We’re being asked to determine the **Gibbs free energy** at **2500 °C** for the given reaction:

C_{2}H_{5}OH_{(l)} + 3 O_{2}_{(g)}→ 2 CO_{2(g) }+ 3 H_{2}O_{(g)}

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

**ΔH° = -726 kJ**

**S° C _{2}H_{5}OH = 126.8 J/mol K**

**S° CO _{2} = 213.7 J/mol K**

**S° H _{2}O = 188.8 J/mol K**

**S° O _{2} = 205.1 J/mol K**

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 ΔS˚_{rxn}.

*Step 2:* Use ΔH˚_{rxn} and ΔS˚_{rxn} to calculate for ΔG˚_{rxn}.

For the combustion of one mole of liquid ethanol, ΔH° = -726 kJ. Which answer is closest to ΔG° for this reaction at 2500 °C, given that S° (J/mol K) for C_{2}H_{5}OH is 126.8, for O_{2} is 205.1, for CO_{2} is 213.7, and for H_{2}O is 188.8.

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