Calculate the pH of a buffer made of a 0.4 M of acetic acid and 0.5M of sodium acetate. The Ka for the acetic acid is 1.8 x 10-5.
Use the Henderson-Hasselbalch equation.
To calculate the pH of a buffer solution, we need to consider the principles of acid-base equilibrium and the Henderson-Hasselbalch equation. The Henderson-Hasselbalch equation states that the pH of a buffer is determined by the ratio of the concentrations of the acid and its conjugate base.
In this case, acetic acid (CH3COOH) is the weak acid, and sodium acetate (CH3COONa) is the conjugate base.
The Henderson-Hasselbalch equation is given by:
pH = pKa + log([A-]/[HA])
Where:
pH = the pH of the solution
pKa = the negative logarithm of the acid dissociation constant (Ka) of the weak acid
[A-] = the concentration of the conjugate base (CH3COO-) of the weak acid
[HA] = the concentration of the weak acid (CH3COOH)
Let's calculate the pH step-by-step:
Step 1: Calculate the pKa:
pKa = -log(Ka)
= -log(1.8 x 10^-5)
≈ 4.74
Step 2: Calculate the ratio [A-]/[HA]:
[A-]/[HA] = [CH3COO-]/[CH3COOH]
= 0.5 M / 0.4 M
= 1.25
Step 3: Substitute the values into the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
= 4.74 + log(1.25)
Step 4: Use logarithmic properties to simplify the equation:
pH = 4.74 + log(1.25)
= 4.74 + 0.097
Step 5: Calculate the pH:
pH ≈ 4.837
Therefore, the pH of the buffer solution made of 0.4 M acetic acid and 0.5 M sodium acetate is approximately 4.837.