Question

The rate of reaction is doubled for every $10{}^\circ C$ rise in temperature the increase in reaction rate as a result of rise in temperature from $10{}^\circ C$ to $100{}^\circ C$ is:
A.$112$
B.$512$
C.$400$
D.$256$

Answer 1

We know that if we increase the temperature the rate of reaction increases because the particles gain more kinetic energy i.e., Heat increases the average energy of the molecules.
Formula:
By using $\dfrac{{{r}_{2}}}{{{r}_{1}}}={{2}^{n}}$ where n is the increased in rate of reaction.

Complete answer:
AS we know that the unit of rate constant depends on the order of the reaction. If we are given a particular rate law equation and asked to identify the order of the reaction, we can directly find out by observing the unit if the rate constant. The rate of reaction becomes twice for every $10{}^\circ C$ rise in temperature.
The temperature is increased from $10{}^\circ C$ to $100{}^\circ C$ thus the temperature is raised by $90{}^\circ C.$ Thus, the temperature coefficient of the reaction $=2$ when the temperature is increased by $90{}^\circ C.$ Since we know that the $\dfrac{{{r}_{2}}}{{{r}_{1}}}={{2}^{n}}$
Here, ${{r}_{2}}$ is rate of heat at ${{T}_{2}}$ which is $100{}^\circ C.$ and ${{r}_{1}}$ is rate of heat at ${{T}_{1}}$ which is $10{}^\circ C$which means there is nine times rise in $10{}^\circ C$ thus, $n=9$ and the increase in reaction rate as a result of rise in temperature is given by thus, the rate of reaction increases by ${{\left( 2 \right)}^{9}}=512$ times.

Therefore, correct answer is option B i.e., the increase in reaction rate as a result of rise in temperature is $512.$

Note:
Remember that the rate of reaction is dependent on rate constant as the rate law expression states, rate is directly proportional to rate constant and temperature. But many reactions are not simple and their rate may actually decrease with increasing temperature.