document_title: Justice League (film)

question_text: who plays the flash in the new justice league movie

text: Justice League (film)

text: Synopsis

text: Months after the events of Batman v Superman: Dawn of Justice[2] and inspired by Superman's apparent sacrifice for humanity, Bruce Wayne and Diana Prince assemble a team of metahumans consisting of Barry Allen, Arthur Curry, and Victor Stone to face the catastrophic threat of Steppenwolf and his army of Parademons, who are on the hunt for three Mother Boxes on Earth.[3][4]

text: Cast

text:
Ben Affleck as Bruce Wayne / Batman:
The benefactor of the group of meta-humans, a wealthy socialite and the owner of Wayne Enterprises, who also dedicates himself to protecting Gotham City from its criminal underworld as a highly trained, masked vigilante equipped with many powerful tools and weapons.

Henry Cavill as Kal-El / Clark Kent / Superman:
A Kryptonian survivor and journalist for the Daily Planet with superhuman abilities, who seemingly died after the events of Batman v Superman: Dawn of Justice. In February 2016, Cavill announced on social media that he had already started exercising for the film in advance of principal photography.[5]

Gal Gadot as Diana Prince / Wonder Woman:
An antiquities dealer and acquaintance of Wayne who is actually an immortal Amazonian warrior princess from Themyscira and daughter of Zeus, who possesses superhuman attributes and abilities inherited from her parents.

Jason Momoa as Arthur Curry / Aquaman:
The king of the undersea nation of Atlantis, whose meta-human aquatic abilities and superhuman physical attributes originate from his Atlantean physiology.

Ezra Miller as Barry Allen / Flash:
A Central City police forensic investigator, who can move at superhuman speeds with his ability to tap into the Speed Force.

Ray Fisher as Victor Stone / Cyborg:
A former college athlete who, after being cybernetically reconstructed with a Mother Box after a nearly fatal accident, has powers that allow him to manipulate technology and to turn his arms to cannons. Fisher portrays the character through the assistance of motion capture performance, for the cybernetic portion of his body.[6]

Ciarán Hinds as Steppenwolf:
A general of the alien race, the New Gods, from the planet Apokolips who is charged with hunting down the three Mother Boxes on Earth for his nephew and commanding officer Darkseid.[4][7] The character had previously appeared in the extended Ultimate Edition of Batman v Superman: Dawn of Justice, in which he communicates with Lex Luthor through Kryptonian hologram technology. In March 2017, Ciarán stated that Steppenwolf is old, tired and trying to get out of his enslaved position under Darkseid.[8] Hinds will portray the villain through use of motion capture performance and received help in that process from his friend Liam Neeson, who had recently done similar work in A Monster Calls.[9]

Amy Adams as Lois Lane: An undaunted and compassionate award-winning journalist for the Daily Planet and the primary love interest for Clark Kent / Superman.[10]
Willem Dafoe as Nuidis Vulko: An Atlantean advisor to Aquaman.[11]
Jesse Eisenberg as Lex Luthor: The hereditary CEO of LexCorp who is incarcerated following the events of Batman v Superman: Dawn of Justice.[12][13][14]
Jeremy Irons as Alfred Pennyworth: Bruce Wayne's butler, chief of security, and trusted confidant.[15]
Diane Lane as Martha Kent: Clark Kent's adoptive mother.[10]
Connie Nielsen as Queen Hippolyta: Diana Prince's mother and the Amazonian queen.[10]
J. K. Simmons as James Gordon: The Commissioner of the Gotham City Police Department and close ally of Batman.[10]

text: Joe Morton and Robin Wright reprise their roles as Dr. Silas Stone, a scientist at S.T.A.R. Labs and Victor Stone's father, and as General Antiope, Hippolyta's sister and Diana's aunt/mentor, from Batman v Superman: Dawn of Justice and Wonder Woman, respectively.[16][17] Amber Heard, Billy Crudup, and Kiersey Clemons will portray Mera, Dr. Henry Allen, and Iris West, respectively.[10][16] Julian Lewis Jones and Michael McElhatton have been cast in undisclosed roles.[18][19]

