How many milliliters of a 0.250 M acetic acid solution must be added to 50.0
mL of a 0.750 M NaOH solution to produce a buffer solution with
pH = 4.500 ?
The pH is given by which we can calculate the concentration of [H+]
How do we approach the problem from there?
Use the Henderson-Hasselbalch equation. Get data from the equation and an ICE chart.
millimoles NaOH = M x mL = apprx 38 but you need a bettr answer than that
millimols CH3COOH = x
.......CH3COOH + NaOH ==> CH3COONa + H2O
I........0.......38.........0.........0
add......x.............................
C.......x+0.....-38.........38.....
E........x........0.........38
Substitute the E line into HH equation and solve for x = millimols CH3COOH.
Then M = millimols/mL
YOu know M and mmols of the acid, solve for mL.
To approach this problem, we can use the Henderson-Hasselbalch equation for a buffer solution:
pH = pKa + log([A-]/[HA])
Since acetic acid (CH3COOH) is a weak acid and its conjugate base is acetate (CH3COO-), we can write the equation as:
pH = pKa + log([CH3COO-]/[CH3COOH])
The pKa of acetic acid is given as 4.76. We are given the pH as 4.500, so we can rearrange the equation to solve for the ratio of acetate to acetic acid:
log([CH3COO-]/[CH3COOH]) = pH - pKa
log([CH3COO-]/[CH3COOH]) = 4.500 - 4.76
log([CH3COO-]/[CH3COOH]) = -0.26
Now, we need to determine the desired concentrations of acetate and acetic acid in the final buffer solution. Let's assume that x milliliters of the 0.250 M acetic acid solution are added to the 50.0 mL of the 0.750 M NaOH solution. After mixing them, the total volume will be (50.0 + x) mL.
According to the equation, we have:
[CH3COO-] = (0.250 M * x mL) / (50.0 mL + x mL)
[CH3COOH] = 0.750 M
Substituting these concentrations into the equation, we have:
log((0.250 * x) / (50.0 + x)) = -0.26
Now, we can solve for x by converting the equation to exponential form:
10^(-0.26) = (0.250 * x) / (50.0 + x)
0.3981 = (0.250 * x) / (50.0 + x)
0.3981 * (50.0 + x) = 0.250 * x
19.905 + 0.3981x = 0.250x
0.3981x - 0.250x = -19.905
0.1481x = -19.905
x = -19.905 / 0.1481
x ≈ -134.43 mL
Since negative volume doesn't make sense, it means there is no need to add any acetic acid solution to the NaOH solution because it already has a higher concentration of hydroxide ions, which will neutralize the acetic acid. Therefore, the answer is 0 mL.
To find the answer to this question, we need to first understand how a buffer solution works. A buffer solution is a solution that can resist changes in pH when small amounts of acid or base are added to it.
In this case, we have acetic acid (CH3COOH) and sodium hydroxide (NaOH), which can react to form water and sodium acetate (CH3COONa). The acetate ion (CH3COO-) acts as a weak base, and acetic acid acts as a weak acid. Together, they create a buffer solution.
To approach the problem, we need to use the Henderson-Hasselbalch equation, which relates the pH of a buffer solution to the concentration of the acid and its conjugate base. The equation is as follows:
pH = pKa + log([A-]/[HA])
Where:
- pH is the desired pH of the buffer solution (4.500 in this case)
- pKa is the negative logarithm of the acid dissociation constant (Ka) of the weak acid
- [A-] is the concentration of the conjugate base (CH3COO-)
- [HA] is the concentration of the acid (CH3COOH)
In this case, we are given the pH and we want to find the concentration of acetic acid, [HA], which we can then use to calculate the volume of the acetic acid solution.
1. Calculate the pKa of acetic acid:
The pKa value for acetic acid is approximately 4.75.
2. Substitute the given values into the Henderson-Hasselbalch equation:
4.500 = 4.75 + log([A-]/[HA])
3. Rearrange the equation to solve for [A-]/[HA]:
[A-]/[HA] = 10^(pH - pKa)
4. Calculate the ratio [A-]/[HA]:
[A-]/[HA] = 10^(4.500 - 4.75) = 10^(-0.25) = 0.5623
5. Since the concentration of the conjugate base and the acid are equal, we can set them both as 'x':
[A-] = x
[HA] = x
6. Now we can use the given information about the NaOH solution to set up a mole ratio equation:
(0.750 M NaOH) * (50.0 mL) = (0.5623 x M) * (V mL)
7. Solve for V, the volume of the acetic acid solution to be added:
V = (0.750 M NaOH) * (50.0 mL) / (0.5623 M)
By following these steps, you can get the value for V, which is the volume of the acetic acid solution (in milliliters) that needs to be added to the 50.0 mL of the NaOH solution to produce the desired buffer solution with a pH of 4.500.