Question

For the first order reaction rate constants in terms of temperature are given below A----->P k1 =10^15e^-1500/T B----->Q k2= 10^14e^-1000/T
If initially both reaction started with same initial concentration of a and be then at what temperature both reactions will have same initial rate

Answer 1

Answer:

see the attachment please

Explanation:

Hope the answer will help you

Answer 2

Answer:

At 217.108K both reactions will have the same initial rates.

Explanation:

The rate of reaction is represented by the Arrhenius equation

$k=Ae^{E_{a}/RT }$

In which,

$k$ is rate constant

$A$ is pre-exponential factor

$E_{a}$ is activation energy

$R$ is the universal gas constant

$T$ is temperature in kelvin

For A→P

$k_{1} =10^{15}e^{\frac{-1500}{T} }$

For B→Q

$k_{2} =10^{14}e^{\frac{-1000}{T} }$

As we have given the rate of both reactions are same.

$k_{1} =k_{2}$

Therefore, for the same rate of both reaction

$10^{15}e^{(-1500/T)} = 10^{14}e^{(-1000/T)}\\10^{(15-14)} =e^{(-1000/T+1500/T)} \\10=e^{500/T}$

Taking $log_{e}$ on both sides,

$log_{e}10= log_{e}e^{500/T} \\2.303=500/Tlog_{e}e\\2.303=500/T\\T=500/2.303\\T=217.108K$

So, at 217.108K both reactions will have the same initial rates.