Chemistry Gibbs Free Energy Solution: Given the thermodynamic data in the table below, c...

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# Solution: Given the thermodynamic data in the table below, calculate the equilibrium constant (at 298 K) for the reaction:2SO2 (g) + O2(g) ⇌ 2SO3(g)a) 2.37 x 1024b) 1.06c) 1.95d) 3.92 x 1023e) More information is needed.

Problem

Given the thermodynamic data in the table below, calculate the equilibrium constant (at 298 K) for the reaction:

2SO2 (g) + O2(g) ⇌ 2SO3(g)

a) 2.37 x 1024

b) 1.06

c) 1.95

d) 3.92 x 1023

Solution

We’re being asked to determine the equilibrium constant (K) at 298 K for the given reaction:

2 SO2(g) + O2(g)  2 SO3(g)

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

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

We’re given the ΔH˚f and S˚ of each reactant and product:

 Substance ΔH˚f (kJ/mol) S˚ (J/mol • K) SO2(g) –297 249 O2(g) 0 205 SO3(g) –395 256

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

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

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.

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