Chapter 17, Problem 17.106P

(a)

Interpretation Introduction

Interpretation:

${\text{K}}_{\text{p}}$ for the given reaction $\text{2NO}\left(\text{g}\right){\text{ + O}}_{\text{2}}\left(\text{g}\right)\underset{}{\rightleftharpoons }{\text{ 2NO}}_{\text{2}}\left(\text{g}\right)$ has to be calculated.

Concept Introduction:

The relation between ${\text{K}}_{\text{p}}$ and ${\text{K}}_{\text{c}}$ is given by the following equation.

${\text{K}}_{\text{p}}{\text{ = K}}_{\text{c}}{\text{(RT)}}^{\Delta {\text{n}}_{\text{gas}}}\boxed{\begin{array}{l}{\text{K}}_{\text{p}}\text{ = }Equilibriumcons\tan tintermsofpartialpressure\\ {\text{K}}_{\text{c}}\text{ = }Equilibriumcons\tan tintermsofconcentration\\ \Delta {\text{n}}_{\text{gas}}\text{ = moles of gaseous product }-\text{ moles of gaseous reactant}\end{array}}$

Only moles of gaseous products and reactants are used for calculating $\Delta {\text{n}}_{\text{gas}}.$

(b)

Interpretation Introduction

Interpretation:

Standard heat of formation for the given reaction , $\text{2NO}\left(\text{g}\right){\text{ + O}}_{\text{2}}\left(\text{g}\right)\underset{}{\rightleftharpoons }{\text{ 2NO}}_{\text{2}}\left(\text{g}\right)$ has to be calculated.

Concept Introduction:

The value of standard heat of formation ${\text{ΔH}}^{\text{ο}}$ of the given reaction is calculated by the formula,

${\text{ΔH}}^{\text{ο}}\text{=}{{\displaystyle \sum {\text{n}}_{\text{p}}{\text{ΔH}}_{\text{f}}^{\text{ο}}}}_{\left(\text{products}\right)}-{{\displaystyle \sum {\text{n}}_{\text{r}}{\text{ΔH}}_{\text{f}}^{\text{ο}}}}_{\left(\text{reactants}\right)}$

Where,

$\begin{array}{c}{\text{ΔH}}_{\text{f}}^{\text{ο}}{}_{\left(\text{reactants}\right)}\text{=}\text{the standard enthalpy of formation for the reactants}\\ {\text{ΔH}}_{\text{f}}^{\text{ο}}{}_{\left(\text{products}\right)}\text{=}\text{the standard enthalpy of formation for the products}\\ {\text{n}}_{\text{p}}\text{=}\text{number of products molecule}\\ {\text{n}}_{\text{r}}\text{=}\text{number of reactants molecule}\end{array}$

(c)

Interpretation Introduction

Interpretation:

Temperature at which $K_c=\text{ 6}\text{.4}\times {10}^9$ for the reaction $\text{2NO}\left(\text{g}\right){\text{ + O}}_{\text{2}}\left(\text{g}\right)\underset{}{\rightleftharpoons }{\text{ 2NO}}_{\text{2}}\left(\text{g}\right)$ has to be calculated.

Concept Introduction:

The van’t Hoff Equation: Effect of temperature on equilibrium constant can be shown as follows,

  $\begin{array}{c}\ln \frac{K_2}{K_1}=-\frac{\Delta H_{rxn}^o}{R}\left(\frac{1}{T_2}-\frac{1}{T_1}\right)\\ \\ where,\\ {\text{K}}_1{\text{ = Equilibrium constant at T}}_{\text{1}}\\ {\text{K}}_2{\text{ = Equilibrium constant at T}}_2\\ \Delta H_{rxn}^o=S\tan dardheatofformationforthegivenreaction\end{array}$