Answer:
The answer to the questions are as follows
Reaction B is 4426.28 times faster than reaction A
(b) Reaction B is faster.
Explanation:
To solve the question we are meant to compare both reactions to see which one is faster
The values of the given activation energies are as follows
For A
Ea = 95.00 kJ mol–1 (22.71 kcal mol–1) and
for B
Ea = 74.20 kJ mol–1 (17.73 kcal mol–1)
T is the same for both reactions and is equal to 298 k
Concentration of both reaction = 1M
The Arrhenius Law is given by
k = ![Ae^{\frac{-E_{a} }{RT} }](https://tex.z-dn.net/?f=Ae%5E%7B%5Cfrac%7B-E_%7Ba%7D%20%7D%7BRT%7D%20%7D)
Where
k = rate constant
Ea = activation energy
R = universal gas constant
T = temperature (Kelvin
)
A = Arrhenius factor
Therefore
For reaction A, the rate constant k₁ is given by k₁ = ![Ae^{\frac{-95000}{(8.314)(298)} }](https://tex.z-dn.net/?f=Ae%5E%7B%5Cfrac%7B-95000%7D%7B%288.314%29%28298%29%7D%20%7D)
And for B the rate constant k₂ is given by k₂ = ![Ae^{\frac{-74200 }{(8.314)(298)} }](https://tex.z-dn.net/?f=Ae%5E%7B%5Cfrac%7B-74200%20%7D%7B%288.314%29%28298%29%7D%20%7D)
k₁ = A×2.225×10⁻¹⁷
k₂ = A×9.850×10⁻¹⁴
As seen from the above Reaction B is faster than reaction A by (A×9.850×10⁻¹⁴)/(A×2.225×10⁻¹⁷) or 4426.28 times