text: Production

text: Development

text: In February 2007, it was announced that Warner Bros. hired husband and wife duo Michele and Kieran Mulroney to write a script for a Justice League film.[20] The news came around the same time that Joss Whedon's long-developed Wonder Woman film had been cancelled,[21] as well as The Flash, written and directed by David S. Goyer.[22] Reportedly titled Justice League: Mortal,[23] Michele and Kiernan Mulroney submitted their script to Warner Bros. in June 2007, receiving positive feedback,[24] which prompted the studio to immediately fast track production in the hopes of filming to begin before the 2007-2008 Writers Guild of America strike.[25] Warner Bros. was less willing to proceed with development with a sequel to Superman Returns, having been disappointed with the box office return. Brandon Routh was not approached to reprise the role of Superman in Justice League: Mortal,[26] nor was Christian Bale from Batman Begins.[27] Warner Bros. intended for Justice League: Mortal to be the start of a new film franchise, and to branch out into separate sequels and spin-offs.[28] Shortly after filming finished with The Dark Knight,[29] Bale stated in an interview that "It'd be better if it doesn't tread on the toes of what our Batman series is doing," though he personally felt it would make more sense for Warner Bros. to release the film after The Dark Knight Rises.[27] Jason Reitman was the original choice to direct Justice League, but he turned it down, as he considers himself an independent filmmaker and prefers to stay out of big budget superhero films.[30] George Miller signed to direct in September 2007,[25] with Barrie Osbourne producing[31] on a projected $220 million budget.[32]

text: The following month roughly 40 actors and actresses were auditioning for the ensemble superhero roles, among them were Joseph Cross, Michael Angarano, Max Thieriot, Minka Kelly, Adrianne Palicki and Scott Porter. Miller intended to cast younger actors as he wanted them to "grow" into their roles over the course of several films.[29] D. J. Cotrona was cast as Superman,[28] along with Armie Hammer as Batman.[33] Jessica Biel reportedly declined the Wonder Woman role after being in negotiations.[34] The character was also linked to actresses Teresa Palmer and Shannyn Sossamon, along with Mary Elizabeth Winstead, who confirmed that she had auditioned.[35] Ultimately Megan Gale was cast as Wonder Woman,[36] while Palmer was cast as Talia al Ghul, whom Miller had in mind to act with a Russian accent.[37] The script for Justice League: Mortal would have featured John Stewart as Green Lantern, a role originally offered to Columbus Short.[38] Hip hop recording artist and rapper Common was cast,[39] with Adam Brody as Barry Allen / Flash,[40] and Jay Baruchel as the lead villain, Maxwell Lord.[41] Longtime Miller collaborator Hugh Keays-Byrne had been cast in an unnamed role, rumored to be Martian Manhunter. Aquaman had yet to be cast.[29][32] Marit Allen was hired as the original costume designer before her untimely death in November 2007,[42] and the responsibilities were assumed by Weta Workshop.[43]

text: However, the writers strike began that same month and placed the film on hold. Warner Bros. had to let the options lapse for the cast,[44] but development was fast tracked once more in February 2008 when the strike ended. Warner Bros. and Miller wanted to start filming immediately,[45] but production was pushed back three months.[28] Originally, the majority of Justice League: Mortal would be shot at Fox Studios Australia in Sydney,[32] with other locations scouted nearby at local colleges,[31] and Sydney Heads doubling for Happy Harbor.[23] The Australian Film Commission had a say with casting choices, giving way for George Miller to cast Gale, Palmer and Keays-Bryne, all Australian natives. The production crew was composed entirely of Australians, but the Australian government denied Warner Bros. a 40 percent tax rebate as they felt they had not hired enough Australian actors.[32][46] Miller was frustrated, stating that "A once-in-a-lifetime opportunity for the Australian film industry is being frittered away because of very lazy thinking. They're throwing away hundreds of millions of dollars of investment that the rest of the world is competing for and, much more significantly, highly skilled creative jobs."[47] Production offices were then moved to Vancouver Film Studios in Canada. Filming was pushed back to July 2008, while Warner Bros was still confident they could release the film for a summer 2009 release.[48][49]

