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

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    152809
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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

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


    This page titled 24.11: The Standard Gibbs Free Energy for H₂(g), I₂(g), and HI(g) is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Paul Ellgen via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.