First slide

Kinetics of chemical reactions

Question

In the reversible reaction
$2 N O_{2} ⇌ N_{2} O_{4}$

The rate of dis appearance of $N O_{2}$ is equal to

Moderate

A

$\frac{2 k_{1}}{k_{2}} {[N O_{2}]}^{2}$
B

$2 k_{1} {[N O_{2}]}^{2} - 2 k_{2} [N_{2} O_{4}]$
C

$2 k_{1} {[N O_{2}]}^{2} - k_{2} [N_{2} O_{4}]$
D

$(2 k_{1} - k_{2}) [N O_{2}]$

Solution

For the given reversible reaction,
$2 N O_{2} ⇌_{k_{2}}^{k_{1}} N_{2} O_{4}$

The rate of disapperane of ${NO}_{2}$ =?

Let the reaction be,

$2 N O_{2} ⇌_{k_{2}}^{k_{1}} N_{2} O_{4}$

For the forward reaction rate $(r_{f}) = - \frac{1}{2} \frac{d [N O_{2}]}{d t} = \frac{d [N_{2} O_{4}]}{d t} = K_{1} {[N O_{2}]}^{2}$

For backward reaction

Rate $= - \frac{d [N_{2} O_{4}]}{d t} = \frac{1}{2} \frac{d [N O_{2}]}{d t} = K_{2} [N_{2} O_{4}] .$

Rate of disappearance of $N O_{2} =$ (Rate of disappearance of $N O_{2} -$ Rate of appearance of $N O_{2}$ )

$= 2 K_{1} {[N O_{2}]}^{2} - 2 K_{2} [N_{2} O_{4}] .$

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