Question

The half life of a first order reaction is 100 seconds at 280 K. If the temperature coefficient is 3.0 its rate constant at 290 K in $s^{-1}$ is:

• A. $2.08\times {10}^{-3}$
• B. $2.08\times {10}^{-2}$
• C. $6.93\times {10}^{-3}$
• D. $6.93\times {10}^{-2}$

Answer 1

Answer: (B)

$2.08\times {10}^{-2}$

It has been observed that in homogeneous thermal reactions, for every ten degree rise in temperature, the rate constant is doubled or tripled. The ratio of rate constants at two temperatures separated by 10°C is called the temperature coefficient.

so $\frac{k_2}{k_1}=3$ ( here )

Rate constant $=\frac{0.693}{100}=0.00693$

$log\frac{k_2}{k_1}=log3$

$log\frac{\left[k_2\right]}{\left(0.00693\right)}=log3$

$log{k}_2-log0.00693=log3$

$log{k}_2=log3+log0.00693$

$log{k}_2=0.4771+(-2.16)$

$log{k}_2=-1.68$

$log{k}_2=0.0208$

$\Rightarrow k_2=2.08\times {10}^{-2}$