Question

For a reaction $AB\left(g\right)\iff A\left(g\right)+B\left(g\right)$, $AB$ is 33% dissociated at a total pressure of $P$, then:

• A. $P=K_P$
• B. $P=3K_P$
• C. $P=4K_P$
• D. $P=8K_P$

Answer 1

Answer: (D)

$P=8K_P$

$AB\rightleftharpoons A+B$
No. of mole initially, $AB-1,A-0,B-0$
No. of moles at equilibrium, $AB-(1-\frac{1}{3}),A-\frac{1}{3},B-\frac{1}{3}$
Total no. of moles$=\frac{2}{3}+\frac{1}{3}+\frac{1}{3}=\frac{4}{3}$
$K_P=\frac{P_A\times P_B}{P_{A}B}$
$K_P=\frac{\left(\frac{1}{3}/\frac{4}{3}\right)P\times \left(\frac{1}{3}/\frac{4}{3}\right)P}{\left(\left(\frac{2}{3}\right)/\left(\frac{4}{3}\right)\right)P}$
$K_P=\frac{1}{8}P$
$\therefore P=8K_P$