text: With production delays continuing, and the success of The Dark Knight in July 2008,[50] Warner Bros. decided to focus on the development of individual films featuring the main heroes, allowing director Christopher Nolan to separately complete his Batman trilogy with The Dark Knight Rises in 2012. Gregory Noveck, senior vice president of creative affairs for DC Entertainment stated "we're going to make a Justice League movie, whether it's now or 10 years from now. But we're not going to do it and Warners is not going to do it until we know it's right."[51] Actor Adam Brody joked "They [Warner Brothers] just didn't want to cross their streams with a whole bunch of Batmans in the universe."[52] Warner Bros. relaunched development for the solo Green Lantern film, released in 2011 as a critical and financial disappointment. Meanwhile, film adaptations for The Flash and Wonder Woman continued to languish in development while filming for a Superman reboot was commencing in 2011 with Man of Steel, produced by Nolan and written by Batman screenwriter David S. Goyer. Shortly after filming had finished for Man of Steel, Warner Bros hired Will Beall to write the script for a new Justice League film.[53] Warner Bros. president Jeff Robinov explained that Man of Steel would be "setting the tone for what the movies are going to be like going forward. In that, it's definitely a first step."[54] The film included references to the existence of other superheroes in the DC Universe,[55] and setting the tone for a shared fictional universe of DC Comics characters on film.[56] Goyer stated that should Green Lantern appear in a future installment, it would be a rebooted version of the character and not connected to the 2011 film.[57]

text: With the release of Man of Steel in June 2013, Goyer was hired to write a sequel, as well as a new Justice League, with the Beall draft being scrapped.[58] The sequel was later revealed to be Batman v Superman: Dawn of Justice, a team up film featuring Ben Affleck as Batman, Gal Gadot as Wonder Woman, and Ray Fisher as Victor Stone / Cyborg in a minor role that will become more significant in leading up to the proposed Justice League film. The universe is separate from Nolan and Goyer's work on The Dark Knight trilogy, although Nolan is still involved as an executive producer for Batman v Superman.[59] In April 2014, it was announced that Zack Snyder would also be directing Goyer's Justice League script.[60] Warner Bros. was reportedly courting Chris Terrio to rewrite Justice League the following July, after having been impressed with his rewrite of Batman v Superman: Dawn of Justice.[61] On October 15, 2014, Warner Bros. announced the film would be released in two parts, with Part One releasing on November 17, 2017, and Part Two on June 14, 2019. Snyder will direct both films.[62] In early July 2015, EW revealed that the script for Justice League Part One had been completed by Terrio.[63] Zack Snyder stated that the film will be inspired by the New Gods comic series by Jack Kirby.[4] Although Justice League was initially announced as a two-part film with the second part releasing two years after the first, Snyder announced in June 2016 that they would be two distinct, separate films and not one film split into two parts, both being stand-alone stories.[64][65]

text: Casting

text: In April 2014, Ray Fisher was cast as Victor Stone / Cyborg, and was set to cameo in Batman v Superman: Dawn of Justice followed by a larger role in Justice League.[66][67] Henry Cavill, Ben Affleck, Gal Gadot, Diane Lane and Amy Adams are also expected to reprise their roles from Batman v Superman: Dawn of Justice.[62][68] In October 2014, Jason Momoa was cast as Arthur Curry / Aquaman and debuted as the character in Dawn of Justice.[69][70] On October 20, 2014, Momoa told ComicBook.com that the Justice League film would be coming first and that is what they were preparing for, and he did not know if the solo Aquaman film would be prior to Justice League or post. He thought it might be the origin of where Aquaman came from.[71] On January 13, 2016, The Hollywood Reporter announced that Amber Heard was in negotiations to appear in the film as Aquaman's love interest Mera.[72] In March 2016, producer Charles Roven said that Green Lantern would not appear in any film before Justice League Part Two, and stated that they "could put Green Lantern in some introduction in Justice League 2, or barring that, a movie after."[73] Also in March, The Hollywood Reporter announced that J. K. Simmons was cast as Commissioner James Gordon,[74] and Heard was confirmed to join the cast as Mera.[75] Adams also confirmed that she would reprise her role as Lois Lane in both Justice League films.[76] The following month, Simmons confirmed that he would play Gordon.[77] By April 2016, Willem Dafoe was cast in an undisclosed role,[78] later revealed to be Nuidis Vulko.[11] Cavill confirmed that he would return for both Justice League films.[79] In May 2016, Jeremy Irons confirmed he will appear as Alfred Pennyworth.[15] That same month, Jesse Eisenberg stated that he would reprise his role as Lex Luthor, and in June 2016, he confirmed in an interview with Shortlist magazine of his return.[80][81] In July 2016, Julian Lewis Jones was cast in an undisclosed role.[18] Laurence Fishburne, who portrays Perry White in the DCEU, said he declined to reprise his role in this film due to scheduling conflicts.[82] In April 2017, Michael McElhatton revealed that he has a role in the film.[19]

