Question

The temperature coefficient of most of the reactions lies between:
A. $2$and $3$
B. $1$ and $2$
C. $2$and $4$
D. $3$and $4$

Answer 1

Temperature coefficient is the factor by which the rate constant of a reaction increases (just double) with increase in temperature by ${10^0}C$. Temperature coefficient is the ratio of rate constants of a reaction at temperature $T$and rate constant when temperature is increased by a factor of ${10^0}C$.

Complete step by step answer:
Temperature coefficient is the ratio of rate constant of a reaction at a temperature and rate constant of the reaction when the temperature increases by ${10^0}C$.
Let suppose a reaction:
$A + B \to C$
Let $K$ be the rate constant of the above reaction at temperature $T$
On increasing the temperature by ${10^0}C$,
The new temperature will be $T + {10^0}$
Let rate constant at new temperature of the above reaction be ${K_{(T + {{10}^0})}}$
So, the temperature coefficient of the reaction will be:
Temperature coefficient : $\dfrac{K}{{{K_{(T + {{10}^0})}}}}$
Temperature coefficient of the most of the reaction lies between $2$and $3$more precisely.

Hence, option A is correct.

Additional Information:
In nuclear engineering, the temperature coefficient of reactivity is defined as the change in reactivity (that causes a change in power), when change in temperature of the reactor components takes place. This is defined as:
${\alpha _T} = \dfrac{{\partial \rho }}{{\partial T}}$
Where $\rho$ is reactivity and $T$ is temperature. The relationship shows that ${\alpha _T}$ is the value of the partial differential of reactivity with respect to temperature and is referred to as the "temperature coefficient of reactivity".
For example, in water moderated nuclear reactors the reactivity changes with respect to temperature are brought when changes in the temperature of the water takes place. Each element of the core has a specific temperature coefficient of reactivity (for example the fuel or cladding).

Note:
The temperature coefficient of the reaction is used to describe the effect of temperature on the rate of the reaction. The temperature coefficient of the reaction is defined as the ratio of the rate constant at two temperatures differ by ${10^0}C$ , usually from ${25^0}C$ to ${35^0}C$ .