Chapter 9, Problem 9.124QA

Interpretation Introduction

To find:

a) Whether the overall reaction $N_{2\left(g\right)}+2 O_{2\left(g\right)}\to 2N{O}_{2\left(g\right)}$ is exothermic or endothermic

b) $∆H_{comb}^0$ for the overall reaction $N_{2\left(g\right)}+2 O_{2\left(g\right)}\to 2N{O}_{2\left(g\right)}$

Answer to Problem 9.124QA

Solution:

a) Reaction $N_{2\left(g\right)}+2 O_{2\left(g\right)}\to 2N{O}_{2\left(g\right)}$ is endothermic.

b) $∆H_{comb}^0$ for the reaction $N_{2\left(g\right)}+2 O_{2\left(g\right)}\to 2N{O}_{2\left(g\right)}$ is $+68 kJ.$

Explanation of Solution

1) Concept:

We are given $∆H_{comb}^0$ values for the two reactions and asked to find the $∆H{°}_{comb}$ for the overall reaction. We can use Hess’s law to get the heat of combustion of the desired equation. Hess’s law of constant heat of summation tells us that the sum of two or more reactions is equal to the sum of the $∆H_{comb}^0$ values of constituent reactions. From the $∆H_{comb}^0$ values of constituent reactions, we can calculate the $∆H_{comb}^0$ of the overall reaction.

2) Given:

i) $N_{2\left(g\right)}+ O_{2\left(g\right)}\to 2N{O}_{\left(g\right)} ∆H_{comb}^0= +180 kJ$

ii) $2 {NO}_{\left(g\right)}+ O_{2\left(g\right)} \to {2 NO}_{2\left(g\right)} ∆H_{comb}^0= -112 kJ$

iii) $N_{2\left(g\right)}+2 O_{2\left(g\right)}\to 2N{O}_{2\left(g\right)} ∆H_{rxn}^0=x kJ$

3) Calculations:

Overall combustion reaction of nitrogen to form nitrogen dioxide is given as

$N_{2\left(g\right)}+2 O_{2\left(g\right)}\to 2N{O}_{2\left(g\right) }∆H_{rxn}^0=x kJ$ Overall reaction

Given equations are:

i) $N_{2\left(g\right)}+ O_{2\left(g\right)}\to 2N{O}_{\left(g\right)} ∆H_{comb}^0= +180 kJ$ Equation 1

ii) $2 {NO}_{\left(g\right)}+ O_{2\left(g\right)} \to {2 NO}_{2\left(g\right)} ∆H_{comb}^0= -112 kJ$ Equation 2

In order to get the overall reaction, we need to combine or add equations 1 and 2. When you add two equations, the $∆H°$ value of each reaction also gets added.

$N_{2\left(g\right)}+ O_{2\left(g\right)}\to 2N{O}_{\left(g\right)} ∆H_{comb}^0= +180 kJ$

$+$

$2 {NO}_{\left(g\right)}+ O_{2\left(g\right)} \to {2 NO}_{2\left(g\right)} ∆H_{comb}^0= -112 kJ$

$N_{2\left(g\right)}+2 O_{2\left(g\right)}\to 2N{O}_{2\left(g\right)} ∆H_{rxn}^0= 180+(-112)=+68 kJ$

So, $+68 kJ$ amount of energy is needed for combustion of $N_2$ to produce $N{O}_2$. As the value is positive, the reaction is endothermic.

Conclusion:

From two or more thermochemical equations, we can get the $∆H°$ for the overall reaction by manipulating the given equations.