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.