Question

The reaction $X_{\left(g\right)}+Y_{\left(g\right)}\rightleftharpoons 2Z_{\left(g\right)}$, 2 moles of X,1 mole of $Y$ and 1 mole of $Z$ are placed in a 10 lit vessel and allowed to reach equilibrium. If final concentration of $Z$ is 0.2 M. The value of $K_c$ is

• A. $\frac{4}{75}$
• B. $2$
• C. $\frac{16}{3}$
• D. Infinity

Answer 1

Answer: (C)

$\frac{16}{3}$

Given; $X+Y\to 2Z$

At initial $2$ $1$ $1$

At equilibrium $2-x$ $1-x$ $1+2x$

Now since equilibrium concentration of $Z$ is 0.2 then,

$\Rightarrow \frac{1+2x}{10}=0.2$

$\Rightarrow x=0.5$

We know

$K_c=\frac{[Z{]}^2}{\left[X\right]\left[Y\right]}=\frac{[1+2x{]}^2}{[2-x][1-x]}=\frac{[2{]}^2}{\left[1.5\right]\left[0.5\right]}$

$K_c=\frac{16}{3}$