The rate constant, activation energy and Arrhenius parameter of a chemical reaction at 25°C are 3.0 x 10-4s-1, 104.4 kJ mol-1and 6.0 x 1014s-1respectively. The value of the rate constant at infinite temperature is isa)6.0 x 1030s-1b)2 x 1018s-1c)6.0 x 1014s-1d)InfinityCorrect answer is option 'C'. Can you explain this answer?

Question

The rate constant, activation energy and Arrhenius parameter of a chemical reaction at 25&#176;C are 3.0 x 10-4s-1, 104.4 kJ mol-1and 6.0 x 1014s-1respectively. The value of the rate constant at infinite temperature is isa)6.0 x 1030s-1b)2 x 1018s-1c)6.0 x 1014s-1d)InfinityCorrect answer is option 'C'. Can you explain this answer?

Answer

The correct answer is option C
Arrhenius equation
⇒ K = Ae−Ea/RT
As T → ∞,
RT → ∞

e^−Ea/RT → 1
Hence K → A as T→∞
∴ Value of K as T → ∞ = 6.0×10¹⁴S⁻¹

Answer

Option C is correct becz maximum value of rate constant is equal to Arrhenius parameter which occur at infinity temperature .

Answer

Given:
Rate constant at 25°C (298 K) = 3.0 x 10^-4 s^-1
Activation energy (Ea) = 104.4 kJ mol^-1
Arrhenius parameter (A) = 6.0 x 10^14 s^-1

To Find:
Rate constant at infinite temperature

Solution:
The Arrhenius equation relates the rate constant (k) of a chemical reaction to the temperature (T), activation energy (Ea), and the Arrhenius parameter (A):

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

where R is the gas constant (8.314 J mol^-1 K^-1).

Step 1: Convert the activation energy from kJ mol^-1 to J mol^-1:
Ea = 104.4 kJ mol^-1 * 1000 J kJ^-1 = 104400 J mol^-1

Step 2: Convert the rate constant at 25°C to Kelvin:
T = 25°C = 298 K

Step 3: Substitute the given values into the Arrhenius equation:

k = 6.0 x 10^14 s^-1 * e^(-104400 J mol^-1 / (8.314 J mol^-1 K^-1 * 298 K))

Step 4: Simplify the equation:

k = 6.0 x 10^14 s^-1 * e^(-104400 J mol^-1 / 2475.592 J mol^-1)

Step 5: Calculate the exponential term:

e^(-104400 J mol^-1 / 2475.592 J mol^-1) = e^(-42.168)

Step 6: Evaluate the exponential term using a calculator:

e^(-42.168) ≈ 1.203 x 10^-19

Step 7: Substitute the value of the exponential term back into the equation:

k = 6.0 x 10^14 s^-1 * 1.203 x 10^-19

Step 8: Simplify the expression:

k ≈ 7.218 x 10^-5 s^-1

Step 9: Since the rate constant at infinite temperature is the maximum possible value, it can be considered as approaching infinity. Therefore, the correct answer is option 'C': 6.0 x 10^14 s^-1.

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