\(K_p\) for the conversion of oxygen to ozone at \(400 \mathrm{~K}\) is \(1.0 \times 10^{-30}\), its…
\(K_p\) for the conversion of oxygen to ozone at \(400 \mathrm{~K}\) is \(1.0 \times 10^{-30}\), its standard Gibbs energy change in \(\mathrm{kJ} \mathrm{mol}^{-1}\) is approximately
229.8
114.9
-229.8
-114.9
Solution
Given, \(K_p\) for the conversion of oxygen to ozone at \(400 \mathrm{~K}\) is \(1.0 \times 10^{-30}\).
\(\left(\Delta G^{\circ}\right)\) standard Gibbs energy change \(=\) ?
\(\Delta G^{\circ}=-R T \ln K_p=2.303 R T \log _{10} K_p\)
Here,
\(R=8.314 \mathrm{~J} / \mathrm{mol}\)
\(\begin{aligned}
T & =400 \mathrm{~K} \\
\Delta G^{\circ} & =-R T \log K_p \\
& =-8.314 \times 400 \times 2.303 \times \log 10^{-30} \\
& =22976570 \mathrm{~J} \mathrm{~mol}^{-1} \\
& =229.765 \mathrm{~kJ} \mathrm{~mol}^{-1}
\end{aligned}\)