| Consider the reaction \[{{N}_{2}}(g)+3{{H}_{2}}(g)\xrightarrow{{}}2N{{H}_{3}}(g)\] |
| The equality relationship between \[\frac{d[N{{H}_{3}}]}{dt}\] and \[-\frac{d[{{H}_{2}}]}{dt}\] is: [AIPMT (S) 2006] |
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 :
| [b] 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 |
| \[-\frac{d[{{N}_{2}}]}{dt}=-\frac{1}{3}\,\frac{d\,[{{H}_{2}}]}{dt}\] |
| \[=+\frac{1}{2}\,\frac{d\,[N{{H}_{3}}]}{dt}\] |
| \[or+\frac{d\,[N{{H}_{3}}]}{dt}=-\frac{2}{3}\,\frac{d\,[{{H}_{2}}]}{dt}\] |
| \[or-\frac{2d\,[{{N}_{2}}]}{dt}\] |
You need to login to perform this action.
You will be redirected in
3 sec
