Mastering Arrhenius Equation Numericals: Step-by-Step Solutions

What is the Arrhenius Equation?

The Arrhenius equation is a formula used to express the dependence of reaction rate on temperature and activation energy. It is written as:

k = A * e^-Ea/RT

Where:

• k = rate constant
• A = frequency factor
• E_a = activation energy (J/mol)
• R = gas constant (8.314 J/mol·K)
• T = temperature in Kelvin

Solved Numerical Example 1

Problem: Calculate the rate constant at 350 K for a reaction with an activation energy of 75,000 J/mol and a frequency factor of 1.5 × 10¹³ s^-1.

Solution:

Using the formula: k = A * e^-Ea/RT

Substitute the values:
A = 1.5 × 10¹³, Ea = 75,000 J/mol, R = 8.314 J/mol·K, T = 350 K

Exponent part: Ea/RT = 75000 / (8.314 × 350) ≈ 25.75

e^-25.75 ≈ 6.72 × 10^-12

k = 1.5 × 10¹³ × 6.72 × 10^-12 ≈ 100.8 s^-1

Solved Numerical Example 2

Problem: Determine the activation energy if the rate constant increases from 5.4 × 10³ to 2.7 × 10⁴ when the temperature increases from 300 K to 310 K.

Solution:

Use the logarithmic form: ln(k2/k1) = Ea/R (1/T1 – 1/T2)

ln(2.7 × 10⁴ / 5.4 × 10³) = Ea / 8.314 × (1/300 – 1/310)

ln(5) ≈ 1.609, and (1/300 – 1/310) ≈ 0.0001075

Ea = 1.609 / 0.0001075 × 8.314 ≈ 124,470 J/mol

Posted on April 24, 2025 | By more-marks.com