1)A well known aphorism in chemistry is that for every 10° increase in temperatu
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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.
Explanation / Answer
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 = e0.307
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 = e0.614
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 = e1.228
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 = e0.602
k2/k1 = 1.83
k2/k1 ~ 2
This shows that the aphorism holds true for other set of temperatures with 10 degree difference.
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