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Chemistry

The change in Gibb’s free energy when a moles of chemical A and b moles of chemical B react to form c moles of chemical C and d moles of chemical D, equal to

RTln( [A ] eqa . [B ]eqb. [C ]c . [D ]d

[A ]a . [B ]b . [C ]e qc . [D ] eqd ), is also the change in Gibb’s free energy when n moles of

electrons are transferred, and is also equal to – nFE if this is a redox reaction meaning that

RTln( [A ] eqa . [B ]eqb. [C ]c . [D ]d

[A ]a . [B ]b . [C ]e qc . [D ] eqd ) will equal – nFE which means that E will equal

– ( RF ) . Tln( [ A ]eqa/n. [B ]eqb /n . [C ]c/n. [D ]d /n

[A ]a /n . [B ]b /n . [C ] eqc/ n. [D ]eqd /n ).During any time interval during this reaction,

the decrease∈[A ]a

=the decrease∈ [B ]

b=the increase∈[C ]

c=the increase∈ [D ]

d and so during

any time

interval during this reaction,

– ∆ [A ]a

=– ∆ [B ]b

=∆ [C ]c

=∆ [D ]d

. This is in units of litre-1.

The balanced chemical equation for this reaction is aA + bB → cC + dD.

R is per mole of chemical, which can be shown more clearly by expressing

RTln( [A ] eqa . [B ]eqb. [C ]c . [D ]d

[A ]a . [B ]b . [C ]e qc . [D ] eqd ) as

aRTln ( [A ]eqa /a . [B ] eqb /a. [C ]c /a . [D ]d /a

[A ]a /a . [B ]b /a . [C ]e qc /a . [D ]eqd /a ) , which, of course, equals

aRTln ( [A ]eq1. [B ]eqb /a . [C ]c /a. [D ]d /a

[A ]1 . [B ]b /a . [C ] eqc /a. [D ]eqd / a ) i.e.aRTln ( [A ]eq❑ . [B ]eqb /a . [C ]c/a . [D ]d /a

[A ]❑ . [B ]b /a . [C ] eqc/a. [D ]eqd /a ) .Or as

bRTln( [A ]eqa/b . [B ] eqb /b. [C ]c /b . [D ]d /b

[ A ]a /b . [B ]b / b. [C ]eqc /b . [D ] eqd /b ) ,which, of course, equals

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bRTln( [A ]eqa/b . [B ] eq1 . [C ]c /b. [D ]d /b

[ A ]a /b . [B ]1 . [C ]e qc /b . [D ]eqd /b ) i.e. bRTln( [A ]eqa/b . [B ] eq❑ . [C ]c /b. [D ]d /b

[ A ]a /b . [B ]❑ . [C ]e qc /b . [D ]eqd /b ).Or as

cRTln ( [A ]eqa /c . [B ] eqb /c . [C ]c /c . [D ]d /c

[A ]a / c . [B ]b / c . [C ] eqc/ c . [D ]eqd /c ), which, of course, equals

cRTln ( [A ]eqa /c . [B ] eqb /c . [C ]1 . [D ]d /c

[A ]a / c . [B ]b / c . [C ] eq1 . [D ]eqd /c ) i.e. cRTln ( [A ]eqa /c . [B ] eqb /c . [C ]❑ . [D ]d /c

[A ]a / c . [B ]b / c . [C ] eq❑ . [D ]eqd /c ) .Or as

dRTln( [A ]eqa /d . [B ]eqb/d . [C ]c/d . [D ]d /d

[ A ]a /d . [B ]b/ d . [C ] eqc/d . [D ]eqd /d ), which, of course, equals

dRTln( [A ]eqa /d . [B ]eqb/d . [C ]c /d . [D ]1

[ A ]a / d . [B ]b/d . [C ] eqc/d . [D ]eq1 ) i.e.dRTln( [A ]eqa /d . [B ]eqb/d . [C ]c /d . [D ]❑

[ A ]a /d . [B ]b/d . [C ] eqc/d . [D ]eq❑) . F is per mole of electrons.

Examples

Example 1.

The change in Gibb’s free energy when one mole of chemical A and one mole of chemical B react to form one mole of chemical C and one mole of chemical D, equal to

RTln( [A ] eq1 . [B ] eq1 . [C ]1 . [D ]1

[A ]1 . [B ]1 . [C ] eq1 . [D ]eq1 ) i.e. RTln( [A ] eq❑ . [B ] eq❑ . [C ]❑ . [D ]❑

[A ]❑ . [B ]❑ . [C ] eq❑ . [D ]eq❑ ),is also the change in Gibb’s free energy when, say, one mole of electrons are transferred, and is also equal to –1 FE i. e . – FE .

During any time interval during this reaction,

– ∆ [A ]1

=– ∆ [B ]1

=∆ [C ]1

=∆ [D ]1

i.e. – ∆ [A ]=– ∆ [B ]=∆ [C ]=∆ [D ] .

The balanced chemical equation for this reaction is 1A + 1B → 1C + 1D i.e. A + B → C + D.

Example 2, the same reaction,

The change in Gibb’s free energy when two moles of chemical A and two moles of chemical B react to form two moles of chemical C and two moles of chemical D, equal to

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RTln( [A ] eq2 . [B ] eq2 . [C ]2 . [D ]2

[A ]2 . [B ]2 . [C ] eq2 . [D ]eq2 ), is also the change in Gibb’s free energy when two moles of

electrons are transferred, and is also equal to –2 FE .

During any time interval during this reaction,

– ∆ [A ]2

=– ∆ [B ]2

=∆ [C ]2

=∆ [D ]2

.

The balanced chemical equation for this reaction is 2A + 2B → 2C + 2D.

Example 3, the same reaction again,

The change in Gibb’s free energy when half a mole of chemical A and half a mole of chemical B react to form half a mole of chemical C and half a mole of chemical D, equal to

RTln( [A ] eq1 /2 . [B ] eq1 /2 . [C ]1/2 . [D ]1 /2

[A ]1/2 . [B ]1 /2 . [C ] eq1 /2 . [D ]eq1/ 2 ), is also the change in Gibb’s free energy when half a mole

of electrons are transferred, and is also equal to – FE2.

During any time interval during this reaction,

–2 ∆ [A ]=–2∆ [B ]=2∆ [C ]=2∆ [D ] .

The balanced chemical equation for this reaction is 12A +

12B →

12C +

12D.

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