Answer
🧪 Understanding Reaction Rate and Temperature
The rate of a chemical reaction increases with temperature, and the relationship is governed by the Arrhenius equation:
k = A · e−Ea/RT
- k = rate constant
- A = frequency factor (constant)
- Ea = activation energy (in J/mol)
- R = 8.314 J/mol·K (gas constant)
- T = temperature in Kelvin
📈 Effect of Increasing Temperature
We compare the rate constants at two temperatures using the Arrhenius ratio form:
ln(k₂/k₁) = (Ea/R) × (1/T₁ − 1/T₂)
- T₁ = 25°C = 298 K
- T₂ = 50°C = 323 K
- Given: Ea = 44,422 J/mol
Now plug in the values:
ln(k₂/k₁) = (44422 / 8.314) × (1/298 − 1/323) ≈ 5342 × (0.003356 − 0.003096) ≈ 5342 × 0.00026 ≈ 1.39
Now take the antilog:
k₂/k₁ = e^1.39 ≈ 4.01
✅ The forward reaction rate will increase by a factor of approximately 4.
✔️ Final Answer:
The forward reaction rate will increase by a factor of 4.