You make 1.00 L of a buffered solution (pH = 5.10) by mixing propanoic acid and potassium propanoate. You have 1.00 M solutions of each component of the buffered solution. What volume of each solution do you mix to make such a buffered solution?
propanoic acid
potassium propanoate
To determine the volume of each solution required to make the buffered solution, we can use the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
In this case, propanoic acid (HA) and potassium propanoate (A-) are the conjugate acid-base pair present in the buffer solution.
Given:
pH = 5.10
[HA] = 1.00 M
[A-] = 1.00 M
We need to find the volumes of propanoic acid and potassium propanoate solutions required.
Let's assume we mix x liters of the propanoic acid solution and (1.00 - x) liters of the potassium propanoate solution.
Now, let's calculate the concentration of propanoic acid and potassium propanoate in the final buffered solution.
[HA] = (moles of propanoic acid) / (total volume of solution) = (1.00 M) * x L
[A-] = (moles of potassium propanoate) / (total volume of solution) = (1.00 M) * (1.00 - x) L
Using the Henderson-Hasselbalch equation:
5.10 = pKa + log([A-]/[HA])
Rearranging the equation, we get:
4.10 = log([A-]/[HA])
10^(4.10) = [A-]/[HA]
Now, substitute the values we know:
10^(4.10) = [(1.00 - x) L] / [x L]
10^(4.10) = (1.00 - x) / x
Solve this equation to find the value of x, which represents the volume of propanoic acid solution in liters. Subtract x from 1.00 to get the volume of potassium propanoate solution.
Please note that to solve this equation, you will need to use logarithmic calculations or a calculator. The result will give you the volume of each solution required to make the buffered solution.