Question

The equilibrium constant $K_p$ of the reaction
$X\left(g\right)\rightleftharpoons Y\left(g\right)+Z\left(g\right),$ when $X\left(g\right)$ decomposes to $50\%$ at 5 atm pressure is:

• A. 4.67
• B. 1.67
• C. 1.5
• D. 3.5

Answer 1

The correct option is B 1.67

We know,
$X\left(g\right)\rightleftharpoons Y\left(g\right)+Z\left(g\right)$
$100\text{Total pressure =P}$
$0.50.50.5$
So partial pressure of $X=p_X=\frac{0.5}{1.5}\times 5$
So partial pressure of $Y=p_Y=\frac{0.5}{1.5}\times 5$
So partial pressure of $Z=p_Z=\frac{0.5}{1.5}\times 5$


At equilibrium,
$K_p=\frac{p_Y\times p_z}{p-X}=\frac{(\frac{0.5}{1.5}\times 5)(\frac{0.5}{1.5}\times 5)}{\frac{0.5}{1.5}\times 5}=\frac{5}{3}=1.67atm$