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I did some research online but I still couldn't get any conclusion. Some said that the buffering capacity decreases when temperature increases because of the increase in ionisation of the weak acid molecules and therefore, some of the conjugate base ion will be used to neutralised the $\ce{H+}$ ion from the ionization of the weak acid molecules. Hence, only a small amount of strong acid is needed to complete remove the conjugate base ion and to break the buffering capacity. But, the problem is that the acid molecules ionise into both $\ce{H+}$ and the conjugate base so doesn't it mean that the number of conjugate base ion will remain the same since the $\ce{H+}$ ion is just reacting with the same conjugate base ion which they were initially bonded together ?

The other assumption is that temperature has no effect on buffering capacity since buffering capacity apparently only depends on two factors: concentration of the buffer solution and the ratio of pH to pKa. So even if the pKa changes due to the change in temperature, the pH also changes accordingly whereby pH increases when pkA increases and vice versa. So the ratio will remain the same no matter what.

So could anyone please give me a solution?

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You question is too broad to answer since there is no "universal answer." In chemistry there is a "tends too" answer and then a list of exceptions.

By and large the root of the question centers around the change in the equilibrium constant as a function of temperature. The equilibrium constants do depend on temperature, but how much "tends" to depend on the particular equilibrium under consideration. However the Arrhenius equation can offer some insight.

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The other assumption is that temperature has no effect on buffering capacity since buffering capacity apparently only depends on two factors: concentration of the buffer solution and the ratio of pH to pKa. So even if the pKa changes due to the change in temperature, the pH also changes accordingly whereby pH increases when pkA increases and vice versa. So the ratio will remain the same no matter what.

This is the better argument. For example, if you start with equal concentrations of conjugate acid and base, and change the temperatures, that ratio will not change much, and the buffer capacity would be similar. The pH will be different as the pKa will change, but you already mentioned that.

There are small secondary effects: The volume of the solution might increase slightly, slightly decreasing the buffer concentration and its buffer capacity. Also, the change in pKa will shift the equilibrium a bit, resulting in the change of pH and in a slight change in the ratio of conjugate acid and base.

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