text: Filming

text: In July 2015, it was revealed that filming would begin in spring 2016 after Wonder Woman ended principal photography.[83] Principal photography commenced on April 11, 2016, with shooting taking place at Warner Bros. Studios, Leavesden, as well as various locations around London, Scotland, Los Angeles and in Djúpavík in the Westfjords [84] of Iceland.[78][85][86] Snyder's longtime cinematographer Larry Fong was replaced by Fabian Wagner due to scheduling conflicts.[86] Affleck was also revealed to be serving as executive producer.[87] In May 2016, it was revealed that Geoff Johns and Jon Berg will be producing the Justice League films and they will also be in charge of the DC Extended Universe after the largely negative critical reception of Batman v Superman: Dawn of Justice.[88] Geoff Johns confirmed on June 3, 2016, that the title of the film is Justice League.[89] That same month, Irons stated that the Justice League storyline will be more linear and simple, in comparison to the theatrical version of Batman v Superman: Dawn of Justice.[90] Johns later stated that the film would be "hopeful and optimistic" in comparison to the previous DCEU films.[91] Filming wrapped in October 2016.[92][93][94]

text: Post-production

text: In May 2017, Snyder stepped down during post-production of the film to properly deal with the death of his daughter. Joss Whedon, who Snyder had previously brought on to rewrite some additional scenes, took over to handle post-production duties in Snyder's place.[95] In July 2017, it was announced the film was undergoing two months of reshoots in London and Los Angeles, with Warner Bros. putting about $25 million into them (more than the typical $6–10 million additional filming costs).[96] The reshoots coincided with Cavill's shooting schedule for Mission: Impossible 6, for which he had grown a mustache which he was contracted to keep while filming, so Justice League's VFX team had to resort to using special effects to digitally remove the mustache in post.[97] Warner Bros. later announced that Whedon would receive a screenwriting credit on the film in recognition of the alterations he made.[98]

text: Music

text: In March 2016, Hans Zimmer, who composed the score for Man of Steel and Batman v Superman: Dawn of Justice, stated that he is officially retired from the "superhero business".[99] By June 2016 he was replaced by Junkie XL, who wrote and composed the soundtrack of Batman v Superman: Dawn of Justice with Zimmer.[100] In June 2017, Danny Elfman was announced to have replaced Junkie XL.[101] Elfman had previously composed Batman, Batman Returns, and the theme song for Batman: The Animated Series.

text: Release

text: Justice League is scheduled to be released on November 17, 2017.[62] The film will get an IMAX release.[102]

text: Sequel

text: A sequel was scheduled to be released in June 2019,[62] but has since been delayed to accommodate the release for a standalone Batman film.[103] In March 2017, producer Charles Roven announced that Zack Snyder would return as director.[104]


document_title: Defining equation (physical chemistry)

question_text: what do brackets in an chemical equation mean

root

text: Defining equation (physical chemistry)

text: Introduction[edit]

text: Theoretical chemistry requires quantities from core physics, such as time, volume, temperature, and pressure. But the highly quantitative nature of physical chemistry, in a more specialized way than core physics, uses molar amounts of substance rather than simply counting numbers; this leads to the specialized definitions in this article. Core physics itself rarely uses the mole, except in areas overlapping thermodynamics and chemistry.

tag: p

text: Notes on nomenclature[edit]

text: Entity refers to the type of particle/s in question, such as atoms, molecules, complexes, radicals, ions, electrons etc.[1]

text: Conventionally for concentrations and activities, square brackets [ ] are used around the chemical molecular formula. For an arbitrary atom, generic letters in upright non-bold typeface such as A, B, R, X or Y etc. are often used.

text: No standard symbols are used for the following quantities, as specifically applied to a substance:

text:
the mass of a substance m,
the number of moles of the substance n,
partial pressure of a gas in a gaseous mixture p (or P),
some form of energy of a substance (for chemistry enthalpy H is common),
entropy of a substance S
the electronegativity of an atom or chemical bond χ.

tag: ul

text: Usually the symbol for the quantity with a subscript of some reference to the quantity is used, or the quantity is written with the reference to the chemical in round brackets. For example, the mass of water might be written in subscripts as mH2O, mwater, maq, mw (if clear from context) etc., or simply as m(H2O). Another example could be the electronegativity of the fluorine-fluorine covalent bond, which might be written with subscripts χF-F, χFF or χF-F etc., or brackets χ(F-F), χ(FF) etc.

