24.11: The Standard Gibbs Free Energy for H₂(g), I₂(g), and HI(g)

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For many diatomic molecules, the data needed to calculate \(G^o_{IG}\) are readily available in various compilations. For illustration, we consider the molecules \(H_2\), \(I_2\), and \(HI\). The necessary experimental data are summarized in Table 2.

Table 2: Data1 for the calculation of partition functions for \(H_2 ~ (g)\), \(I_2 ~ (g)\), and \(HI ~ (g)\)
Compound	Molar mass, g	\(D_0\), kJ mol^-1	\(\nu\), hertz	\(r_XY\), m
\(H_2\)	\(2.016\)	\(432.073\)	\(1.31948 \times 10^{14}\)	\(7.4144 \times 10^{−11}\)
\(I_2\)	\(253.82\)	\(148.81\)	\(6.43071 \times 10^{12}\)	\(2.666 \times 10^{−10}\)
\(HI\)	\(127.918\)	\(294.67\)	\(6.69227 \times 10^{13}\)	\(1.60916 \times 10^{−10}\)

The terms in the simplified equation for the standard Gibbs free energy at \(298.15\) K are given in Table 3.

Table 3: Gibbs free energy components
Compound	\(\ln \left[ \left( \frac{2 \pi mkT}{h^2} \right)^{3/2} \frac{kT}{p_o} \right]\)	\(\ln \left( \frac{8 \pi^2 IkT}{\sigma h^2} \right)\)	\(- \ln \left( 1 - e^{-h \nu/kT} \right)\)	\(\frac{D_0}{RT}\)
\(H_2\)	126.23929	0.6312*	0.0000	174.295
\(I_2\)	133.49256	7.932	0.4388	60.0289
\(HI\)	132.46470	3.4604	0.00002	118.868
*Calculated as a sum of terms (see Table 1) rather than as the integral approximation.

Finally, the standard molar Gibbs Free Energies at \(298.15\) K are summarized in Table 4.

Table 4: Calculated Gibbs free energies
Compound	\(G^o_{298 ~ \text{K}}, ~ \text{kJ mole}^{-1}\)
\(H_2\)	−746.577
\(I_2\)	−500.471
\(HI\)	−631.622

These results can be used to calculate the standard Gibbs free energy change, at \(298.15\) K, for the reaction

\[H_2\left(g\right)+I_2\left(g\right)\to 2HI\left(g\right). \nonumber \]

We find

\[{\Delta }_rG^o_{298}=2G^o\left(HI,\ g,\ 298.15\ \mathrm{K}\right)-G^o\left(H_2,\ g,\ 298.15\ \mathrm{K}\right)-G^o\left(I_2,\ g,\ 298.15\ \mathrm{K}\right)=-16.20\ \mathrm{kJ} \nonumber \]