We’re being asked to determine the equilibrium constant (K) at 298 K for the given reaction:
2 SO_{2}(g) + O_{2}(g) ⇌ 2 SO_{3}(g)
Recall that ΔG˚_{rxn} and K are related to each other:
$\overline{){\mathbf{\Delta G}}{{\mathbf{\xb0}}}_{{\mathbf{rxn}}}{\mathbf{=}}{\mathbf{-}}{\mathbf{RTlnK}}}$
We’re given the ΔH˚_{f} and S˚ of each reactant and product:
Substance | ΔH˚_{f} (kJ/mol) | S˚ (J/mol • K) |
SO_{2}(g) | –297 | 249 |
O_{2}(g) | 0 | 205 |
SO_{3}(g) | –395 | 256 |
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 the following 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.
Given the thermodynamic data in the table below, calculate the equilibrium constant (at 298 K) for the reaction:
2SO_{2} (g) + O_{2}(g) ⇌ 2SO_{3}(g)
a) 2.37 x 10^{24}
b) 1.06
c) 1.95
d) 3.92 x 10^{23}
e) More information is needed.
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Based on our data, we think this problem is relevant for Professor Bindell's class at UCF.