The rate constant of a reaction is 5.8 * 10-3 s-1 at 25°c, and the activation energy is 33.6 kj/mol. what is k at 75°c? enter your answer in scientific notation.

k₂ = 4.06 x 10⁻² s⁻¹.

Explanation:

From Arrhenius law: K = Ae (-Ea/RT)

where, K is the rate constant of the reaction.

A is the Arrhenius factor.

Ea is the activation energy.

R is the general gas constant.

T is the temperature.

At different temperatures:

ln (k₂/k₁) = Ea/R [ (T₂-T₁) / (T₁T₂) ]

k₁ = 5.8 * 10⁻³ s⁻¹, k₂ = ?, Ea = 33600 J/mol, R = 8.314 J/mol. K, T₁ = 298.0 K, T₂ = 348.0 K.

ln (k₂/5.8 * 10⁻³ s⁻¹) = (33600 J/mol / 8.314 J/mol. K) [ (348.0 K - 298.0 K) / (298.0 K x 348.0 K) ] = (4041.37) (4.82 x 10⁻⁴) = 1.9479. Taking exponential of both sides:

(k₂/5.8 * 10⁻³ s⁻¹) = 7.014.

∴ k₂ = 4.06 x 10⁻² s⁻¹.