# Problem: Use data from Appendix IIB in the textbook to calculate the equilibrium constants at 25 ˚C for each of the following reactions.2 CO(g) + O2(g) ⇌ 2 CO2(g)

###### FREE Expert Solution

Recall that ΔG˚rxn and K are related to each other:

$\overline{){\mathbf{\Delta G}}{{\mathbf{°}}}_{{\mathbf{rxn}}}{\mathbf{=}}{\mathbf{-}}{\mathbf{RTlnK}}}$

We can use the following equation to solve for ΔG˚rxn:

$\overline{){\mathbf{\Delta G}}{{\mathbf{°}}}_{{\mathbf{rxn}}}{\mathbf{=}}{\mathbf{\Delta H}}{{\mathbf{°}}}_{{\mathbf{rxn}}}{\mathbf{-}}{\mathbf{T\Delta S}}{{\mathbf{°}}}_{{\mathbf{rxn}}}}$

Step 1: We can use the following equation to solve for ΔH˚rxn:

Note that we need to multiply each ΔH˚f by the stoichiometric coefficient since ΔH˚f is in kJ/mol.

Also, note that ΔH˚f for elements in their standard state is 0.

We also need to convert ΔH˚rxn from kJ/mol to J/ mol so our units remain consistent.

ΔH˚rxn = –5.89 × 105 J/mol

Step 2: We can use the following equation to solve for ΔS˚rxn:

Note that we need to multiply each S˚ by the stoichiometric coefficient since S˚ is in J/mol • K.

ΔS˚rxn = –498.18 J/mol • K

Step 3: Now that we have ΔH˚rxn and ΔS˚rxn, we can now solve for ΔG˚rxn

The given temperature is 298 K.

$\mathbf{\Delta G}{\mathbf{°}}_{\mathbf{rxn}}\mathbf{=}\mathbf{\Delta H}{\mathbf{°}}_{\mathbf{rxn}}\mathbf{-}\mathbf{T\Delta S}{\mathbf{°}}_{\mathbf{rxn}}$

ΔG˚rxn = –440542.36 J/mol

Step 4: Solving for K:

$\mathbf{\Delta G}\mathbf{°}\mathbf{=}\mathbf{-}\mathbf{RTlnK}$

###### Problem Details

Use data from Appendix IIB in the textbook to calculate the equilibrium constants at 25 ˚C for each of the following reactions.

CO(g) + O2(g) ⇌ 2 CO2(g)