For alanine, Ka1 = 5.1 x 10 -3, Ka2 = 1.8 x 10 -10
a) Calculate the ratios [Z] / [C
+] and [Z] / [A
−] at pH = 10.50
b) Calculate the pH when [Z] = [C
+] and when [Z] = [A
−] if pH= - log [H
In strongly acidic conditions, most of the alanine molecules will gain a proton. but there is no pH at which every alanine molecule gains a proton.
Likewise, in strongly alkaline conditions, most of the alanine molecules will lose a proton. but there is no pH at which every alanine molecule loses a proton.
On reflection, I guess I misunderstood the question. When you say, “[Z] = [C+]”, I read it that you meant that every alanine molecule gains a proton. But now I reckon you mean that the concentration of zwitterions is equal to the concentration of positive ions. And similarly for when you say “[Z] = [A−]”.
I assume that each Kₐ is defined as [H⁺][ion without H]/[ion with H]. Because, in each scenario, [ion without H] = [ion with H], these cancel in the arithmetic so Kₐ=[H⁺].
For Kₐ=5.1 × 10⁻³, [H⁺]=5.1 × 10⁻³ and pH=-log(5.1 × 10⁻³)=2.3
For Kₐ=1.8 × 10⁻¹⁰, [H⁺]=1.8 × 10⁻¹⁰ and pH=-log(1.8 × 10⁻¹⁰)=9.7