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The activation energy of a reaction is 75.2 kJ mol-1 in the absence of a catalyst and it lowers to 50.14 kJmol-1 with a catalyst. How many times will the rate of reaction grow in the presence of a catalyst if the reaction proceeds at 25°C ?
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The activation energy of a reaction is 75.2 kJ mol-1 in the absence of...
 According to Arrhenius equation,

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The activation energy of a reaction is 75.2 kJ mol-1 in the absence of...

Calculation of Rate Enhancement with Catalyst

- The rate of a reaction is given by the Arrhenius equation:

k = A * e^(-Ea / RT)

- Where:
k = rate constant
A = pre-exponential factor
Ea = activation energy
R = gas constant (8.314 J/mol-K)
T = temperature in Kelvin

Rate of Reaction without Catalyst

- For the reaction without a catalyst:
Ea = 75.2 kJ/mol = 75,200 J/mol
T = 25°C = 298 K

k1 = A * e^(-75200 / (8.314 * 298))
k1 = A * e^(-31.84)

Rate of Reaction with Catalyst

- For the reaction with a catalyst:
Ea' = 50.14 kJ/mol = 50,140 J/mol

k2 = A * e^(-50140 / (8.314 * 298))
k2 = A * e^(-21.26)

Comparison of Rates

- The rate enhancement due to the catalyst can be calculated as:

Rate enhancement = k2 / k1
= (A * e^(-21.26)) / (A * e^(-31.84))
= e^(10.58)
≈ 370

Explanation

- The rate of reaction will grow by approximately 370 times in the presence of a catalyst at 25°C. This is due to the lower activation energy provided by the catalyst, which allows more molecules to overcome the energy barrier and participate in the reaction. As a result, the reaction proceeds faster with the catalyst compared to without it. This significant rate enhancement demonstrates the importance of catalysts in accelerating chemical reactions.
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The activation energy of a reaction is 75.2 kJ mol-1 in the absence of a catalyst and it lowers to 50.14 kJmol-1 with a catalyst. How many times will the rate of reaction grow in the presence of a catalyst if the reaction proceeds at 25°C ?
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