Determining pH using the Henderson-Hasselbalch Equation

Calculating the pH for a Ratio of Amine to Ammonium Ion

The pH at which the ratio of amine to ammonium ion will be 1 to 100 is approximately -0.4. To determine the pH at which the ratio of amine to ammonium ion will be 1 to 100 using the Henderson-Hasselbalch equation, we need to use the pKa values and the equation: pH = pKa + log ([A-]/[HA]),

where [A-] is the concentration of the deprotonated form (amine) and [HA] is the concentration of the protonated form (ammonium ion).

Given the pKa values:

pKa1 = 1.6 (for HN-CH-0-OH),

pKa2 = 9.6 (for CH CEO OH),

pKa3 = 3.6.

To have a ratio of 1 to 100 between amine and ammonium ion, we want [A-]/[HA] = 1/100.

Let's assume the concentration of the amine is C and the concentration of the ammonium ion is 100C.

Using the Henderson-Hasselbalch equation, we have:

1/100 = 10^(pH - pKa),

where pKa is the pKa value for the relevant reaction.

Rearranging the equation, we have:

pH - pKa = log(1/100) = -2.

Substituting the pKa value into the equation, we have:

pH - 1.6 = -2,

pH = -2 + 1.6,

pH = -0.4.

Therefore, the pH at which the ratio of amine to ammonium ion will be 1 to 100 is approximately -0.4.