text: Neither is standard. For the purpose of this article, the nomenclature is as follows, closely (but not exactly) matching standard use.

text: For general equations with no specific reference to an entity, quantities are written as their symbols with an index to label the component of the mixture - i.e. qi. The labeling is arbitrary in initial choice, but once chosen fixed for the calculation.

text: If any reference to an actual entity (say hydrogen ions H+) or any entity at all (say X) is made, the quantity symbol q is followed by curved ( ) brackets enclosing the molecular formula of X, i.e. q(X), or for a component i of a mixture q(Xi). No confusion should arise with the notation for a mathematical function.

text: Quantification[edit]

text: General basic quantities[edit]

text:
Quantity (Common Name/s)
(Common) Symbol/s
SI Units
Dimension

Number of molecules
N
dimensionless
dimensionless

Mass
m
kg
[M]

Number of moles, amount of substance, amount
n
mol
[N]

Volume of mixture or solvent, unless otherwise stated
V
m3
[L]3

tag: table

text: General derived quantities[edit]

text:
Quantity (Common Name/s)
(Common) Symbol/s
Defining Equation
SI Units
Dimension

Relative atomic mass of an element
Ar, A, mram

A

r

(

X

)

=

⟨
m

(

X

)

⟩

m

(

12

C

)

/

12

{\displaystyle A_{r}\left({\rm {X}}\right)={\frac {\langle m\left({\rm {X}}\right)\rangle }{m\left(^{12}{\rm {C}}\right)/12}}}

The average mass

⟨
m

(

X

)

⟩

{\displaystyle \langle m\left({\rm {X}}\right)\rangle }

 is the average of the T masses mi(X) corresponding the T isotopes of X (i is a dummy index labelling each isotope):

⟨
m

(

X

)

⟩
=

1
T

∑

i

T

m

(

X

i

)

{\displaystyle \langle m\left({\rm {X}}\right)\rangle ={\frac {1}{T}}\sum _{i}^{T}m\left({\rm {X}}_{i}\right)}

dimensionless
dimensionless

Relative formula mass of a compound, containing elements Xj
Mr, M, mrfm

M

r

(

Y

)

=

∑

j

N

(

X

j

)

A

r

(

X

j

)

=

∑

j

N

(

X

j

)

⟨
m

(

X

j

)

⟩

m

(

12

C

)

/

12

{\displaystyle M_{r}\left({\rm {Y}}\right)=\sum _{j}N\left({\rm {X}}_{j}\right)A_{r}\left({\rm {X}}_{j}\right)={\frac {\sum _{j}N\left({\rm {X}}_{j}\right)\langle m\left({\rm {X}}_{j}\right)\rangle }{m\left(^{12}{\rm {C}}\right)/12}}}

j = index labelling each element,
N = number of atoms of each element Xi.

dimensionless
dimensionless

Molar concentration, concentration, molarity of a component i in a mixture
ci, [Xi]

c

i

=

[

X

i

]

=

d

n

i

d

V

{\displaystyle c_{i}=\left[{\rm {X}}_{i}\right]={\frac {\mathrm {d} n_{i}}{\mathrm {d} V}}}

mol dm−3 = 10−3 mol m−3
[N] [L]−3

Molality of a component i in a mixture
bi, b(Xi)

b

i

=

n

i

m

s
o
l
v

{\displaystyle b_{i}={\frac {n_{i}}{m_{\rm {solv}}}}}

where solv = solvent (liquid solution).

mol kg−1
[N] [M]−1

Mole fraction of a component i in a mixture
xi, x(Xi)

x

i

=

n

i

n

m
i
x

{\displaystyle x_{i}={\frac {n_{i}}{n_{\rm {mix}}}}}

where Mix = mixture.

dimensionless
dimensionless

Partial pressure of a gaseous component i in a gas mixture
pi, p(Xi)

p

(

X

i

)

=

x

i

p

(

m
i
x

)

{\displaystyle p\left({\rm {X}}_{i}\right)=x_{i}p\left({\rm {mix}}\right)}

where mix = gaseous mixture.

