Question

Consider the reaction:

${\mathrm{N}}_2{\mathrm{O}}_4\left(\mathrm{g}\right)\rightleftharpoons 2{\mathrm{NO}}_2\left(\mathrm{g}\right)$

The temperature at which $K_c=20.4$ and $K_p=600.1$, is ___________K.

Answer 1

• It is given that in reaction: ${\mathrm{N}}_2{\mathrm{O}}_4\left(\mathrm{g}\right)\rightleftharpoons 2{\mathrm{NO}}_2\left(\mathrm{g}\right)$ $K_c=20.4$ and $K_p=600.1$ .
• We know that for reactions at equilibrium: $K_p=K_c{\left(RT\right)}^{∆n}$ where $K_p$ is equilibrium constant of pressure, $K_c$ is the equilibrium constant of concentration, $R$ is gas constant, $T$ is the temperature of the reaction, and $∆n$is the difference in the number of moles of product and reactant.
• On solving the equation we get:

$$\begin{gathered} 600.1=20.4{\left(0.0831\times T\right)}^1 \\ \frac{600.1}{20.4}=0.0831\times T \\ T=354K \end{gathered}$$

• Therefore, the temperature of the given reaction is $354K$.