[mrlucky0]

The problem: What percentage of acetic acid is ionized at pH 5.0? The pka of acetic acid is 4.76.

My Attempt:

I started with the Henderson Hasselbalch equation:

pH = pka + log ( [A-][H+]/[HA] )
5 = 4.76 + log ( [A-][H+]/[HA] )

For percent ionization, I think I need to solve for the ratio, [A-]/[HA]. But what about the [H+]? Alternatively I have seen a equation for % ionization but I have no clue why it works. I was hoping I could derive it from first principles or the HH equation. Can anyone help?

[mrlucky0]

The problem: What percentage of acetic acid is ionized at pH 5.0? The pka of acetic acid is 4.76.

My Attempt:

I started with the Henderson Hasselbalch equation:

pH = pka + log ( [A-][H+]/[HA] )
5 = 4.76 + log ( [A-][H+]/[HA] )


For percent ionization, I think I need to solve for the ratio, [A-]/[HA]. But what about the [H+]? Alternatively I have seen a equation for % ionization but I have no clue why it works. I was hoping I could derive it from first the HH equation. Can anyone help?

[AWK]

[H₃O⁺] = cα=K_a(1-α)/α
hence
α/(1-α)=[H3O+]/K_a
If α is small then 1-α ≈1

[mrlucky0]

Thanks for the reply AWK. I don't think I've stated by question very well. So here's another shot:

I'm working on a chemistry problem and I'm trying to follow the derivation for % ionization (of a weak acid or base) but I can't seem to understand how rearrangement of eq. 6 results in eq. 7.

In more general terms, I started with the Hendreson Hasselbalch equation:

pH = pka + log(A-/AH)

What I want to find is the % ionization: A-/(AH + A-)

Attached is the equation for percent ionization but I can't figure out how you derive it from the HH equation.

[AWK]

Put (6) into denominator of left side of (7) and rearrange

[mrlucky0]

Thanks!

[AWK]

Note, my first post is absolutely equivalent to your derivation without using HH equation