Chemical Thermodynamics: Chemical Potential 1

Error

There was an error loading the page.

Contributors

Feedback

From users who are members of Thermodynamics for Chemistry :

Frances Docherty

said

Ready to use

1 week, 2 days ago

History

○

Frances Docherty 1 week, 2 days ago

Published this.

○

Frances Docherty 1 week, 2 days ago

Gave some feedback: Ready to use

○

Frances Docherty 1 week, 2 days ago

Created this as a copy of Chemical Potential.

Name	Status	Author	Last Modified
Chemical Thermodynamics: Chemical Potential 1	Ready to use	Frances Docherty	30/03/2025 18:40
Chemical Thermodynamics: Chemical Potential 2	Ready to use	Frances Docherty	30/03/2025 18:41

There are 2 other versions that do you not have access to.

Question statement

Give any introductory information the student needs.

			Name	Type	Generated Value

arrow	list	[ "<", ">" ]
rand	integer	1
outcome	list	List of 2 items

Automatically regenerate variables?

Name

Data type

Value

(text strings)

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `list`

[ "<", ">" ]

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
3. Gap Gap 2. Number entry
  Add
4. Gap Gap 3. Choose one from a list
  Add

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

What is $\mathrm{\Delta G_{reaction}}$ for the reaction:

$\mathrm{2SO_2\space +\space O_2\space \rightleftharpoons\space 2SO_3}$

when $\mathrm{\Delta n}$ moles of $\mathrm{O_2}$ are used up?

Express your answer in terms of chemical potentials, $\mathrm{\mu_{_X}}$ (your coefficients may be negative).

$\mathrm{\Delta G_{reaction}=}$ Gap 0. $\mathrm{\mu_{_{SO_2}}} +$ Gap 1. $\mathrm{\mu_{_{O_2}}} +$ Gap 2. $\mathrm{\mu_{_{SO_3}}}$ .

Given that $\mathrm{\mu_{_{SO_3}}\var{arrow[rand]}\space \mu_{_{SO_2}}+0.5\mu_{_{O_2}}}$ at a certain reaction coordinate, will the quantity of $\mathrm{SO_3}$ increase or decrease?

Gap 3.

Advice

The chemical potential of a substance in a mixture, $\mathrm{\mu_x}$ , is the contribution of that substance to the total Gibbs free energy, $\mathrm{G}$ , of the mixture. It is effectively the molar Gibbs free energy inherent to that substance under a particular set of conditions.

As a substance is formed, more of its chemical potential is introduced - and as a substance is consumed, its chemical potential is removed - from the total $\mathrm{G}$ value. Since $\mathrm{\mu_x}$ is molar (i.e. it results from one mole of the substance), the change in $\mathrm{G}$ when a substance is formed or consumed is proportional to the number of moles of the substance formed or consumed which we denote $\mathrm{\Delta n}$ :

$\mathrm{\Delta G=\Delta n\cdot \mu_x}$

We are told that $\mathrm{\Delta n}$ moles of $\mathrm{O_2}$ are used up in the reaction:

$\mathrm{2SO_2\space +\space O_2\space \rightleftharpoons\space 2SO_3}$ .

Since $\mathrm{\Delta n}$ moles are consumed, we will re-express the change in moles of $\mathrm{O_2}$ as $\mathrm{-\Delta n}$ .

From the reaction, we can see that twice as much $\mathrm{SO_2}$ is consumed, so the change in moles of $\mathrm{SO_2}$ is $\mathrm{-2\Delta n}$ .

Similarly, we can see that twice as much $\mathrm{SO_3}$ is formed than $\mathrm{O_2}$ consumed, but we must pay attention to the fact that that much $\mathrm{SO_3}$ is being formed, so the change in moles of $\mathrm{SO_3}$ is $\mathrm{+2\Delta n}$ .

Knowing all this, we can express the net change in the Gibbs free energy of the mixture in terms of the chemical potentials of the three substances:

$\mathrm{\Delta G=-2\Delta n\mu_{_{SO_2}}-(1)\Delta n\mu_{_{O_2}}+2\Delta n\mu_{_{SO_3}}}$ .

Additionally, $\mathrm{\Delta G_{reaction}}$ is defined as the molar Gibbs free energy change (i.e. the change per one mole of specified substance formed or consumed), which we simply divide our previous answer by $\mathrm{\Delta n}$ to obtain:

$\mathrm{\Delta G_{reaction}=\frac{\Delta G}{\Delta n}=-2\mu_{_{SO_2}}-(1)\mu_{_{O_2}}+2\mu_{_{SO_3}}}$ .

Finally, we are told that, for the certain set of conditions we are concerned with:

$\mathrm{\mu_{_{SO_3}}\var{arrow[rand]}\space \mu_{_{SO_2}}+0.5\mu_{_{O_2}}}$ .

We can double this to compare it to our expression for $\mathrm{\Delta G_{reaction}}$ :

$\mathrm{2\mu_{_{SO_3}}\var{arrow[rand]}\space 2\mu_{_{SO_2}}+\mu_{_{O_2}}}$ .

From this, we can deduce whether our $\mathrm{\Delta G_{reaction}}$ will be positive or negative:

$\mathrm{\Delta G_{reaction}=-2\mu_{_{SO_2}}-\mu_{_{O_2}}+2\mu_{_{SO_3}}=2\mu_{_{SO_3}}-(2\mu_{_{SO_2}}+\mu_{_{O_2}})}$ ,

$\mathrm{2\mu_{_{SO_3}}\var{arrow[rand]}\space 2\mu_{_{SO_2}}+\mu_{_{O_2}}}$

$\mathrm{\Rightarrow\space\space\space 2\mu_{_{SO_3}}-(2\mu_{_{SO_2}}+\mu_{_{O_2}})\space \var{arrow[rand]}\space 0}$

$\mathrm{\Rightarrow\space\space\space \Delta G_{reaction}\space \var{arrow[rand]}\space 0}$ .

Thus, {outcome[rand]}

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Choose one from a list
Choose one from a list		Hasn't run yet

This question is not used in any exams.

Loading...

Error

Chemical Thermodynamics: Chemical Potential 1

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Frances Docherty 1 week, 2 days ago

Frances Docherty 1 week, 2 days ago

Frances Docherty 1 week, 2 days ago

Error in variable testing condition

Error

Warning

Generated value: `list`

Parts

Gap-fill

Loading...

Error

Chemical Thermodynamics: Chemical Potential 1

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Frances Docherty 1 week, 2 days ago

Frances Docherty 1 week, 2 days ago

Frances Docherty 1 week, 2 days ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Gap-fill

Generated value: `list`