Q17.74P - Chemistry: Molecular Nature Of Matter And Change

Question

The formation of methanol is important to the processing of new fuels. At $\mathbf{298}\mathbf{ }\mathit{K}\mathbf{,}{\mathit{K}}_{\mathbf{P}}\mathbf{=}\mathbf{2}\mathbf{.}\mathbf{25}\mathbf{\times }{\mathbf{10}}^{\mathbf{4}}$ for the reaction

$\mathit{C}\mathit{O}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{+}\mathbf{2}{\mathit{H}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{ }\mathbf{\rightleftharpoons }\mathbf{ }\mathit{C}{\mathit{H}}_{\mathbf{3}}\mathit{O}\mathit{H}\mathbf{\left(}\mathbf{I}\mathbf{\right)}$

If$\mathbf{∆}{\mathit{H}}_{\mathbf{ran}}\mathbf{=}\mathbf{-}\mathbf{128}\mathbf{ }\mathit{k}\mathit{J}\mathbf{/}\mathit{m}\mathit{o}\mathit{l}\mathit{C}{\mathit{H}}_{\mathbf{3}}\mathit{O}\mathit{H}$, calculate ${\mathit{K}}_{\mathbf{p}}$ at ${\mathbf{0}}^{\mathbf{°}}\mathit{C}$.

Step-by-Step Solution

Answer

Answer

The value of $K_P$ is $2.55\times {10}^6$.

Step 1: Definition of Concept

Reactions: A balanced chemical reaction equation shows the mole relationships of reactants and products, while a chemical reaction equation gives the reactants and products. The amount of energy involved in the reaction is frequently stated. Reaction stoichiometry is the study of the quantitative aspects of chemical reactions.

Step 2: Calculate K P

Considering the given information: 

Given isotopic equilibrium

$$\begin{gathered} CO\left(g\right)+2H_2\left(g\right) \rightleftharpoons C{H}_{3}OH\left(l\right) \\ ∆H{°}_{rxm}=-128 kJ/mol \\ {K}_P=2.25\times {10}^4 at T_1 = 298 K \\ {K}_P=? at T_2=0°C \end{gathered}$$

We'll start by converting the temperature value from $°C$ to K:

$$\begin{gathered} T=0°C+273.15 \\ T=273.15 K \end{gathered}$$

We will use Van't Hoff equation to calculate $K_P$ at $T_2=0°C$:

$$\begin{gathered} In\frac{K_2}{K_1}=-\frac{∆H_{rxm}^{°}}{R}\left[\frac{1}{T_2}-\frac{1}{T_1}\right] \\ In\frac{K_P}{2.25\times {10}^4}=-\frac{-128\times {10}^3 J/mol}{8.314 J/mol\times K}\left[\frac{1}{273.15}-\frac{1}{298 K}\right] \\ K_P=2.55\times {10}^6 \end{gathered}$$

Therefore, the required value is $2.55\times {10}^6$.