A) \[\frac{d\,[N{{H}_{3}}]}{dt}=-\frac{1}{3}\,\frac{d\,[{{H}_{2}}]}{dt}\]
B) \[+\frac{d\,[N{{H}_{3}}]}{dt}=-\frac{2}{3}\,\frac{d\,[{{H}_{2}}]}{dt}\]
C) \[+\frac{d\,[N{{H}_{3}}]}{dt}=-\frac{3}{2}\,\frac{d\,[{{H}_{2}}]}{dt}\]
D) \[\frac{d\,[N{{H}_{3}}]}{dt}=-\,\frac{d\,[{{H}_{2}}]}{dt}\]
Correct Answer: B
Solution :
For the reaction, \[{{N}_{2}}(g)+3{{H}_{2}}(g)\xrightarrow[{}]{{}}2N{{H}_{3}}(g)\] The rate of reaction w.r.t. \[{{N}_{2}}=-\frac{d\,[{{N}_{2}}]}{dt}\] The rate of reaction w.r.t \[{{H}_{2}}=-\frac{1}{3}\,\frac{d\,[{{H}_{2}}]}{dt}\] The rate of reaction w.r.t \[N{{H}_{3}}=+\frac{1}{2}\,\frac{d\,[N{{H}_{3}}]}{dt}\] Hence, at a fixed time \[-\frac{d[{{N}_{2}}]}{dt}=-\frac{1}{3}\,\frac{d\,[{{H}_{2}}]}{dt}\] \[=+\frac{1}{2}\,\frac{d\,[N{{H}_{3}}]}{dt}\] \[or+\frac{d\,[N{{H}_{3}}]}{dt}=-\frac{2}{3}\,\frac{d\,[{{H}_{2}}]}{dt}\] \[or-\frac{2d\,[{{N}_{2}}]}{dt}\]
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