Pa = N m−2
[M][T][L]−1

Density, mass concentration
ρi, γi, ρ(Xi)

ρ
=

m

i

/

V

{\displaystyle \rho =m_{i}/V\,\!}

kg m−3
[M] [L]3

Number density, number concentration
Ci, C(Xi)

C

i

=

N

i

/

V

{\displaystyle C_{i}=N_{i}/V\,\!}

m− 3
[L]− 3

Volume fraction, volume concentration
ϕi, ϕ(Xi)

ϕ

i

=

V

i

V

m
i
x

{\displaystyle \phi _{i}={\frac {V_{i}}{V_{\rm {mix}}}}}

dimensionless
dimensionless

Mixing ratio, mole ratio
ri, r(Xi)

r

i

=

n

i

n

m
i
x

−

n

i

{\displaystyle r_{i}={\frac {n_{i}}{n_{\rm {mix}}-n_{i}}}}

dimensionless
dimensionless

Mass fraction
wi, w(Xi)

w

i

=

m

i

/

m

m
i
x

{\displaystyle w_{i}=m_{i}/m_{\rm {mix}}\,\!}

m(Xi) = mass of Xi

dimensionless
dimensionless

Mixing ratio, mass ratio
ζi, ζ(Xi)

ζ

i

=

m

i

m

m
i
x

−

m

i

{\displaystyle \zeta _{i}={\frac {m_{i}}{m_{\rm {mix}}-m_{i}}}}

m(Xi) = mass of Xi

dimensionless
dimensionless

text: Kinetics and equilibria[edit]

text: The defining formulae for the equilibrium constants Kc (all reactions) and Kp (gaseous reactions) apply to the general chemical reaction:

text: and the defining equation for the rate constant k applies to the simpler synthesis reaction (one product only):

text: where:

text:
i = dummy index labelling component i of reactant mixture,
j = dummy index labelling component i of product mixture,
Xi = component i of the reactant mixture,
Yj = reactant component j of the product mixture,
r (as an index) = number of reactant components,
p (as an index) = number of product components,
νi = stoichiometry number for component i in product mixture,
ηj = stoichiometry number for component j in product mixture,
σi = order of reaction for component i in reactant mixture.

text: The dummy indices on the substances X and Y label the components (arbitrary but fixed for calculation); they are not the numbers of each component molecules as in usual chemistry notation.

text: The units for the chemical constants are unusual since they can vary depending on the stoichiometry of the reaction, and the number of reactant and product components. The general units for equilibrium constants can be determined by usual methods of dimensional analysis. For the generality of the kinetics and equilibria units below, let the indices for the units be;

text: For the constant Kc;

text: Substitute the concentration units into the equation and simplify:,

text: The procedure is exactly identical for Kp.

text: For the constant k

text:
Quantity (Common Name/s)
(Common) Symbol/s
Defining Equation
SI Units
Dimension

Reaction progress variable, extent of reaction
ξ

ξ

{\displaystyle \xi }

dimensionless
dimensionless

Stoichiometric coefficient of a component i in a mixture, in reaction j (many reactions could occur at once)
νi

ν

i
j

=

d

N

i

d

ξ

j

{\displaystyle \nu _{ij}={\frac {\mathrm {d} N_{i}}{\mathrm {d} \xi _{j}}}\,}

where Ni = number of molecules of component i.

dimensionless
dimensionless

Chemical affinity
A

A
=
−

(

∂
G

∂
ξ

)

P
,
T

{\displaystyle A=-\left({\frac {\partial G}{\partial \xi }}\right)_{P,T}}

J
[M][L]2[T]−2

Reaction rate with respect to component i
r, R

R

i

=

1

ν

i

d

[

X

i

]

d

t

{\displaystyle R_{i}={\frac {1}{\nu _{i}}}{\frac {\mathrm {d} \left[\mathrm {X} _{i}\right]}{\mathrm {d} t}}}

mol dm−3 s−1 = 10−3 mol m−3 s−1
[N] [L]−3 [T]−1

Activity of a component i in a mixture
ai

a

i

=

e

(

μ

i

−

μ

i

⊖

)

