For an acetic acid-sodium acetate buffer to have a pH of 4.64, what molar ratio

of CH3COOH to Na+ CH3COO– is needed?

I know that the Ka value for acetic acid is 1.8e-5 and that I have to divide this value by the value of sodium acetate but I do not understand how you get the value for sodium acetate.

You want the molar ratio. The easy way to do that is to use the Henderson-Hasselbalch equation.

pH = pKa + log (base)/(acid)
4.64 = 4.74 + log(acetate)/(acetic acid)
Solve for the ratio of
acetate/acetic acid.

The other way to do it is

Ka = (H^+)(Ac^-)/(HAc)
Ka/(H^+) = (Ac^-)/(HAc)
1.8E-5/2.29E-5 = (Ac^-)/(HAc)

For the second way, where did the 2.29e-5 come from?

pH of 4.64. (H^+) = 2.29E-5

To determine the molar ratio of acetic acid (CH3COOH) to sodium acetate (CH3COONa), we need to use the equilibrium expression for the dissociation of acetic acid in water. The equilibrium expression is given by:

Ka = [CH3COO-][H3O+]/[CH3COOH]

Where Ka is the acid dissociation constant, [CH3COO-] is the concentration of the acetate ion, [H3O+] is the concentration of the hydronium ion (which can be assumed to be equal to the acetate ion concentration), and [CH3COOH] is the concentration of acetic acid.

Since we have a buffer solution, the pH is defined by the pKa value, which is the negative logarithm of the Ka value. In this case, since the pH is 4.64, we can determine the pKa value using:

pKa = -log10(Ka)

Now, let's solve the equation to find the ratio of the concentrations of CH3COOH to CH3COO-:

Ka = [CH3COO-][H3O+]/[CH3COOH]

Since [H3O+] is approximately equal to [CH3COO-], we can simplify the equation:

Ka = [CH3COO-]^2/[CH3COOH]

Rearranging the equation, we have:

[CH3COO-]/[CH3COOH] = √(Ka)

Substituting the value of Ka (1.8e-5), we can calculate the molar ratio:

[CH3COO-]/[CH3COOH] = √(1.8e-5)

Simplifying the expression:

[CH3COO-]/[CH3COOH] = 0.0042426

This means that for every 1 molecule of acetic acid (CH3COOH), we need a molar ratio of 0.0042426 sodium acetate (CH3COONa) molecules to achieve a pH of 4.64 in the acetic acid-sodium acetate buffer.