What are the concentrations of acetic acid (pKa = 4.76) and acetate in a buffer solution of 0.15 M at pH 4.5?
Please help me do this problem. I have no idea how to do it.
To determine the concentrations of acetic acid (CH3COOH) and acetate (CH3COO-) in a buffer solution, we can use the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
In this case, pKa = 4.76, pH = 4.5, and [A-] represents the concentration of acetate while [HA] represents the concentration of acetic acid.
Let's solve for [A-]:
4.5 = 4.76 + log([A-]/[HA])
Rearrange the equation:
log([A-]/[HA]) = 4.5 - 4.76
log([A-]/[HA]) = -0.26
To eliminate the logarithm, we need to convert it back to a numerical expression:
[A-]/[HA] = 10^(-0.26)
[A-]/[HA] = 0.442
Now we know that the ratio of acetate to acetic acid in the buffer solution is 0.442.
Since the total concentration of the buffer solution is given as 0.15 M, we can set up the following equation:
[A-] + [HA] = 0.15
Substitute [A-]/[HA] = 0.442 into the equation:
0.442[HA] + [HA] = 0.15
Combine like terms:
1.442[HA] = 0.15
Solve for [HA]:
[HA] = 0.15 / 1.442
[HA] ≈ 0.104 M
Now, substitute the value of [HA] back into the equation to find [A-]:
[A-] = 0.442 * [HA]
[A-] ≈ 0.442 * 0.104
[A-] ≈ 0.046 M
Therefore, in a buffer solution of 0.15 M at pH 4.5, the concentration of acetic acid (CH3COOH) is approximately 0.104 M, and the concentration of acetate (CH3COO-) is approximately 0.046 M.