Chapter 19, Problem 19.53QA

Interpretation Introduction

To calculate:

a) $∆H_{rxn}$ for the production of acetylene from the controlled combustion of methane.

b) Is the given reaction endothermic or an exothermic?

Answer to Problem 19.53QA

Solution:

a) $∆H_{rxn}$ for the production of acetylene from the controlled combustion of methane is $681.2 kJ$.

b) The reaction is endothermic.

Explanation of Solution

1) Concept:

We can calculate the $∆H_{rxn}$ from the difference between the standard molar enthalpies of reactants and products.

2) Formula:

$∆{\mathrm{H}}_{\mathrm{r}\mathrm{x}\mathrm{n}}=\sum {\mathrm{n}}_{\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{d}\mathrm{u}\mathrm{c}\mathrm{t}\mathrm{s}}\times ∆{\mathrm{H}}_{\mathrm{f},\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{d}\mathrm{u}\mathrm{c}\mathrm{t}\mathrm{s}}^0-\sum {\mathrm{n}}_{\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{s}}\times ∆{\mathrm{H}}_{\mathrm{f},\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{s}}^0$

“n” is the coefficient of the compounds given in the reactions.

3) Given:

The given reaction is

$6C{H}_4\left(g\right)+O_2\left(g\right)\to 2C_2{H}_2\left(g\right)+2CO \left(g\right)+10 H_2\left(g\right)$

From appendix 4, the value of $∆{\mathrm{H}}_{\mathrm{f}}^0$ are

	$∆{\mathrm{H}}_{\mathrm{f}}^0(\mathrm{k}\mathrm{J}/\mathrm{m}\mathrm{o}\mathrm{l})$
$C{H}_4 \left(g\right)$	$-74.8$
$O_2\left(g\right)$	$0.0$
$C_2{H}_2\left(g\right)$	$226.7$
$CO \left(g\right)$	$-110.5$
$H_2\left(g\right)$	$0.0$

4) Calculation:

a) Calculation for $∆{\mathrm{H}}_{\mathrm{r}\mathrm{x}\mathrm{n}}^0$:

$∆{\mathrm{H}}_{\mathrm{r}\mathrm{x}\mathrm{n}}=\sum {\mathrm{n}}_{\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{d}\mathrm{u}\mathrm{c}\mathrm{t}\mathrm{s}}\times ∆{\mathrm{H}}_{\mathrm{f},\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{d}\mathrm{u}\mathrm{c}\mathrm{t}\mathrm{s}}^0-\sum {\mathrm{n}}_{\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{s}}\times ∆{\mathrm{H}}_{\mathrm{f},\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{s}}^0$

$∆{\mathrm{H}}_{\mathrm{r}\mathrm{x}\mathrm{n}}=\left[\left(2\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\times ∆{\mathrm{H}}_{\mathrm{f},C_2{H}_2\left(g\right)}^0\right)+\left(2\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\times ∆{\mathrm{H}}_{\mathrm{f},CO \left(g\right)}^0\right)+(10\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\times ∆{\mathrm{H}}_{\mathrm{f},H_2\left(g\right)}^0)\right]-\left[\left(6\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\times ∆{\mathrm{H}}_{\mathrm{f},C{H}_4 \left(g\right)}^0\right)+\left(1\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\times ∆{\mathrm{H}}_{\mathrm{f},O_2\left(g\right)}^0\right)\right]$

$∆{\mathrm{H}}_{\mathrm{r}\mathrm{x}\mathrm{n}}=\left[\left(2\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\times 226.7\frac{\mathrm{k}\mathrm{J}}{\mathrm{m}\mathrm{o}\mathrm{l}}\right)+\left(2\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\times \left(-110.5\frac{\mathrm{k}\mathrm{J}}{\mathrm{m}\mathrm{o}\mathrm{l}}\right)\right)+(10\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\times 0.0\frac{\mathrm{k}\mathrm{J}}{\mathrm{m}\mathrm{o}\mathrm{l}})\right]-\left[\left(6\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\times \left(-74.8\frac{\mathrm{k}\mathrm{J}}{\mathrm{m}\mathrm{o}\mathrm{l}}\right)\right)+\left(1\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\times 0.0\frac{\mathrm{k}\mathrm{J}}{\mathrm{m}\mathrm{o}\mathrm{l}}\right)\right]$

$∆{\mathrm{H}}_{\mathrm{r}\mathrm{x}\mathrm{n}}=\left(232.4\right)-(-448.8)$

$∆{\mathrm{H}}_{\mathrm{r}\mathrm{x}\mathrm{n}}=681.2 kJ$

$∆H_{rxn}$ for the production of acetylene from the controlled combustion of methane is $681.2 kJ$.

b) The sign of calculated value $∆{\mathrm{H}}_{\mathrm{r}\mathrm{x}\mathrm{n}}$ is positive. This indicates that the reaction is endothermic.

Conclusion:

Based on the values of $∆H_f^0,$ the value of $∆{\mathrm{H}}_{\mathrm{r}\mathrm{x}\mathrm{n}}$ for the production of acetylene from controlled combustion of methane is calculated, and the reaction is endothermic.