Temperature and equilibriums

There's a straightforward relationship between temperature and pK_a- and K_a-values. Hence temperature has an impact on equilibriums.

The relationship is dependent of the difference in Heat of formation dH^o-values for the ions and compounds in a given equilibrium relation.

An example of how to calculate the difference in dH^o values between product and substrate is given below:

dH^o NH₄⁺ - 133.26 kj/mol

dH^o NH₃ - 80.83 kj/mol

dH^o H⁺ 0 kj/mol

The difference is then (- 80,83 - (-133,26) = 52.43 kj)

To calculate the K_a-value at a temperature different from the standard temperature (25^o Celcius) we apply the Van't Hoff equation.

Notice Log_e means the natural logarithm.

This can be rewritten by applying exp on both sides of the equation - then we got:

Now its very easy to isolate the thing we are looking for - K_a^'

In the equilibrium example above the difference in dH^obetween products and substrate is 52430 joule.

Lets say we need to calculate the pK_a-value of NH₄⁺ at 37 degrees Celcius (310 Kelvin). At 25 degrees Celcius we do know the pK_a-value of ammonium as 9.24. The only thing we have to do now is to substitute into our formula:

=10^-8.88

If you do this on a calculator you won't get the result 10^-8.88 on your screen, but its easy to rewrite your result to 10^-8.88.

The result shows, that at any given pH-value, you have relatively less NH4+ at higher temperatures.

At www.beggiatoa.com you can learn more about how to remove NH₃ by nitrification.

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