Answered

Consider the reaction.

$H_2 O(g)+Cl_2 O(g) \longleftrightarrow 2 HClO(g)$



At equilibrium, the concentrations of the different species are as follows:

$\begin{array}{l}

{\left[H_2 O\right]=0.077 M} \\

{\left[Cl_2 O\right]=0.077 M} \\

{[HClO]=0.023 M}

\end{array}$



What is the equilibrium constant for the reaction at this temperature?


A0.089
B3.9
C0.26
D11

Verified Answer :

  • The equilibrium constant expression for the reaction is defined as \(K_c = \frac{[\text{HClO}]^2}{[\text{H}_2\text{O}][\text{Cl}_2\text{O}]}\).
  • Substitute the given equilibrium concentrations: \(K_c = \frac{(0.023)^2}{(0.077)(0.077)}\).
  • Perform the calculation: \(K_c = \left(\frac{0.023}{0.077}\right)^2 \approx 0.089\).
  • The final answer is \(\boxed{0.089}\).

Explanation

  1. Setting up the Equilibrium Constant Expression

The chemical reaction is given by \(\text{H}_2\text{O}(g) + \text{Cl}_2\text{O}(g) \longleftrightarrow 2\text{HClO}(g)\). The equilibrium constant \(K_c\) for a balanced chemical equation \(aA + bB \longleftrightarrow cC + dD\) is expressed as:
\[K_c = \frac{[\text{C}]^c [\text{D}]^d}{[\text{A}]^a [\text{B}]^b}\]
For our reaction, the equilibrium constant expression is:
\[K_c = \frac{[\text{HClO}]^2}{[\text{H}_2\text{O}][\text{Cl}_2\text{O}]}\]
We are given the following equilibrium concentrations:
\([\text{H}_2\text{O}] = 0.077 \text{ M}\)
\([\text{Cl}_2\text{O}] = 0.077 \text{ M}\)
\([\text{HClO}] = 0.023 \text{ M}\)

  1. Calculation and Final Result

Substitute the given concentrations into the expression for \(K_c\):
\[K_c = \frac{(0.023)^2}{(0.077)(0.077)}\]
This can be simplified to:
\[K_c = \left(\frac{0.023}{0.077}\right)^2\]
Calculating this, we get:
\[K_c \approx (0.2987)^2 \approx 0.0892\]
Rounding to the appropriate number of significant figures, the equilibrium constant is \(0.089\). This corresponds to option (a).

Examples

Equilibrium constants are crucial in industrial chemistry. For instance, in the production of fertilizers or fuels, understanding the equilibrium constant helps chemical engineers optimize conditions—such as temperature or pressure—to maximize the yield of the desired product. If a reaction has a small \(K_c\), it indicates that at equilibrium, the concentrations of reactants are higher than those of products. By adjusting reaction conditions, engineers can shift the equilibrium to favor product formation, making chemical processes more efficient and economically viable.

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