Question

Suppose a reaction has a rate constant of 0.720 1/h at 30.0 C. This reaction also has an activation energy of 50.0 kJ/mol. What is the rate constant of the reaction at 5.00 C (in 1/h)?

Answer 1

Solution :-

Given data

Rate constant K1 = 0.720 h-1

Temperature T1 = 30.0 C +273 = 303 K

Rate constant K2 = ?

Temperature T2 = 5.00 C +273 = 278 K

Activation energy Ea = 50.0 kJ per mol * 1000 J / 1 kJ = 50000 J per mol

Using the Arrhenius equation we can calculate the rate constant K2 at the given temperature

Formula , ln(K2/K1) = Ea/R [(1/T1)-(1/T2)]

Where R= 8.314 J per mol . K

Lets put the values in the formula

ln(K2/0.720) = 50000 J per mol / 8.314 J per mol. K *[(1/303)-(1/278)]

ln(K2/0.720) = 50000 J per mol / 8.314 J per mol K *[-0.00029679]

ln(K2/0.720) = -1.785

K2/0.720 = anti ln [-1.785]

K2/0.720 = 0.168

K2 = 0.168 * 0.720 h-1

K2 = 0.121 h-1

Therefore the rate constant at 5.00 C = 0.121 1/h