Question

A particular first-order reaction has a rate constant of 1.35 × 102 s-1 at 25.0°C. What is the magnitude of k at 45.0°C if Ea = 55.5 kJ/mol?

Answer 1

Arrhenius equation is given Below

k = Ae(-Ea/RT)
Let us take Ln both side
LnK = LnA - Ea / RT

K =  1.35 × 102 s-1

T = 298 k

Ea = 55.5 kJ/mol

Have to calculate LnA at 298K

4.90 = ln A - 55.5 x10³ /8.314 x 298

4.9 = ln A - 22.4

ln A = 27.300

Log A = 11.85

A = 1.39 x 10^-12

using this lnA at 318K to find LnK

LnK = LnA - Ea / RT

ln K = ln   1.39 x 10^-12 - 55.5 x 103 / 8.314 x 318

K = 1.8 x 10^-3 s-1

magnitude of k at 45.0°C is K = 1.8 x 10^-3 s-1

3 ) convert from LnK into k via log operations