MCQ
$4.5$ moles each of hydrogen and iodine heated in a sealed ten litre vessel. At equilibrium, $3$ moles of $HI$ were found. The equilibrium constant for ${H_2}_{(g)}+ {I_2}_{(g)}$ $\rightleftharpoons$ $2HI_{(g)}$ is
  • $1$
  • B
    $10$
  • C
    $5$
  • D
    $0.33$

Answer

Correct option: A.
$1$
(a)                   ${H_2}\; + \;{I_2}$ 

(a)                    ${N_2} + 3{H_2}$ $ \rightleftharpoons $ $2N{H_3}$

Initial conc.          $1$             $3$               $0$

at equilibrium       $1-0.81$     $3-2.43$       $1.62$

                              $0.19$       $0.57$

No. of moles of ${N_2} = \frac{{28}}{{28}} = 1$ $mole$

No. of moles of ${H_2} = \frac{6}{2} = 3$ $mole$

No. of moles of $N{H_3} = \frac{{27.54}}{{17}} = 1.62$ $mole$

${K_c} = \frac{{{{[N{H_3}]}^2}}}{{[{N_2}]\,\,{{[{H_2}]}^3}}} = \frac{{{{[1.62]}^2}}}{{[0.19]\,\,{{[0.57]}^3}}}$$=75$

$2HI$

Initial conc.        $4.5$         $4.5$        $0$

                            $x$           $x$          $2x$

from question $2x = 3$

$x = \frac{3}{2} = 1.5$

So conc. at eqm. $4.5 - 1.5$ of ${H_2}$

$ = 4.5 - 1.5$ of ${I_2}$ and $3$ of $HI$

$K = \frac{{{{[HI]}^2}}}{{[{I_2}]\,\,[{H_2}]}} = \frac{{3 \times 3}}{{3 \times 3}} = 1$.

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