Question

Two $1^{st}$ order reactions having same reactant concentrations proceed at ${25}^{o}C$ at the same rate. The temperature coefficient of the rate of the first reaction is 2 and that of the second reaction is 3. Find the ratio of the rate of these reactions at ${75}^{o}C$:

• A. 7.59375
• B. 15
• C. 15.59
• D. None of these

Answer 1

The correct option is A 7.59375

The temperature coefficient of the first reaction is 2. This means that the rate of the reaction is doubled for every ${10}^{0}C$ rise in temperature.

The temperature coefficient of the first reaction is 3. This means that the rate of the reaction is tripled for every ${10}^{0}C$ rise in temperature.

	${25}^{0}C$	${35}^{0}C$	${45}^{0}C$	${55}^{0}C$	${65}^{0}C$	${75}^{0}C$
First reaction	k	2k	4k	8k	16k	32k
Second reaction:	k	3k	9k	27k	81k	243k

The ratio of the rates of two reactions at ${75}^{0}C$ is $\frac{243k}{32k}=7.5937$