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How many times the rate of reaction increases at 200C for a reaction having the activation energies in the presence and absence of catalyst as 50 kJ/mol and 75 kJ/mol?
- a)1000
- b)10000
- c)30000
- d)50000
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
How many times the rate of reaction increases at 200C for a reaction h...
The rate of reaction will increase 28,592 times, i.e. 30,000 times.
Most Upvoted Answer
How many times the rate of reaction increases at 200C for a reaction h...
Given:
Activation energy with catalyst (Ec) = 50 kJ/mol
Activation energy without catalyst (Enc) = 75 kJ/mol
Formula:
The rate constant (k) 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
T = temperature
Analysis:
The rate constant is directly proportional to the rate of reaction.
Case 1: With catalyst (Ec)
Let's assume the rate constant with catalyst is kc.
Case 2: Without catalyst (Enc)
Let's assume the rate constant without catalyst is knc.
Calculation:
To compare the rate of reaction at two different temperatures, we can use the ratio of rate constants.
At 200°C:
Temperature (T) = 200 + 273 = 473 K
Case 1: With catalyst (Ec)
kc = A * e^(-Ec/RT)
Case 2: Without catalyst (Enc)
knc = A * e^(-Enc/RT)
Taking the ratio of rate constants:
kc/knc = [A * e^(-Ec/RT)] / [A * e^(-Enc/RT)]
The pre-exponential factor (A) cancels out, so we are left with:
kc/knc = e^(-Ec/RT) / e^(-Enc/RT)
Since the temperatures (T) and the gas constant (R) are the same in both cases, we can simplify the equation further:
kc/knc = e^(-Ec/RT + Enc/RT)
Using the properties of exponents, we can rewrite the equation as:
kc/knc = e^[-(Ec - Enc)/RT]
Substituting the given activation energies:
kc/knc = e^[-(50 - 75)/(8.314 * 473)]
Simplifying the exponent:
kc/knc = e^(25/8.314 * 473)
Calculating the value:
kc/knc ≈ 29999
Therefore, the rate of reaction increases approximately 30,000 times at 200°C.
Activation energy with catalyst (Ec) = 50 kJ/mol
Activation energy without catalyst (Enc) = 75 kJ/mol
Formula:
The rate constant (k) 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
T = temperature
Analysis:
The rate constant is directly proportional to the rate of reaction.
Case 1: With catalyst (Ec)
Let's assume the rate constant with catalyst is kc.
Case 2: Without catalyst (Enc)
Let's assume the rate constant without catalyst is knc.
Calculation:
To compare the rate of reaction at two different temperatures, we can use the ratio of rate constants.
At 200°C:
Temperature (T) = 200 + 273 = 473 K
Case 1: With catalyst (Ec)
kc = A * e^(-Ec/RT)
Case 2: Without catalyst (Enc)
knc = A * e^(-Enc/RT)
Taking the ratio of rate constants:
kc/knc = [A * e^(-Ec/RT)] / [A * e^(-Enc/RT)]
The pre-exponential factor (A) cancels out, so we are left with:
kc/knc = e^(-Ec/RT) / e^(-Enc/RT)
Since the temperatures (T) and the gas constant (R) are the same in both cases, we can simplify the equation further:
kc/knc = e^(-Ec/RT + Enc/RT)
Using the properties of exponents, we can rewrite the equation as:
kc/knc = e^[-(Ec - Enc)/RT]
Substituting the given activation energies:
kc/knc = e^[-(50 - 75)/(8.314 * 473)]
Simplifying the exponent:
kc/knc = e^(25/8.314 * 473)
Calculating the value:
kc/knc ≈ 29999
Therefore, the rate of reaction increases approximately 30,000 times at 200°C.
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How many times the rate of reaction increases at 200C for a reaction having the activation energies in the presence and absence of catalyst as 50 kJ/mol and 75 kJ/mol?a)1000b)10000c)30000d)50000Correct answer is option 'C'. Can you explain this answer?
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How many times the rate of reaction increases at 200C for a reaction having the activation energies in the presence and absence of catalyst as 50 kJ/mol and 75 kJ/mol?a)1000b)10000c)30000d)50000Correct answer is option 'C'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about How many times the rate of reaction increases at 200C for a reaction having the activation energies in the presence and absence of catalyst as 50 kJ/mol and 75 kJ/mol?a)1000b)10000c)30000d)50000Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many times the rate of reaction increases at 200C for a reaction having the activation energies in the presence and absence of catalyst as 50 kJ/mol and 75 kJ/mol?a)1000b)10000c)30000d)50000Correct answer is option 'C'. Can you explain this answer?.
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