Questions: The equilibrium constant for the reaction: PCl5 ⇌ PCl3 + Cl2 is 0.0245 at 25°C. What molar concentration of PCl5 would be present at equilibrium if the concentrations of PCl3 and Cl2 were both 0.227 M?

The equilibrium constant for the reaction: PCl5 ⇌ PCl3 + Cl2 is 0.0245 at 25°C. What molar concentration of PCl5 would be present at equilibrium if the concentrations of PCl3 and Cl2 were both 0.227 M?
Transcript text: The equilibrium constant for the reaction: \[ \mathrm{PCl}_{5} \rightleftarrows \mathrm{PCl}_{3}+\mathrm{Cl}_{2} \] is 0.0245 at $25^{\circ} \mathrm{C}$. What molar concentration of $\mathrm{PCl}_{5}$ would be present at equilibrium if the concentrations of $\mathrm{PCl}_{3}$ and $\mathrm{Cl}_{2}$ were both 0.227 M ?
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Solution

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Solution Steps

Step 1: Write the Expression for the Equilibrium Constant

The equilibrium constant expression for the reaction is given by:

\[ K_c = \frac{[\mathrm{PCl}_3][\mathrm{Cl}_2]}{[\mathrm{PCl}_5]} \]

Step 2: Substitute Known Values into the Equilibrium Expression

Given that \( K_c = 0.0245 \), and the concentrations of \(\mathrm{PCl}_3\) and \(\mathrm{Cl}_2\) are both 0.227 M, substitute these values into the expression:

\[ 0.0245 = \frac{(0.227)(0.227)}{[\mathrm{PCl}_5]} \]

Step 3: Solve for the Concentration of \(\mathrm{PCl}_5\)

Rearrange the equation to solve for \([\mathrm{PCl}_5]\):

\[ [\mathrm{PCl}_5] = \frac{(0.227)(0.227)}{0.0245} \]

Calculate the value:

\[ [\mathrm{PCl}_5] = \frac{0.051529}{0.0245} \approx 2.103 \, \text{M} \]

Final Answer

\(\boxed{2.103 \, \text{M}}\)

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