Chapter 9, Problem 9.72QA

Interpretation Introduction

To calculate:

a) $∆H_{rxn}^0$ for the conversion of diamond into graphite.

b) Whether conversion of diamond into graphite is exothermic or endothermic.

Answer to Problem 9.72QA

Solution:

a) $∆H_{rxn}^0$ for the conversion of diamond into graphite is $-1.9 kJ.$

b) Conversion of diamond into graphite is exothermic.

Explanation of Solution

1) Concept:

To calculate the value of $∆{\mathrm{H}}_{\mathrm{r}\mathrm{x}\mathrm{n}}^{\mathrm{o}}$ of the overall reaction, we can use Hess’s law. We can algebraically manipulate the two equations for which $∆{\mathrm{H}}_{\mathrm{r}\mathrm{x}\mathrm{n}}^{\mathrm{o}}$ values are known so that we can calculate the $∆{\mathrm{H}}_{\mathrm{r}\mathrm{x}\mathrm{n}}^{\mathrm{o}}$ of the overall reaction. Then, by applying Hess’s law, we can calculate the unknown value. And from  $∆H_{rxn,}^0$ we can decide whether the reaction is endothermic or exothermic.

2) Given:

i) $C_{(s,diamond)}+O_{2\left(g\right)} \to {CO}_{2\left(g\right)} ∆H_{rxn}^0= -395.4 kJ$

ii) $2 {CO}_{\left(g\right)}+ O_{2\left(g\right)} \to {2 CO}_{2\left(g\right)} ∆H_{rxn}^0= -566.0 kJ$

iii) $2 {CO}_{\left(g\right)}\to {C_{(s,graphite)}+ CO}_{2\left(g\right) } ∆H_{rxn}^0= -172.5 kJ$

iv)$C_{(s,diamond)} \to C_{(s,graphite)} ∆H_{rxn}^0= ?$

3) Calculations:

Conversion reaction of diamond to graphite is shown as

$C_{(s,diamond)} \to C_{(s,graphite)} ∆H_{rxn}^0= ?$

Given equations are

Equation 1 $C_{(s,diamond)}+O_{2\left(g\right)} \to {CO}_{2\left(g\right)} ∆H_{rxn}^0= -395.4 kJ$

Equation 2 $2 {CO}_{\left(g\right)}+ O_{2\left(g\right)} \to {2 CO}_{2\left(g\right)} ∆H_{rxn}^0= -566.0 kJ$

Equation 3 $2 {CO}_{\left(g\right)}\to {C_{(s,graphite)}+ CO}_{2\left(g\right) }∆H_{rxn}^0= -172.5 kJ$

Now combine equation 1, 2, and 3 to get the overall equation. We have to reverse the equation 2 in order to cancel ${ O}_2$,$2CO,$ and $2C{O}_2$ from the reaction.

Adding the equations 1, 2, and 3, we get

$C_{(s,diamond)}+O_{2\left(g\right)} \to {CO}_{2\left(g\right)} ∆H_{rxn}^0= -395.4 kJ$

${2 CO}_{2\left(g\right)}\to 2 {CO}_{\left(g\right)}+ O_{2\left(g\right)} ∆H_{rxn}^0= +566.0 kJ$

$2 {CO}_{\left(g\right)}\to {C_{(s,graphite)}+ CO}_{2\left(g\right) } ∆H_{rxn}^0= -172.5 kJ$

$C_{(s,diamond)} \to C_{(s,graphite)} ∆H_{rxn}^0= \left(-395.4\right)+ 566.0+ \left(-172.5\right)=-1.9 kJ$

So $-1.9 kJ$ amount of energy is needed to convert diamond into graphite. As the value is negative, the reaction is exothermic, which means there is evolution of heat taking place as the reaction proceeds.

Conclusion:

We have calculated the enthalpy change of the conversion of diamond to graphite. The value of heat of reaction is negative, so the reaction is exothermic.