Question

At 550 K, the $K_c$ for the following reaction is ${10}^{4}mo{l}^{-1}L:X\left(g\right)+Y\left(g\right)\rightleftharpoons Z\left(g\right)$. At equilibrium, it was observed that
$\left[X\right]=\frac{1}{2}\left[Y\right]=\frac{1}{2}\left[Z\right]$.
What is the value of [Z] $\left(inmol{L}^{-1}\right)$ at equilibrium?

• A. $2\times {10}^{-4}$
• B. ${10}^{-4}$
• C. $2\times {10}^4$
• D. ${10}^4$

Answer 1

The correct option is A $2\times {10}^{-4}$

For the equilibrium

$X+Y\to Z$

$K_C=\frac{\left[Z\right]}{\left[X\right]\left[Y\right]}$

${10}^4=\frac{\left[Z\right]}{1/2\left[Z\right]\left[Z\right]}$ [since [X] = 1/2[Y]=1/2[Z]]

$=\frac{[1}{1/2\left[Z\right]}=\frac{2}{\left[Z\right]}$

$\left[Z\right]=\frac{2}{{10}^4}=2\times {10}^{-4}$