The equilibrium constant for the reaction: 3 ⇌ is 4.0 at T K. If the equilibrium concentration of is — Chemical Equilibrium Chemistry Question

💡 Solution & Explanation

Step 1 - State the chemical equation and define the equilibrium constant expression ($K_c$) The balanced chemical equation represents the trimerization of gaseous acetylene (\ce{C2H2}) into benzene (\ce{C6H6}): \[\ce{3C2H2(g) <=> C6H6(g)}\] According to the law of chemical equilibrium, the concentration-based equilibrium constant ($K_c$) is written as the ratio of the equilibrium concentration of the product to that of the reactant, with each concentration term raised to the power of its stoichiometric coefficient: \[K_c = \frac{[\ce{C6H6}]}{[\ce{C2H2}]^3}\] Step 2 - Substitute the given values into the formula We are given the following values at temperature $T\text{ K}$: * Equilibrium constant, $K_c = 4.0$ * Equilibrium concentration of acetylene, $[\ce{C2H2}] = 0.5\text{ M}$ Substituting these values into our equilibrium constant expression: \[4.0 = \frac{[\ce{C6H6}]}{(0.5\text{ M})^3}\] Step 3 - Calculate the equilibrium concentration of benzene ($[\ce{C6H6}]$) First, let us calculate the cube of the concentration of acetylene: \[(0.5\text{ M})^3 = 0.5 \times 0.5 \times 0.5\text{ M}^3 = 0.125\text{ M}^3\] Now, substitute this value back into the equation to isolate the concentration of benzene: \[4.0 = \frac{[\ce{C6H6}]}{0.125\text{ M}^3}\] \[[\ce{C6H6}] = 4.0 \times 0.125\text{ M}\] \[[\ce{C6H6}] = \boxed{0.5\text{ M}}\] Thus, the equilibrium concentration of benzene is $0.5\text{ M}$. Step 4 - Evaluate the options * **Option (A) $0.5\text{ M}$**: Correct. As calculated above, the concentration of benzene at equilibrium is exactly $0.5\text{ M}$. * **Option (B) $1.5\text{ M}$**: Incorrect. This value corresponds to a common mistake where the reactant concentration is multiplied by its stoichiometric coefficient ($3 \times 0.5\text{ M} = 1.5\text{ M}$), which does not represent the correct chemical equilibrium relationship. * **Option (C) $5 \times 10^{-2}\text{ M}$**: Incorrect. This value represents an arithmetic error. * **Option (D) $0.25\text{ M}$**: Incorrect. This value represents a calculation error, such as squaring $0.5$ instead of cubing it.