Question

: The temperature coefficient for the reaction rate of a reaction is 2. The rate decreases if we decrease the temperature from 400K to 320K is:

Answer 1

The rate of a reaction increases with increase in the temperature. This is evident from the Arrhenius equation that for a small rise in temperature, the rate of reaction increases exponentially.

Complete step by step answer:
It is given in the question that the temperature coefficient of the reaction is 2.
From this, we can make out that for every $10{\text{K}}$rise in the temperature, the rate of the reaction becomes double. Similarly, for every $10{\text{K}}$decrease in the temperature, the rate of reaction reduces to half of the initial rate.
It is given in the question, that the temperature is reduced from 400K to 320K. The temperature of the reaction decreases by $80{\text{K}}$.
So the rate of reaction will decrease by ${\left( {\dfrac{1}{2}} \right)^8}$ times
Thus, the rate of reaction becomes $\dfrac{1}{{256}}$ times of the initial.
Additional information: While studying a chemical reaction, it is important for us to consider not only the chemical properties of the reactants, but also the conditions under which the reaction is taking place, the mechanism by which it is proceeding, the rate at which it is occurring, and the equilibrium toward which it is moving.
The law of mass action states that, at a constant temperature the rate of a chemical reaction at a constant temperature depends only on the concentrations of the substances influencing the rate. The substances influencing the rate of reaction are usually one or more of the reactants, but occasionally include products. Catalysts, which do not appear in the balanced overall chemical equation, also influence reaction rate.

Note:
The rate law is an experimentally determined quantity and can be used to predict the relationship between the concentrations of reactants and the rate of the reaction. For elementary reactions, the rate equation can be simply derived from first principles using the collision theory. The rate equation of a reaction with a multi-step mechanism cannot be calculated from the stoichiometric coefficients of the overall reaction.