The pKa for the side chain of histidine is 6.0. What is the ratio of the deprotonated imidazole side chain to the protonated side chain at pH 5.0 and at pH 7.5?

When the pKa is 6.0, we can determine the fraction of protonated H is by:

pH = pKa + log [A]/[HA]

Where

A = Deprotonated imidazole side

HA = Protonated side

Given, pH = 5.0

5 = 6 + log [A]/[HA]

log [A]/[HA] = - 1 (take antilog of both side)

[A]/[HA] = 0.1

The ratio of the deprotonated imidazole side chain to the protonated side chain at pH 5.0 = 0.1

Given, pH = 7.5

7.5 = 6 + log [A]/[HA]

log [A]/[HA] = 1.5 (take antilog of both sides)

[A]/[HA] = 31.62

The ratio of the deprotonated imidazole side chain to the protonated side chain at pH 5.0 = 31.62