The rate of a reaction doubles when its temperature changes from 300K to 310K. Activation energy of such a reaction will be :(R=8.314 JK⁻¹mol⁻¹ and log2=0.301)

As per Arrhenius equation:
lnk₂/k₁ = -Ea/2.303R(1/T₂ - 1/T₁)
Given that the rate of reaction doubles when temperature changes from 300K to 310K.
Therefore, k₂/k₁ = 2
log(k₂/k₁) = log2 = 0.301
R = 8.314 JK⁻¹mol⁻¹
T₁ = 300K
T₂ = 310K
Ea = ?
Substituting the values in Arrhenius equation:
0.301 = -Ea/(2.303 × 8.314)(1/310 - 1/300)
0.301 = -Ea/(2.303 × 8.314)(-10/300 × 310)
0.301 = -Ea/(19.147)(-10/93000)
0.301 = -Ea/(-19.147 × 10/93000)
0.301 = Ea/(19.147 × 10⁻³)
Ea = 0.301 × 19.147 × 10⁻³
Ea = 5.765 × 10⁻³ × 1000
Ea = 5765 Jmol⁻¹
Ea = 5.765 kJmol⁻¹
The closest answer is 58.5kJmol⁻¹