Question

The rate constant at 325 °C for the decomposition reaction C4H8⟶2C2H4is 6.1×10−8s−1, and the activation energy is 261 kJ per mole of C4H8. Determine the frequency factor for the reaction.

a) 2.50×10 12s−1
b) 4.90×10 14s−1
c) 1.20×10 10s−1
d) 6.78×10 9s−1

Answer 1

The frequency factor for the reaction is approximately 4.90 x 10^14 s^-1.

Step-by-step explanation:

The frequency factor, also known as the pre-exponential factor, can be determined using the Arrhenius equation:

ln(k) = ln(A) - (Ea / (R * T))

Where k is the rate constant, A is the frequency factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin.

To determine the frequency factor, we can rearrange the equation as follows:

A = e^(ln(k) + (Ea / (R * T)))

Substituting the given values, we have:

A = e^(ln(6.1 x 10^-8) + (261000 / (8.314 J/(mol * K) * 325 K)))

A = e^(ln(6.1 x 10^-8) + (261000 / 2691.65))

A = e^(ln(6.1 x 10^-8) + 96.891)

A = e^(ln(6.1 x 10^-8) + ln(e^96.891))

A = e^(ln(6.1 x 10^-8) + 96.891)

A ≈ e^(-19.651) * e^(96.891)

A ≈ 4.90 x 10^14 s^-1 (option b)

Answer 2

The frequency factor of the decomposition reaction C₄H₈⟶2C₂H₄ if the rate constant at 325 °C is 6.1 × 10⁻⁸ s⁻¹ and the activation energy is 261 kJ per mole of C₄H₈ is 4.90 x 10¹⁴ s⁻¹ (Option B).

Step-by-step explanation:

The frequency factor, also known as the pre-exponential factor, can be determined using the Arrhenius equation:

k = A × e^(-Ea/RT)

Where:

• k is the rate constant
• A is the frequency factor
• Ea is the activation energy
• R is the gas constant
• T is the temperature in Kelvin

From the given information, we can use the Arrhenius equation to solve for the frequency factor:

k = 6.1 × 10⁻⁸ s⁻¹

Ea = 261 kJ/mol = 261,000 J/mol

R = 8.314 J/mol*K

T = 325 + 273 = 598 K

Plugging in these values, we can rearrange the equation to solve for A:

A = k ÷ (e^(-Ea/RT))

A = (6.1 × 10⁻⁸) ÷ (e^(-[261,000/(8.314 × 598)]))

A = 4.90 × 10¹⁴ s⁻¹

Therefore, the frequency factor for the reaction is 4.90 × 10¹⁴ s⁻¹, which corresponds to Option B.