Question

the thermodynamics of ethanol
gibbs free energy
the thermodynamic data for the combustion of ethanol is given below.
δs₍comb₎ = 217.9 j/mol k
δh₍comb₎ = -1,325 kj/mol c₂h₅oh
calculate the standard free energy for the combustion of ethanol.
what is the standard free energy change (δg⁰), in kj/mol, for the combustion of ethanol?
-1390. kj/mol

1. kj/mol

-1260. kj/mol

1. kj/mol

Explanation:

Step1: Recall the Gibbs free energy formula

The formula for standard Gibbs free energy change (\(\Delta G^\circ\)) is \(\Delta G^\circ=\Delta H^\circ - T\Delta S^\circ\). For standard conditions, \(T = 298\space K\) (room temperature, which is the standard temperature for thermodynamic calculations).

Step2: Convert units of \(\Delta S\)

Given \(\Delta S_{comb}=217.9\space J/mol\space K\). We need to convert this to \(kJ/mol\space K\) by dividing by 1000. So, \(\Delta S_{comb}=\frac{217.9}{1000}=0.2179\space kJ/mol\space K\).

Step3: Substitute values into the formula

We know \(\Delta H_{comb}=- 1325\space kJ/mol\), \(T = 298\space K\), and \(\Delta S_{comb}=0.2179\space kJ/mol\space K\). Plugging into the formula:
\[

$$\begin{align*} \Delta G^\circ&=\Delta H^\circ - T\Delta S^\circ\\ &=-1325-(298\times0.2179)\\ &=-1325 - 65.0342\\ &=- 1390.0342\approx - 1390\space kJ/mol \end{align*}$$

\]

Answer:

-1390. kJ/mol