Question

1)A well known aphorism in chemistry is that for every 10° increase in temperature, the rate of a reaction will increase twofold. If the reaction were performed at 45° C predict whether it would occur at twice the rate of the reaction performed at 35° C (Show relevant calculations to confirm your answer. If your second set of kinetic trials was performed at a temperature other than 35°, use a temperature exactly 10° higher for the calculation, for example if your second set of trials was run at 38° C, compare 38° to 48°C.

Answer 1

Though the energy of activation (Ea) is constant for a set of reactions, it plays a major role in determining the ratio of reactivity at different temperatures.

Let us consider a reaction with low Ea of 25 kJ mol^-1.

T1 = 35 + 273 = 308 K and T2 = 45 + 273 = 318 K

R = 8.314 J mol^-1 K^-1

The Arrhenius equation is given as:

ln k2/k1 = Ea / R [ 1/T1- 1/T2]

ln k2/k1 = 25000 J / 8.314 J mol^-1 K^-1 [ 1/308- 1/318]K

ln k2/k1 = 3006.98[ 10/308 X 318]

ln k2/k1 = 0.307

k2/k1 = e^0.307

k2/k1 = 1.36

Thus for low Ea the reaction that were performed at 45° C does not occur at twice the rate of the reaction performed at 35° C.

Now consider a reaction with moderate Ea of 50 kJ mol^-1.

T1 = 35 + 273 = 308 K and T2 = 45 + 273 = 318 K

R = 8.314 J mol^-1 K^-1

The Arrhenius equation is given as:

ln k2/k1 = Ea / R [ 1/T1- 1/T2]

ln k2/k1 = 50000 J / 8.314 J mol^-1 K^-1 [ 1/308- 1/318]K

ln k2/k1 = 6013.95[ 10/308 X 318]

ln k2/k1 = 0.614

k2/k1 = e^0.614

k2/k1 = 1.85

k2/k1 ~ 2

Thus for moderate Ea the reaction that were performed at 45° C occurs at twice the rate of the reaction performed at 35° C.

Now consider a reaction with high Ea of 100 kJ mol^-1.

T1 = 35 + 273 = 308 K and T2 = 45 + 273 = 318 K

R = 8.314 J mol^-1 K^-1

The Arrhenius equation is given as:

ln k2/k1 = Ea / R [ 1/T1- 1/T2]

ln k2/k1 = 100000 J / 8.314 J mol^-1 K^-1 [ 1/308- 1/318]K

ln k2/k1 = 12027.90[ 10/308 X 318]

ln k2/k1 = 1.228

k2/k1 = e^1.228

k2/k1 = 3.4

Thus for high Ea the reaction that were performed at 45° C does not occur at twice the rate of the reaction performed at 35° C.

Thus the well-known aphorism in chemistry that for every 10° increase in temperature, the rate of a reaction will increase twofold is true for reactions with moderate energy of activation.

In the second set of trials let us consider T1 = 38 + 273 = 311 K and T2 = 48 + 273 = 321 K

for a reaction with moderate Ea of 50 kJ mol^-1.

R = 8.314 J mol^-1 K^-1

The Arrhenius equation is given as:

ln k2/k1 = Ea / R [ 1/T1- 1/T2]

ln k2/k1 = 50000 J / 8.314 J mol^-1 K^-1 [ 1/311- 1/321]K

ln k2/k1 = 6013.95[ 10/311 X 321]

ln k2/k1 = 0.602

k2/k1 = e^0.602

k2/k1 = 1.83

k2/k1 ~ 2

This shows that the aphorism holds true for other set of temperatures with 10 degree difference.