Chapter 20, Problem 20.84AP

Interpretation Introduction

Interpretation: The standard free energy change of the hypothetical formation of glycine in comets is to be calculated.

Concept introduction: The term $\Delta G^{\text{ο}}$ is a thermodynamic function. The superscript on this function represents its standard form. The term $\Delta$ represents the change. This function is known as the standard Gibb’s free energy change.

To determine: The standard free energy change of the hypothetical formation of glycine in comets.

Answer to Problem 20.84AP

Solution

The standard free energy change of the hypothetical formation of glycine in comets is $\underset{\_}{-89.8kJ}$.

Explanation of Solution

Explanation

Given

The given reaction is as follows,

${\text{CH}}_{\text{3}}\text{OH}\left(l\right)+\text{HCN}\left(g\right)+{\text{H}}_{\text{2}}\text{O}\left(l\right)\to {\text{NH}}_{\text{2}}{\text{CH}}_2\text{COOH}\left(s\right)+{\text{H}}_{\text{2}}\left(g\right)$

The standard free energy of formation values   $\left(\Delta G_{\text{f}}^{\text{ο}}\right)$ from the Appendix 4 are given as,

$\begin{array}{cc}\text{Compounds}& \Delta G_{\text{f}}^{\text{ο}}\\ {\text{CH}}_{\text{3}}\text{OH}\left(l\right)& -166.4\text{kJ/mol}\\ \text{HCN}\left(g\right)& \text{125}\text{.0}\text{kJ/mol}\\ {\text{H}}_2\text{O}\left(l\right)& -\text{237}\text{.2}\text{kJ/mol}\\ {\text{H}}_2{\text{NCH}}_2\text{COOH}\left(s\right)& -\text{368}\text{.4}\text{kJ/mol}\\ {\text{H}}_2\left(g\right)& \text{0}\text{kJ/mol}\end{array}$

The value of standard Gibb’s free energy change $\left(\Delta G^{\text{ο}}\right)$ of the given reaction is calculated by the formula,

$\Delta G^{\text{ο}}={{\displaystyle \sum n_{\text{p}}\Delta G_{\text{f}}^{\text{ο}}}}_{\left(\text{products}\right)}-{{\displaystyle \sum n_{\text{r}}\Delta G_{\text{f}}^{\text{ο}}}}_{\left(\text{reactants}\right)}$

Where,

• $\Delta G_{\text{f}}^{\text{ο}}{}_{\left(\text{reactants}\right)}$ are the standard free energy of formation for the reactants.
• $\Delta G_{\text{f}}^{\text{ο}}{}_{\left(\text{products}\right)}$ are the standard free energy of formation for the products.
• $n_{\text{p}}$ is the number of products molecule.
• $n_{\text{r}}$ is the number of reactants molecule.
• ${\displaystyle \sum }$ is the symbol of summation.

For the given reaction the representation in the above form is written as,

$\begin{array}{c}\Delta G^{\text{ο}}={{\displaystyle \sum n_{\text{p}}\Delta G_{\text{f}}^{\text{ο}}}}_{\left(\text{products}\right)}-{{\displaystyle \sum n_{\text{r}}\Delta G_{\text{f}}^{\text{ο}}}}_{\left(\text{reactants}\right)}\\ \Delta G^{\text{ο}}=\left[\Delta G_{\text{f}}^{\text{ο}}{}_{{\text{NH}}_2{\text{CH}}_2\text{COOH}\left(s\right)}+\Delta G_{\text{f}}^{\text{ο}}{}_{{\text{H}}_2\left(g\right)}\right]-\left[\Delta G_{\text{f}}^{\text{ο}}{}_{{\text{CH}}_3{\text{OH}}_2\left(l\right)}+\Delta G_{\text{f}}^{\text{ο}}{}_{{\text{H}}_2\text{O}\left(l\right)}+\Delta G_{\text{f}}^{\text{ο}}{}_{\text{HCN}\left(g\right)}\right]\end{array}$

Substitute the values of Gibb’s energy of formations in the above equation.

$\begin{array}{c}\Delta G^{\text{ο}}=\left[\Delta G_{\text{f}}^{\text{ο}}{}_{{\text{NH}}_2{\text{CH}}_2\text{COOH}\left(s\right)}+\Delta G_{\text{f}}^{\text{ο}}{}_{{\text{H}}_2\left(g\right)}\right]-\left[\Delta G_{\text{f}}^{\text{ο}}{}_{{\text{CH}}_3{\text{OH}}_2\left(l\right)}+\Delta G_{\text{f}}^{\text{ο}}{}_{{\text{H}}_2\text{O}\left(l\right)}+\Delta G_{\text{f}}^{\text{ο}}{}_{\text{HCN}\left(g\right)}\right]\\ \Delta G^{\text{ο}}=\left[\left[\begin{array}{l}1\text{mol}\times \left(-368.4\text{kJ/mol}\right)+\\ \left(0\text{kJ/mol}\right)\end{array}\right]-\left[\begin{array}{l}1\text{mol}\times \left(-166.4\text{kJ/mol}\right)+\\ 1\text{mol}\times \left(-237.2\text{kJ/mol}\right)+\\ 1\text{mol}\times \left(125.0\text{kJ/mol}\right)\end{array}\right]\right]\\ \Delta G^{\text{ο}}=\left(-368.4\text{kJ}\right)-\left(-278.6\text{kJ}\right)\\ \Delta G^{\text{ο}}=\underset{\_}{-89.8kJ}\end{array}$

Conclusion

The standard free energy change of the hypothetical formation of glycine in comets is $\underset{\_}{-89.8kJ}$