/

R
T

{\displaystyle a_{i}=e^{\left(\mu _{i}-\mu _{i}^{\ominus }\right)/RT}}

dimensionless
dimensionless

Mole fraction, molality, and molar concentration activity coefficients
γxi for mole fraction, γbi for molality, γci for molar concentration.
Three coefficients are used;

a

i

=

γ

x
i

x

i

{\displaystyle a_{i}=\gamma _{xi}x_{i}\,}

a

i

=

γ

b
i

b

i

/

b

⊖

{\displaystyle a_{i}=\gamma _{bi}b_{i}/b^{\ominus }\,}

a

i

=

γ

c
i

[

X

i

]

/

[

X

i

]

⊖

{\displaystyle a_{i}=\gamma _{ci}\left[\mathrm {X} _{i}\right]/\left[\mathrm {X} _{i}\right]^{\ominus }\,}

dimensionless
dimensionless

Rate constant
k

k
=

d

[

Y

]

/

d

t

∏

i
=
1

r

[

X

i

]

σ

i

{\displaystyle k={\frac {\mathrm {d} \left[\mathrm {Y} \right]/\mathrm {d} t}{\prod _{i=1}^{r}\left[\mathrm {X} _{i}\right]^{\sigma _{i}}}}}

(mol dm−3)(S2) s−1
([N] [L]−3)(S2) [T]−1

General equilibrium constant [2]
Kc

K

c

=

∏

j
=
1

p

[

Y

j

]

η

j

∏

i
=
1

r

[

X

i

]

ν

i

{\displaystyle K_{c}={\frac {\prod _{j=1}^{p}\left[\mathrm {Y} _{j}\right]^{\eta _{j}}}{\prod _{i=1}^{r}\left[\mathrm {X} _{i}\right]^{\nu _{i}}}}}

(mol dm−3)(S1)
([N] [L]−3)(S1)

General thermodynamic activity constant [3]
K0

K

0

=

∏

j
=
1

p

a

(

Y

j

)

η

j

∏

i
=
1

r

a

(

X

i

)

ν

i

{\displaystyle K_{0}={\frac {\prod _{j=1}^{p}a\left(\mathrm {Y} _{j}\right)^{\eta _{j}}}{\prod _{i=1}^{r}a\left(\mathrm {X} _{i}\right)^{\nu _{i}}}}}

a(Xi) and a(Yj) are activities of Xi and Yj respectively.

(mol dm−3)(S1)
([N] [L]−3)(S1)

Equilibrium constant for gaseous reactions, using Partial pressures
Kp

K

p

=

∏

j
=
1

p

p

(

Y

j

)

η

j

∏

i
=
1

r

p

(

X

i

)

ν

i

{\displaystyle K_{p}={\frac {\prod _{j=1}^{p}p\left(\mathrm {Y} _{j}\right)^{\eta _{j}}}{\prod _{i=1}^{r}p\left(\mathrm {X} _{i}\right)^{\nu _{i}}}}}

Pa(S1)
([M] [L]−1 [T]−2)(S1)

Logarithm of any equilibrium constant
pKc

p

K

c

=
−

log

10

K

c

=

∑

j
=
1

p

η

j

log

10

[

Y

j

]

−

∑

i
=
1

r

ν

i

log

10

[

X

i

]

{\displaystyle \mathrm {p} K_{c}=-\log _{10}K_{c}=\sum _{j=1}^{p}\eta _{j}\log _{10}\left[\mathrm {Y} _{j}\right]-\sum _{i=1}^{r}\nu _{i}\log _{10}\left[\mathrm {X} _{i}\right]}

dimensionless
dimensionless

Logarithm of dissociation constant
pK

p

K
=
−

log

10

K

{\displaystyle \mathrm {p} K=-\log _{10}K}

dimensionless
dimensionless

Logarithm of hydrogen ion (H+) activity, pH
pH

pH

=

−

log

10

[

H

+

]

{\displaystyle {\ce {pH=-\log _{10}[H+]}}}

dimensionless
dimensionless

Logarithm of hydroxide ion (OH−) activity, pOH
pOH

pOH

=

−

log

10

[

OH

−

]

{\displaystyle {\ce {pOH=-\log _{10}[OH^{-}]}}}

dimensionless
dimensionless

text: Electrochemistry[edit]

text: Notation for half-reaction standard electrode potentials is as follows. The redox reaction

text: split into:

text:
a reduction reaction:

B

+

+

e

−

↽

−

−

⇀

B

{\displaystyle {\ce {{B+}+{e^{-}}<=>{B}}}}

text:
and an oxidation reaction:

