Chemical Thermodynamics: Gibbs Free Energy of Formation 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, 1 day ago

History

○

Frances Docherty 4 weeks, 1 day ago

Gave some feedback: Ready to use

○

Frances Docherty 4 weeks, 1 day ago

Published this.

○

Frances Docherty 4 weeks, 1 day ago

Created this as a copy of Gibbs Free Energy of Formation - Alt 2 (O).

Name	Status	Author	Last Modified
Chemical Thermodynamics: Gibbs Free Energy of Formation 1	Ready to use	Frances Docherty	30/03/2025 18:18
Chemical Thermodynamics: Gibbs Free Energy of Formation 2	Ready to use	Frances Docherty	30/03/2025 18:19
Chemical Thermodynamics: Gibbs Free Energy of Formation 3	Ready to use	Frances Docherty	30/03/2025 18:20
Chemical Thermodynamics: Non-Standard Chemical Potential 1	Ready to use	Frances Docherty	30/03/2025 18:43
Chemical Thermodynamics: Non-Standard Chemical Potential 2	Ready to use	Frances Docherty	30/03/2025 18:44

There are 6 other versions that do you not have access to.

Question statement

Give any introductory information the student needs.

			Name	Type	Generated Value

n2	number	0.8
h2	number	4
nh3	number	2
q	number	0.2795084972
standard_kj	number	-17.5
gibbs	number	-20658.2169855102
gibbskj	number	-20.6582169855
k	number	1168.3723167406
standard	number	-17500

Automatically regenerate variables?

Name

Data type

Value

A random number between and (inclusive) with step size

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: `number`

0.8

This variable doesn't seem to be used anywhere.

Parts

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

Gap-fill

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

The equilibrium constant for the standard formation of ammonia is found to be $\mathrm{\var{scientificnumberlatex(siground(k,5))}}$ at $\mathrm{298\space K}$ .

What is the Gibbs free energy of formation of ammonia when the partial pressures of the $\mathrm{N_2}$ , $\mathrm{H_2}$ and $\mathrm{NH_3}$ (treated as perfect gases) are $\mathrm{\var{dpformat(n2,1)}\space bar}$ , $\mathrm{\var{dpformat(h2,1)}\space bar}$ , and $\mathrm{\var{dpformat(nh3,1)}\space bar}$ respectively?

Gap 0. $\mathrm{kJ\space mol^{-1}}$

Will the quantity of ammonia increase or decrease in this case?

Gap 1.

Advice

The Gibbs free energy of a reacting mixture, $\mathrm{\Delta G}$ , is given by the following equation:

$\mathrm{\Delta G=\Delta G^\circ + RTln(Q)}$ ,

where $\mathrm{\Delta G^\circ}$ is the standard Gibbs free energy, in $\mathrm{J \space mol^{-1}}$ ; $\mathrm{R=8.314\space J \space K^{-1}\space mol^{-1}}$ is the universal gas constant; $\mathrm{T}$ is the temperature of the system, in $\mathrm{K}$ ; and $\mathrm{Q}$ is the reaction quotient, given by:

$\mathrm{Q=\frac{[C]^c[D]^d}{[A]^a[B]^b}}$ for the reaction $\mathrm{aA\space +\space bB\space\rightleftharpoons\space cC\space +\space dD}$ .

We are asked to calculate $\mathrm{\Delta G}$ for the standard formation of ammonia. By considering the stoichiometries of hydrogen and nitrogen within ammonia, we can fairly easily deduce the chemical equation for this formation:

$\mathrm{N_2\space +\space 3H_2\space\rightleftharpoons\space 2NH_3}$ .

We must, however, pay attention to the fact that we will eventually be using $\mathrm{\Delta G^\circ}$ , for the standard formation of ammonia, i.e. the formation of 1 mole of ammonia under standard conditions. Thus, we half the stoichiometries of our equation:

$\mathrm{0.5N_2\space +\space 1.5H_2\space\rightleftharpoons\space NH_3}$ .

This gives us a reaction quotient of:

$\mathrm{Q=\frac{[NH_3]}{[N_2]^{0.5}[H_2]^{1.5}}}$ .

Since all three substances are gaseous at $\mathrm{298\space K}$ , we swap out their 'concentrations' for their partial pressures:

$\mathrm{Q=\frac{p_{_{NH_3}}}{p_{_{N_2}}^{0.5}p_{_{H_2}}^{1.5}}}$ .

Substituting this expression for $\mathrm{Q}$ into our original equation, we now have:

$\mathrm{\Delta G=\Delta G^\circ + RTln(\frac{p_{_{NH_3}}}{p_{_{N_2}}^{0.5}p_{_{H_2}}^{1.5}})}$ .

We are given the temperature of the system, $\mathrm{T=298\space K}$ ; and the partial pressures of all three gases, $\mathrm{p_{_{NH_3}}=\var{dpformat(nh3,1)}\space bar}$ , $\mathrm{p_{_{N_2}}=\var{dpformat(n2,1)}\space bar}$ , and $\mathrm{p_{_{H_2}}=\var{dpformat(h2,1)}\space bar}$ .

We are also given the equilibrium constant for the standard formation of ammonia, $\mathrm{k=\var{scientificnumberlatex(siground(k,5))}}$ . From this, we can calculate the standard Gibbs free energy of formation, using the formula:

$\mathrm{\Delta G^\circ =-RTln(k)}$

$\mathrm{\Rightarrow\space\space\space\Delta G^\circ =-8.314\times 298\times ln(\var{scientificnumberlatex(siground(k,5))})=\var{standard} \space J \space mol^{-1}}$

We can thus calculate $\mathrm{\Delta G}$ for our reaction:

$\mathrm{\Delta G=\var{standard} + (8.314\times 298\times ln[\frac{\var{dpformat(nh3,1)}}{{\var{dpformat(n2,1)}}^{0.5}\times{\var{dpformat(h2,1)}}^{1.5}}])=\var{sigformat(gibbs,3)}\space J\space mol^{-1}}$ .

To quote our answer in the units asked for, we divide by one thousand to obtain:

$\mathrm{\Delta G=\var{sigformat(gibbskj,3)}\space kJ\space mol^{-1}}$ .

The Gibbs free energy we have calculated is negative, which tells us that the reaction will proceed spontaneously in the forward direction, i.e. ammonia will be formed. Thus, the quantity of ammonia will increase.

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
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: Gibbs Free Energy of Formation 2

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Frances Docherty 4 weeks, 1 day ago

Frances Docherty 4 weeks, 1 day ago

Frances Docherty 4 weeks, 1 day ago

Error in variable testing condition

Error

Warning

Generated value: `number`

Parts

Gap-fill

Loading...

Error

Chemical Thermodynamics: Gibbs Free Energy of Formation 2

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Frances Docherty 4 weeks, 1 day ago

Frances Docherty 4 weeks, 1 day ago

Frances Docherty 4 weeks, 1 day ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`