Answer: At 34°c
Explanation:
Using The Arrhenius Equation:
k = Ae − Ea/RT
k represents rate constant
A represents frequency factor and is constant
R represents gas constant which is = 8.31J/K/mol
Ea represents the activation energy
T represents the absolute temperature.
By taking the natural log of both sides,
ln k = ln A- Ea/RT
Reactions at temperatures T1 and T2 can be written as;
ln k1= ln A− Ea/RT1
ln k2= ln A− Ea/RT2
Therefore,
ln(k1/k2) = −Ea/RT1 + Ea/RT2
Since k2=2k1 this becomes:
ln(1/2) = Ea/R*[1/T2 − 1/T1]
Theefore,
-0.693 = 37.2 x 10^3/8.31 * [ 1/T2 - 1/293]
1/T2 - 1/293 = -1.55 x 10^-4
1/T2 = -1.55 x 10^-4 + 34.13x 10^-4
1/T2 = 32.58 x 10^-4
Therefore T2 = 307K
T2 = 307 - 273 = 34 °c
