Question

The first order of gaseous the decomposition of n₂o₄ in to no₂ has rate constant of 4.5 ×10³ at 1°c and activation energy of 58kj/mol. at what temperature would the rate constant be 10²s¯¹?

Answer 1

To solve this problem, we can use the Arrhenius equation, which relates the rate constant (k) to the temperature (T) and activation energy (Ea):

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

Where: k = rate constant A = pre-exponential factor or frequency factor Ea = activation energy R = gas constant (8.314 J/(mol·K)) T = temperature in Kelvin

We need to find the temperature (T) at which the rate constant (k) is 10^2 s^(-1). Let's denote this temperature as T₂.

Given data: k₁ = 4.5 × 10^3 s^(-1) (at 1°C = 1 + 273.15 = 274.15 K) Ea = 58 kJ/mol = 58000 J/mol k₂ = 10^2 s^(-1)

We can rearrange the Arrhenius equation to solve for T:

T₂ = (-Ea / (R * ln(k₂ / A)))⁻¹

First, let's calculate the value of A. Since it is not given, we need additional information to determine it.