JEE MAIN - Chemistry (2002 - No. 39)
The differential rate law for the reaction H2 + I2 $$\to$$ 2HI is
$$ - {{d\left[ {{H_2}} \right]} \over {dt}}$$ = $$ - {{d\left[ {{I_2}} \right]} \over {dt}}$$ = $$ - {{d\left[ {{HI}} \right]} \over {dt}}$$
$$ {{d\left[ {{H_2}} \right]} \over {dt}}$$ = $$ {{d\left[ {{I_2}} \right]} \over {dt}}$$ = $$ {{d\left[ {{HI}} \right]} \over {dt}}$$
$${1 \over 2}{{d\left[ {{H_2}} \right]} \over {dt}}$$ = $${1 \over 2}{{d\left[ {{I_2}} \right]} \over {dt}}$$ = $$ - {{d\left[ {{HI}} \right]} \over {dt}}$$
$$ - 2{{d\left[ {{H_2}} \right]} \over {dt}}$$ = $$ - 2{{d\left[ {{I_2}} \right]} \over {dt}}$$ = $${{d\left[ {{HI}} \right]} \over {dt}}$$
Explanation
rate of appearance of $$HI = {1 \over 2}{{d\left[ {HI} \right]} \over {dt}}$$
rate of formation of $${H_2} = {{ - d\left[ {{H_2}} \right]} \over {dt}}$$
rate of formation of $${I_2} = {{ - d\left[ {{I_2}} \right]} \over {dt}}$$
hence $${{ - d\left[ {{H_2}} \right]} \over {dt}} = - {{ - d\left[ {{I_2}} \right]} \over {dt}} = {1 \over 2}{{d\left[ {HI} \right]} \over {dt}}$$
or $$\,\,\,\,$$ $$ - {{2d\left[ {{H_2}} \right]} \over {dt}} = - {{2d\left[ {{I_2}} \right]} \over {dt}} = {{d\left[ {HI} \right]} \over {dt}}$$
rate of formation of $${H_2} = {{ - d\left[ {{H_2}} \right]} \over {dt}}$$
rate of formation of $${I_2} = {{ - d\left[ {{I_2}} \right]} \over {dt}}$$
hence $${{ - d\left[ {{H_2}} \right]} \over {dt}} = - {{ - d\left[ {{I_2}} \right]} \over {dt}} = {1 \over 2}{{d\left[ {HI} \right]} \over {dt}}$$
or $$\,\,\,\,$$ $$ - {{2d\left[ {{H_2}} \right]} \over {dt}} = - {{2d\left[ {{I_2}} \right]} \over {dt}} = {{d\left[ {HI} \right]} \over {dt}}$$
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