Chapter 17, Problem 17.76P

Interpretation Introduction

Interpretation:

The given reaction is

  ${\text{D}}_{\text{2}}{\text{(g) + H}}_{\text{2}}\text{(g) }\rightleftharpoons \text{2 DH(g)}{\text{K}}_{\text{p}}\text{ = 1}\text{.80 at 298 K}$.

If ${\text{ΔH}}_{\text{r×n}}^{\text{°}}\text{ is 0}\text{.32 kJ/mol DH}$, ${\text{K}}_{\text{p}}\text{ at 500 K}$ has to be calculated.

Concept Introduction:

Van’t Hoff equation gives the effect of equilibrium constant by change in temperature.  The van’t Hoff equation is given as

  $\begin{array}{l}\text{ln}\frac{{\text{K}}_{\text{2}}}{{\text{K}}_{\text{1}}}\text{ = -}\frac{{\text{ΔH}}_{\text{r×n}}^{\text{°}}}{\text{R}}\left(\frac{\text{1}}{{\text{T}}_{\text{2}}}\text{-}\frac{\text{1}}{{\text{T}}_{\text{1}}}\right)\\ \\ \text{where, K = Rate constant}\\ \\ \text{R = Universal gas constant = 8}\text{.314 J/mol}\text{.K}\\ \\ \text{T = Temperature}\\ \\ {\text{ΔH}}_{\text{r×n}}^{\text{°}}\text{= enthalpy of the reaction}\end{array}$