Question

The equilibrium constant, \(K_C\) for \(3C_2H_2(g) \rightleftharpoons C_6H_6(g)\) is 4 L\(^2\)mol\(^{-2}\). If the equilibrium concentration of benzene is 0.5 mol/L, then what is the value of concentration of ethylene?

• A. 0.05 mol/L
• B. 0.5 mol/L
• C. 0.25 mol/L
• D. 0.025 mol/L

Hint:

Remember to cube the concentration of the reactant when using equilibrium constant expressions for reactions involving stoichiometric coefficients.

Answer 1

The Correct Option is B

The balanced equation is: \[ 3C_2H_2(g) \rightleftharpoons C_6H_6(g) \] Let the concentration of ethylene \(C_2H_2\) at equilibrium be \(x\) mol/L, and the concentration of benzene \(C_6H_6\) is given as 0.5 mol/L. Using the equilibrium constant expression: \[ K_C = \frac{[C_6H_6]}{[C_2H_2]^3} \] Substitute the given values: \[ 4 = \frac{0.5}{x^3} \] Now, solve for \(x\): \[ x^3 = \frac{0.5}{4} = 0.125 \] \[ x = \sqrt[3]{0.125} = 0.5 \] Thus, the concentration of ethylene is 0.5 mol/L.