what is the [CH3COO^-]/[CH3COOH] ration in an acetate buffer (Ka=1.76 x 10^-5) at pH 3.8? show calculations

Use the Henderson-Hasselbalch equation.

pH = pKa + log[(base)(acid)]
3.8 = 4.75 + log [(CH3COO^-)/(CH3COOH)]
Solve for the ratio.
If I didn't goof on the calculator I get approximately 0.1.

To calculate the ratio of [CH3COO^-]/[CH3COOH] in an acetate buffer solution, we can use the Henderson-Hasselbalch equation:

pH = pKa + log([A^-]/[HA])

In this case, CH3COO^- represents the conjugate base and CH3COOH represents the weak acid. The pKa value for acetic acid (CH3COOH) is given as 1.76 x 10^-5.

Let's substitute the given values into the equation:

pH = 3.8
pKa = -log(1.76 x 10^-5)

First, let's find the pKa value:

pKa = -log(1.76 x 10^-5)
pKa ≈ 4.753

Now, let's rearrange the Henderson-Hasselbalch equation to solve for the ratio [A^-]/[HA]:

log([A^-]/[HA]) = pH - pKa

[A^-]/[HA] = 10^(pH - pKa)

Substituting the given values:

[A^-]/[HA] = 10^(3.8 - 4.753)
[A^-]/[HA] = 10^(-0.953)

Now, calculate the ratio:

[A^-]/[HA] = 0.106

Therefore, the [CH3COO^-]/[CH3COOH] ratio in the acetate buffer at pH 3.8 is approximately 0.106.

To find the [CH3COO-]/[CH3COOH] ratio in an acetate buffer at pH 3.8, we need to use the Henderson-Hasselbalch equation for a weak acid-buffer system:

pH = pKa + log([A-]/[HA])

Here:
pH = 3.8 (Given)
pKa = -log(Ka) = -log(1.76 x 10^-5) = 4.75 (Given)

We want to find [A-]/[HA], which represents the ratio of the concentration of the conjugate base (acetate ion, CH3COO-) to the concentration of the weak acid (acetic acid, CH3COOH).

Let's substitute the values into the Henderson-Hasselbalch equation and solve for [A-]/[HA]:

3.8 = 4.75 + log([A-]/[HA])

Simplifying the equation:

-0.95 = log([A-]/[HA])

To remove the logarithm, we can rewrite the equation in exponential form:

10^-0.95 = [A-]/[HA]

Find the value of 10^-0.95 using a scientific calculator:

10^-0.95 ≈ 0.1129

So, the [A-]/[HA] ratio is approximately 0.1129.

This means that for every 1 molecule of acetic acid (CH3COOH), there are approximately 0.1129 molecules of acetate ion (CH3COO-) in the acetate buffer at pH 3.8.