Question

The rate of reaction is given by the rate equation$\text{ rate = k}{{\left[ \text{NO} \right]}^{\text{2}}}\left[ \text{C}{{\text{l}}_{\text{2}}} \right]\text{ }$. The value of the rate constant can be increased by:
$\text{ 2NO + C}{{\text{l}}_{\text{2}}}\text{ }\to \text{ 2NOCl }$
A) Increasing the temperature
B) Increasing the concentration of [$\text{ NO }$
C) Increasing the concentration of $\text{C}{{\text{l}}_{\text{2}}}$
D) Doing all of the above

Answer 1

Hint: The rate law expressed the relation between the rate of the reaction and the concentration of the reactant. For $\text{ A}\to \text{ B }$ ,
$\text{ rate = k }\left[ \text{A} \right]\text{ }$
Where k is the proportionality constant. The rate of reaction is affected by the concentration of the reactant. The relation of the rate constant with the activation energy is expressed as follow,
$\text{ K = A }{{{e}}^{\dfrac{{-Ea}}{{RT}}}}{ }$
Where k is the rate of the reaction, A is the pre-exponential factor, Ea is activation energy or the energy barrier, T is the temperature and R is gas constant.

Complete step by step solution:
The rate of reaction is the study of the rate of the chemical reaction.
For $\text{ 2NO + C}{{\text{l}}_{\text{2}}}\text{ }\to \text{ 2NOCl }$reaction, the Rate constant is given as $\text{ rate = k}{{\left[ \text{NO} \right]}^{\text{2}}}\left[ \text{C}{{\text{l}}_{\text{2}}} \right]\text{ }$ .The rate constant is independent on the concentration of the reactant. Thus increase in the concentration of $\text{ NO }$ or $\text{C}{{\text{l}}_{\text{2}}}$ do not have an effect on the rate constant.
Temperature is one of the factors which affect the rate of reaction. According to the kinetic theory of gases, the molecules moving with a certain velocity collide with each other such that the one gas particle transfers its energy to the other. This collision of reactant or gas particles results in the product.
The molecular velocity of any gas is proportional to the absolute temperature. The velocity of gas rises with temperature. This increases the fraction of molecules that have high velocities and high energy. These particles have enough energy to cross the energy barrier and result in the product.
The effect of temperature on the rate of reaction is well explained by the Arrhenius equation. It has established a relation between the rate of reaction and the temperature of the system. The expression is as shown below,
$K = A {e^{\dfrac{-Ea}{RT}}}$
Where k is the rate constant, A is the pre-exponential factor, Ea is activation energy or the energy barrier, T is the temperature and R is the gas constant.
The activation energy is the minimum amount of energy required by reactant molecules such that the collision of reactant results in the product. From the Arrhenius equation, it is clear that the rate of reaction K is directly related to the temperature.
It is found that when the temperature of the reaction is increased by the $\text{ 1}{{\text{0}}^{\text{0}}}\text{C }$ rate of reaction gets doubled.
Thus rate constant for $\text{ 2NO + C}{{\text{l}}_{\text{2}}}\text{ }\to \text{ 2NOCl }$ increases with increasing the temperature.

Hence, (A) is the correct option.

Note: Note that, rate constant k is a proportionality factor. It does affect the rate of reaction but it is not a rate of reaction. The temperature has a remarkable effect on the rate constant thus on the rate of reaction. Apart from temperature, the rate constant depends on the catalyst. As it lowers the activation energy and favours the reaction.