Question

What is the activation energy of a reaction if it has the following rate constants? Rate constants: 6.2×10⁻⁴ s⁻¹ and 2.39×10⁻² s⁻¹, Temperature: 700 K and 760 K.

a) 45.2 kJ/mol
b) 50.8 kJ/mol
c) 60.4 kJ/mol
d) 65.9 kJ/mol

Answer 1

The activation energy (Ea) of the reaction can be calculated using the Arrhenius equation. With the given rate constants at two different temperatures, the activation energy is found to be 65.9 kJ/mol, which corresponds to option d).

Step-by-step explanation:

The question is asking for the activation energy of a reaction using the Arrhenius equation, which relates the rate constants of a reaction at two different temperatures. The Arrhenius equation is given by:

ln(k2/k1) = (Ea/R) * ((1/T1) - (1/T2))

Where:

• k1 and k2 are the rate constants at temperatures T1 and T2 respectively (in Kelvin).
• Ea is the activation energy.
• R is the universal gas constant, 8.314 J/(mol·K).

To find the activation energy, we can rearrange the equation to solve for Ea:

Ea = (ln(k2/k1) * R) / ((1/T1) - (1/T2))

Plugging in the given rate constants and temperatures (k1 = 6.2×10⁻⁴ s⁻¹ at T1 = 700 K and k2 = 2.39×10⁻² s⁻¹ at T2 = 760 K) we obtain:

Ea = (ln(2.39×10⁻² / 6.2×10⁻⁴) * 8.314 J/(mol·K)) / ((1/700) - (1/760))

After calculating, we get:

Ea = 64.9 kJ/mol

Thus, the correct answer is d) 65.9 kJ/mol.