Question

The temperature coefficient of a reaction is 2. When the temperature is increased from $30{}^{\circ }C$ to$100{}^{\circ }C$, rate of the reaction increases by:
A. 128 times
B. 100 times
C. 500 times
D. 250 times

Answer 1

Hint: Think about what the term temperature coefficient means and how it is related to the rate of the reaction. Relate the formula for the temperature coefficient with the increase in temperature and the corresponding increase in rate.

Complete answer:
The temperature coefficient is defined as the ratios of the relative rates of the reaction at an increase of 10 Kelvin in the temperature. If the temperature coefficient is 1, it means that there is no change in rate. If it is 2, the reaction rate doubles at an increase of 10 Kelvin, and so on.
The temperature coefficient of this reaction is 2. That means every 10 degree rise in temperature makes the rate of reaction double. Initially, our temperature was $30{}^{\circ }C$. If we raise this temperature by 10 degrees to $40{}^{\circ }C$. The rate of the reaction becomes twice. If we rise the temperature again by 10 degrees to $50{}^{\circ }C$, the rate of reaction increases as four times as the original reaction. If we increase the temperature again by 10 degrees to $60{}^{\circ }C$, the rate of reaction will increase by eight times. From $30{}^{\circ }C$ to $100{}^{\circ }C$, we increased the temperature by 10 degrees 7 times. So, the rate of reaction will be $2^7$ times.
$$2^7=128$$
Thus, we can generalize this formula as:
$$\text{Increase in rate = (temperature coefficient}{\text{)}}^{({\displaystyle \frac{\mathrm{\Delta }T}{10}})}$$
Therefore, the correct option is ‘A. 128 times’

Additional Information:
The rate of a reaction is the term which refers to the speed at which the reaction takes place. We can express the rate of reaction by the rate of disappearance of reactants in a reaction or rate of formation of products in a reaction.

Note: When we are writing the rate of reaction in terms of the rate of disappearance of reactant species, we will give a negative sign which means the reaction will move forward only when the reactant species decreases with time.