A

+

+

e

−

↽

−

−

⇀

A

{\displaystyle {\ce {{A+}+{e^{-}}<=>{A}}}}

text:
(written this way by convention) the electrode potential for the half reactions are written as

E

⊖

(

A

+

|

A

)

{\displaystyle E^{\ominus }\left({\ce {A+}}\vert {\ce {A}}\right)}

 and

E

⊖

(

B

+

|

B

)

{\displaystyle E^{\ominus }\left({\ce {B+}}\vert {\ce {B}}\right)}

 respectively.

text: For the case of a metal-metal half electrode, letting M represent the metal and z be its valency, the half reaction takes the form of a reduction reaction:

text:
Quantity (Common Name/s)
(Common) Symbol/s
Defining Equation
SI Units
Dimension

Standard EMF of an electrode

E

⊖

,

E

⊖

(

X

)

{\displaystyle E^{\ominus },E^{\ominus }\left({\ce {X}}\right)}

Δ

E

⊖

(

X

)

=

E

⊖

(

X

)

−

E

⊖

(

Def

)

{\displaystyle \Delta E^{\ominus }\left({\ce {X}}\right)=E^{\ominus }\left({\ce {X}}\right)-E^{\ominus }\left({\ce {Def}}\right)}

where Def is the standard electrode of definition, defined to have zero potential. The chosen one is hydrogen:

E

⊖

(

H

+

)

=

E

⊖

(

H

+

|

H

)

=
0

{\displaystyle E^{\ominus }\left({\ce {H+}}\right)=E^{\ominus }\left({\ce {H+}}\vert {\ce {H}}\right)=0}

V
[M][L]2[I][T]−1

Standard EMF of an electrochemical cell

E

c
e
l
l

⊖

,
Δ

E

⊖

{\displaystyle E_{\mathrm {cell} }^{\ominus },\Delta E^{\ominus }}

E

c
e
l
l

⊖

=

E

⊖

(

C
a
t

)

−

E

⊖

(

A
n

)

{\displaystyle E_{\mathrm {cell} }^{\ominus }=E^{\ominus }\left(\mathrm {Cat} \right)-E^{\ominus }\left(\mathrm {An} \right)}

where Cat is the cathode substance and An is the anode substance.

V
[M][L]2[I][T]−1

Ionic strength
I
Two definitions are used, one using molarity concentration,

I
=

1
2

∑

i
=
1

N

z

i

2

[

X

i

]

{\displaystyle I={\frac {1}{2}}\sum _{i=1}^{N}z_{i}^{2}\left[{\rm {X}}_{i}\right]}

and one using molality,[4]

I
=

1
2

∑

i
=
1

N

z

i

2

b

i

{\displaystyle I={\frac {1}{2}}\sum _{i=1}^{N}z_{i}^{2}b_{i}}

The sum is taken over all ions in the solution.

mol dm−3
or
mol dm−3 kg−1
[N] [L]−3 [M]−1

Electrochemical potential (of component i in a mixture)

μ
¯

i

{\displaystyle {\bar {\mu }}_{i}\,\!}

μ
¯

i

=
μ
−
z
e

N

A

ϕ

{\displaystyle {\bar {\mu }}_{i}=\mu -zeN_{A}\phi \,\!}

φ = local electrostatic potential (see below also) zi = valency (charge) of the ion i

J
[M][L]2[T]−2

text: Quantum chemistry[edit]

text:
Quantity (Common Name/s)
(Common) Symbol/s
Defining Equation
SI Units
Dimension

Electronegativity
χ
Pauling (difference between atoms A and B):

χ

A

−

χ

B

=
(

e
V

)

−
1

/

2

E

d

(

A
B

)
−
[

E

d

(

A
A

)
+

E

d

(

B
B

)
]

/

2

{\displaystyle \chi _{\rm {A}}-\chi _{\rm {B}}=({\rm {eV}})^{-1/2}{\sqrt {E_{\rm {d}}({\rm {AB}})-[E_{\rm {d}}({\rm {AA}})+E_{\rm {d}}({\rm {BB}})]/2}}}

Mulliken (absolute):

χ
=

10

−
3

[
187

(

E

I

+

E

E
A

)

+
170
]

{\displaystyle \chi =10^{-3}\left[187\left(E_{I}+E_{EA}\right)+170\right]\,}

Energies (in eV) Ed = Bond dissociation EI = Ionization EEA = Electron affinity

dimensionless
dimensionless