We’re asked to calculate the equilibrium pressure of CO_{2} at 410°C using standard thermodynamic data for the given balanced reaction:
PbCO_{3} (s) ⇌ PbO(s) + CO_{2} (g)
Recall that the equilibrium constant is the ratio of the products and reactants. We use K_{p} when dealing with pressure
$\overline{){{\mathbf{K}}}_{{\mathbf{p}}}{\mathbf{=}}\frac{{\mathbf{P}}_{\mathbf{products}}}{{\mathbf{P}}_{\mathbf{reactants}}}}$
Note that solid and liquid compounds are ignored in the equilibrium expression.
Also, recall that ΔG˚_{rxn} and K are related to each other:
$\overline{){\mathbf{\Delta G}}{{\mathbf{\xb0}}}_{{\mathbf{rxn}}}{\mathbf{=}}{\mathbf{-}}{\mathbf{RTlnK}}}$
The thermodynamic data ( ΔH˚_{f} and ΔS˚) of each reactant and product can be found in textbooks/online:
Substance | ΔH˚_{f} (kJ/mol) | S˚ (J/mol • K) |
PbCO_{3} (s) | –699.1 | 131.0 |
PbO(s) | –217.3 | 68.7 |
CO_{2} (g) | –393.5 | 213.8 |
We can use the following equation to solve for ΔG˚_{rxn}:
$\overline{){\mathbf{\Delta G}}{{\mathbf{\xb0}}}_{{\mathbf{rxn}}}{\mathbf{=}}{\mathbf{\Delta H}}{{\mathbf{\xb0}}}_{{\mathbf{rxn}}}{\mathbf{-}}{\mathbf{T\Delta S}}{{\mathbf{\xb0}}}_{{\mathbf{rxn}}}}$
For this problem we need to do these steps:
Step 1: Calculate ΔH˚_{rxn}.
Step 2: Calculate ΔS˚_{rxn}.
Step 3: Use ΔH˚_{rxn} and ΔS˚_{rxn} to calculate for ΔG˚_{rxn}.
Step 4: Calculate for K (K_{p}).
Step 5 : From K_{p}, solve for equilibrium partial pressure of CO_{2}
Using data in Appendix C in the textbook, calculate the equilibrium pressure of CO_{2} in the system at 410 ^{o}C.
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