Chemical Thermodynamics: Chemical Potential 2

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

4 weeks ago

History

○

Frances Docherty 4 weeks ago

Created this as a copy of Chemical Potential - Alt (O).

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	0
outcome	list	List of 2 items
m	integer	20
gso2	number	-300.8
go2	integer	0
gso3	number	-371.2
gfmo2	number	31.998
n	number	0.6250390649
gibbs	number	-88.0055003438

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 Number entry
  Add

Gap-fill

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

Calculate $\mathrm{\Delta G}$ for the reaction:

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

when $\mathrm{\var{m}\space g}$ of $\mathrm{O_2}$ are consumed, given the measured chemical potentials $\mathrm{\mu_{_{SO_2}}=\var{gso2}\space kJ\space mol^{-1}}$ , $\mathrm{\mu_{_{O_2}}=\var{go2}\space kJ\space mol^{-1}}$ , and $\mathrm{\mu_{_{SO_3}}=\var{gso3}\space kJ\space mol^{-1}}$ (you may assume these values remain constant during the specified consumption of oxygen):

Unnamed gap $\mathrm{kJ}$

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 $\mathrm{\Delta n}$ :

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

Let's say 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:

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

Now, we have all three chemical potentials, so before we use this equation, we just need to calculate $\mathrm{\Delta n}$ , i.e. the number of moles of $\mathrm{O_2}$ consumed.

Note: You may have noticed that the chemical potentials we were given were expressed in $\mathrm{kJ\space mol^{-1}}$ . We have no need to convert these to $\mathrm{J\space mol^{-1}}$ , as the equation we are going to use them in only involves multiplication by constants, and addition; in this case we only need to make sure that the chemical potentials are all expressed in the same units, so that we can sum them together fairly; the only consequence being that our answer will also be scaled up by one thousand, so we will obtain a value for $\mathrm{\Delta G}$ already expressed in $\mathrm{kJ}$ , which we are asked for anyways.

We can calculate $\mathrm{\Delta n}$ from the mass of $\mathrm{O_2}$ consumed, $\mathrm{\Delta m=\var{m}\space g}$ , noting that the $\mathrm{gFM}$ of $\mathrm{O_2}$ is $\mathrm{\var{gfmo2}\space g\space mol^{-1}}$ :

$\mathrm{n=\frac{m}{gFM}}$

$\mathrm{\Rightarrow\space\space\space \Delta n=\frac{\Delta m}{gFM}}$

$\mathrm{\Rightarrow\space\space\space \Delta n=\frac{\var{m}}{\var{gfmo2}}=(\var{sigformat(n,5)}\cdots)\space mol}$ .

Note: You should try to leave this value in your calculator for the next calculation, or note it down to at least the number of significant figures shown.

We can now use our equation to calculate $\mathrm{\Delta G}$ for the reaction (for ease, we will first factor $\mathrm{\Delta n}$ out in front):

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

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

$\mathrm{\Rightarrow\space\space\space \Delta G=(\var{sigformat(n,5)}\cdots)\times([-2\times\var{gso2}]-0+[2\times\var{gso3}])=\var{sigformat(gibbs,4)}\space kJ}$ .

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

This question is not used in any exams.

Loading...

Error

Chemical Thermodynamics: Chemical Potential 2

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Frances Docherty 4 weeks ago

Frances Docherty 4 weeks ago

Frances Docherty 4 weeks ago

Error in variable testing condition

Error

Warning

Generated value: `list`

Parts

Gap-fill

Loading...

Error

Chemical Thermodynamics: Chemical Potential 2

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Frances Docherty 4 weeks ago

Frances Docherty 4 weeks ago

Frances Docherty 4 weeks ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Gap-fill

Generated value: `list`