100 mL of a 0.1 mM buffer solution made from acetic acid and sodium acetate with pH 5.0 is diluted to 1 L. What is the pH of the diluted solution?

Question

100 mL of a 0.1 mM buffer solution made from acetic acid and sodium acetate with pH 5.0 is diluted to 1 L. What is the pH of the diluted solution?

Answer 1

To determine the pH of the diluted solution, we need to use the Henderson-Hasselbalch equation, which relates the pH of a buffer solution to the ratio of the concentration of the conjugate base to the concentration of the weak acid.

The Henderson-Hasselbalch equation is given by:

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

Where:
- pH is the desired pH of the solution.
- pKa is the negative logarithm of the acid dissociation constant of the weak acid.
- [A-] is the concentration of the conjugate base.
- [HA] is the concentration of the weak acid.

In this case, acetic acid (CH3COOH) is a weak acid, and sodium acetate (CH3COONa) is its conjugate base. The pKa value for acetic acid is 4.76, which we can use in the Henderson-Hasselbalch equation.

First, we need to calculate the concentrations of acetic acid and sodium acetate in the diluted solution.

Given:
- Initial volume = 100 mL = 0.1 L
- Initial concentration = 0.1 mM = 0.1 × 10^-3 mol/L

Since it's diluted to 1 L, the final volume of the solution is 1 L.

To find the final concentrations of acetic acid and sodium acetate in the diluted solution, we can use the dilution equation:

C1V1 = C2V2

Where:
- C1 = initial concentration
- V1 = initial volume
- C2 = final concentration (unknown)
- V2 = final volume

For acetic acid:
C1 = 0.1 × 10^-3 mol/L
V1 = 0.1 L
C2 = unknown
V2 = 1 L

Using the dilution equation:

(0.1 × 10^-3 mol/L)(0.1 L) = C2(1 L)

C2 = (0.1 × 10^-3 mol)/(0.1 L) = 10^-3 mol/L

So, the final concentration of acetic acid in the diluted solution is 10^-3 mol/L.

For sodium acetate:
C1 = 0.1 × 10^-3 mol/L
V1 = 0.1 L
C2 = unknown
V2 = 1 L

Using the dilution equation:

(0.1 × 10^-3 mol/L)(0.1 L) = C2(1 L)

C2 = (0.1 × 10^-3 mol)/(0.1 L) = 10^-3 mol/L

So, the final concentration of sodium acetate in the diluted solution is 10^-3 mol/L.

Now we can use the Henderson-Hasselbalch equation to calculate the pH of the diluted solution:

pH = pKa + log([A-]/[HA])
= 4.76 + log(10^-3 mol/L / 10^-3 mol/L)
= 4.76 + log(1)
= 4.76 + 0
= 4.76

Therefore, the pH of the diluted solution is 4.76.

Answer 2

In round numbers the pH is 5.0. You dilute the base along with the acid and by the same amount; therefore, the ratio of base to acid stays the same and the pH doesn't change. Dilution has no effect on the pH of a buffer but of course we all know that has limitations.

100 mL of a 0.1 mM buffer solution made from acetic acid and sodium acetate with pH 5.0 is diluted to 1 L. What is the pH of the diluted solution?

21

To determine the pH of the diluted solution, we need to use the Henderson-Hasselbalch equation, which relates the pH of a buffer solution to the ratio of the concentration of the conjugate base to the concentration of the weak acid.

In round numbers the pH is 5.0. You dilute the base along with the acid and by the same amount; therefore, the ratio of base to acid stays the same and the pH doesn't change. Dilution has no effect on the pH of a buffer but of course we all know that has limitations.