Chemical Kinetics - Result Question 7
####7. The rate of the reaction $2 N_2 O_5 \to 4 NO_2+O_2$ can be written in three ways :
[2011 M]
$\frac{-d[N_2 O_5]}{dt}=k[N_2 O_5]$
$\frac{d[NO_2]}{dt}=k^{\prime}[N_2 O_5]$
$\frac{d[O_2]}{dt}=k^{\prime \prime}[N_2 O_5]$
The relationship between $k$ and $k^{\prime}$ and between $k$ and $k^{\prime \prime}$ are :
(a) $k^{\prime}=2 k ; k^{\prime}=k$
(b) $k^{\prime}=2 k ; k^{\prime \prime}=k / 2$
(c) $k^{\prime}=2 k ; k^{\prime \prime}=2 k$
(d) $k^{\prime}=k ; k^{\prime \prime}=k$
Show Answer
Solution:
- (b) Rate of disappearance of reactants = Rate of appearance of products
$-\frac{1}{2} \frac{d(N_2 O_5)}{d t}=\frac{1}{4} \frac{d(NO_2)}{d t}=\frac{d(O_2)}{d t}$
$\frac{1}{2} k(N_2 O_5)=\frac{1}{4} k^{\prime}(N_2 O_5)=k^{\prime \prime}(N_2 O_5)$
$\frac{k}{2}=\frac{k^{\prime}}{4}=k^{\prime \prime}$
$k^{\prime}=2 k, \quad k^{\prime \prime}=\frac{k}{2}$
