$\mathrm{Q}$ 2. In a vacuum chamber of $0.01 \mathrm{~atm}$, the air is heated to $3000 \mathrm{~K}$. Determine convertion ratio of NO at chemical equilibrium state?
$$
\begin{array}{l}
\begin{array}{|l|}
\text { Air at } 0.01 \mathrm{~atm}, 3000 \mathrm{~K} \
\mathrm{O}_{2}+3.76 \mathrm{~N}_{2} \text { à } \mathrm{xNO}+(1-\mathrm{x} / 2) \mathrm{O}_{2}+ \
(3.76-\mathrm{x} / 2) \mathrm{N}_{2} \
\hline
\end{array} \
\mathrm{x}=\text { ? } \
\end{array}
$$

Question

Accepted Answer

∻Solution∻ ‖ 1 ⋮ **Identify the reaction**: The given reaction is the formation of NO from O$_2$ and N$_2$ in air at 0.01 atm and 3000 K. The reaction can be written as: $$ \mathrm{O}_{2} + 3.76 \mathrm{~N}_{2} \rightarrow \mathrm{xNO} + (1 - \frac{\mathrm{x}}{2}) \mathrm{O}_{2} + (3.76 - \frac{\mathrm{x}}{2}) \mathrm{N}_{2} $$ ‖ ‖ 2 ⋮ **Determine the equilibrium constant (K)**: At high temperatures, the equilibrium constant for the formation of NO can be approximated using the van't Hoff equation. For simplicity, we assume the equilibrium constant $K$ is known or can be found in tables for the given temperature (3000 K). ‖ ‖ 3 ⋮ **Set up the equilibrium expression**: The equilibrium constant expression for the reaction is: $$ K = \frac{[\mathrm{NO}]^2}{[\mathrm{O}_2][\mathrm{N}_2]^3.76} $$ Given the partial pressures at equilibrium, we can express the concentrations in terms of $x$: $$ [\mathrm{NO}] = \frac{x}{V}, \quad [\mathrm{O}_2] = \frac{1 - \frac{x}{2}}{V}, \quad [\mathrm{N}_2] = \frac{3.76 - \frac{x}{2}}{V} $$ where $V$ is the volume of the chamber. ‖ ‖ 4 ⋮ **Solve for x**: Substitute these expressions into the equilibrium constant equation and solve for $x$: $$ K = \frac{\left(\frac{x}{V}\right)^2}{\left(\frac{1 - \frac{x}{2}}{V}\right)\left(\frac{3.76 - \frac{x}{2}}{V}\right)^{3.76}} $$ Simplify and solve for $x$: $$ K = \frac{x^2}{(1 - \frac{x}{2})(3.76 - \frac{x}{2})^{3.76}} $$ This equation can be solved numerically to find the value of $x$. ‖ ∻Answer∻ ⚹ The conversion ratio of NO at chemical equilibrium state is determined by solving the equilibrium constant expression for $x$. ⚹ ∻Key Concept∻ ⚹ The equilibrium constant expression relates the concentrations of reactants and products at equilibrium. ⚹ ∻Explanation∻ ⚹ By setting up the equilibrium constant expression and solving for the unknown $x$, we can determine the conversion ratio of NO in the given conditions. ⚹◊What is the expression for the equilibrium constant ($K_{p}$) of the reaction given in the image?⍭ Generate me a similar question◊

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