MCQ
At a certain temperature the equilibrium constant $K_c$ is $0.25$ for the reaction

${A_2}\left( g \right) + {B_2}\left( g \right) \rightleftharpoons {C_2}\left( g \right) + {D_2}\left( g \right)$

If we take $1\  mole$ of each of the four gases in a $10\  litre$ container, what would be equilibrium concentration of $A_2(g)$?

  • A
    $0.331\  M$
  • B
    $0.033\  M$
  • $0.133\  M$
  • D
    $1.33\  M$

Answer

Correct option: C.
$0.133\  M$
c
$Q_{c}=\frac{1 \times 1}{1 \times 1}=1$

$\therefore \mathrm{Q}_{\mathrm{c}}>\mathrm{K}_{\mathrm{c}}$ so reaction will proceed in backward direction

$\mathrm{A}_{2}(\mathrm{g})+\mathrm{B}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{C}_{2}(\mathrm{g})+\mathrm{D}_{2}(\mathrm{g})$

conc. eqm. $\frac{1+x}{10} \quad \frac{1+x}{10} \quad \frac{1-x}{10} \quad \frac{1-x}{10}$

$0.25=\frac{\left(\frac{1-\mathrm{x}}{10}\right)^{2}}{\left(\frac{1+\mathrm{x}}{10}\right)^{2}} \Rightarrow \mathrm{x}=0.333$

$\left[\mathrm{A}_{2}(\mathrm{g})\right]=\frac{1+\mathrm{x}}{10}=\frac{1.333}{10}=0.133$

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