Question

The rate of reaction increase significantly with increase in temperature. Generally, rates of reactions are doubled for every ${10}^{\circ }$ rise in temperature. Temperature coefficient gives us an idea about the change in the rate of a reaction for every ${10}^{\circ }$ change in temperature.
Temperature coefficient $\left(\mu \right)=\frac{Rateconstantof(T+10{)}^{\circ }C}{Rateconstantat{T}^{\circ }}$
Arrhenius gave an equation which describes rate constant k as a function of temperature $k=A{e}^{-E_a/RT}$ where k is the rate constant, A is the frequency factor or pre-exponetial factor, $E_a$ is the activation energy, T is the teperature in kelvin, and R is the universal gas constant.
Equation when expressed in logarithmic form becomes
log $k=logA-\frac{E_a}{2.303RT}$

For the given reactions, following data is given
$P\to Q{k}_1={10}^{15}exp\left(\frac{-2000}{T}\right)$
$C\to D{k}_2={10}^{14}exp\left(\frac{-1000}{T}\right)$
Temperature at which $k_1=k_2$ is:

• A. $434.22$ K
• B. $1000$ K
• C. $2000$ K
• D. $868.44$ K

Answer 1

Answer: (A)

$434.22$ K

$k_1={10}^{15}exp\left(\frac{-2000}{T}\right);$

$k_2={10}^{14}exp\left(\frac{-1000}{T}\right)$
When $k_1=k_2;{10}^{15}exp\left(\frac{-2000}{T}\right)$

$={10}^{14}exp\left(\frac{-1000}{T}\right)$
Or

$T=434.22$ K