Question

If the rate of reaction increases to two times with every ${10^ \circ }{\text{C}}$ rise in temperature, then if we raise the temperature by ${40^ \circ }{\text{C}}$, the new rate of reaction will be:
A) 4 times
B) 8 times
C) 16 times
D) 32 times

Answer 1

Hint: The rate of the reaction increases with increase in temperature. This is because when the temperature is raised the kinetic energy of the particles increases which results in increased number of collisions.

Complete step by step answer:
The rate of reaction increases two times with every ${10^ \circ }{\text{C}}$ rise in the temperature.
Thus, the rate of reaction changes by ${2^n}$ times.
Where n is the number of times the temperature is increased.
The temperature is increased from ${10^ \circ }{\text{C}}$ to ${40^ \circ }{\text{C}}$. Thus, the temperature has increased 4 times.
Thus, the new rate of reaction is,
New rate of reaction = ${2^n}$
Substitute 4 for the number of times the temperature is increased. Thus,
New rate of reaction = ${2^4}$
New rate of reaction = 16
Thus, if we raise the temperature by ${40^ \circ }{\text{C}}$, the new rate of reaction will be increased by 16 times.

Thus, the correct option is (C) 16 times.

Additional Information: When temperature of the reaction is increased, the collision between the reactant molecules increases. As the number of collisions increase, the rate of reaction increases.
The equation that gives the relationship between the rate of the reaction and the temperature is known as the Arrhenius equation. The equation is as follows:
$\ln k = - \dfrac{{{E_a}}}{{RT}} + \ln A$
Where k is the rate constant for the reaction,
${E_a}$ is the energy of activation,
R is the universal gas constant,
T is the temperature in Kelvin’
A is the pre-exponential factor.

Note: The rate of any reaction increases two times when the temperature is raised by ${10^ \circ }{\text{C}}$. This ratio of the rate constant is known as the temperature coefficient for reaction.