател – Macedonian

values: പി.എച്ച്. മൂല്യം – Malayalam

values: पी.एच. मूल्य – Marathi

values:
https://ms.wikipedia.org/wiki/PH
PH – Malay
ms
ms
interlanguage-link-target

values:
https://my.wikipedia.org/wiki/PH
PH – Burmese
my
my
interlanguage-link-target

values:
https://nl.wikipedia.org/wiki/PH
PH – Dutch
nl
nl
interlanguage-link-target

values: 水素イオン指数 – Japanese

values:
https://no.wikipedia.org/wiki/PH
PH – Norwegian
no
no
interlanguage-link-target

values:
https://nn.wikipedia.org/wiki/PH
PH – Norwegian Nynorsk
nn
nn
interlanguage-link-target

values:
https://nov.wikipedia.org/wiki/PH
PH – Novial
nov
nov
interlanguage-link-target

values:
https://oc.wikipedia.org/wiki/PH
PH – Occitan
oc
oc
interlanguage-link-target

values:
https://uz.wikipedia.org/wiki/PH
PH – Uzbek
uz
uz
interlanguage-link-target

values: ਪੀ.ਐੱਚ. (ਹਾਈਡਰੋਜਨ ਸ਼ਕਤੀ) – Punjabi

values:
https://nds.wikipedia.org/wiki/PH-Weert
PH-Weert – Low German
nds
nds
interlanguage-link-target

values:
https://pl.wikipedia.org/wiki/Skala_pH
Skala pH – Polish
pl
pl
interlanguage-link-target

values:
https://pt.wikipedia.org/wiki/PH
PH – Portuguese
pt
pt
interlanguage-link-target

values:
https://ro.wikipedia.org/wiki/PH
PH – Romanian
ro
ro
interlanguage-link-target

values: Водородный показатель – Russian

values:
https://sco.wikipedia.org/wiki/PH
PH – Scots
sco
sco
interlanguage-link-target

values:
https://sq.wikipedia.org/wiki/PH
PH – Albanian
sq
sq
interlanguage-link-target

values:
https://scn.wikipedia.org/wiki/PH
PH – Sicilian
scn
scn
interlanguage-link-target

values:
https://simple.wikipedia.org/wiki/PH
PH – Simple English
simple
simple
interlanguage-link-target

values:
https://sl.wikipedia.org/wiki/PH
PH – Slovenian
sl
sl
interlanguage-link-target

values:
https://so.wikipedia.org/wiki/PH
PH – Somali
so
so
interlanguage-link-target

values: PH вредност – Serbian

values:
https://su.wikipedia.org/wiki/PH
PH – Sundanese
su
su
interlanguage-link-target

values:
https://fi.wikipedia.org/wiki/Happamuus
Happamuus – Finnish
fi
fi
interlanguage-link-target

values:
https://sv.wikipedia.org/wiki/PH
PH – Swedish
sv
sv
interlanguage-link-target

values:
https://tl.wikipedia.org/wiki/PH
PH – Tagalog
tl
tl
interlanguage-link-target

values: காரகாடித்தன்மைச் சுட்டெண் – Tamil

values:
https://te.wikipedia.org/wiki/PH
PH – Telugu
te
te
interlanguage-link-target

values: พีเอช (เคมี) – Thai

values:
https://tr.wikipedia.org/wiki/PH
PH – Turkish
tr
tr
interlanguage-link-target

values:
https://uk.wikipedia.org/wiki/PH
PH – Ukrainian
uk
uk
interlanguage-link-target

values:
https://vi.wikipedia.org/wiki/PH
PH – Vietnamese
vi
vi
interlanguage-link-target

values:
https://vls.wikipedia.org/wiki/PH
PH – West Flemish
vls
vls
interlanguage-link-target

values:
https://war.wikipedia.org/wiki/PH
PH – Waray
war
war
interlanguage-link-target

values: mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject page-PH rootpage-PH skin-vector action-view