A buffer is prepared by adding 300.0 mL of 2.0 M NaOH to 500.0 mL of 2.0 M CH3COOH. What is the pH of this buffer? Ka = 1.8 × 10-5
To find the pH of this buffer, we need to calculate the concentration of the hydronium ion (H3O+) in the solution, which will determine the pH.
A buffer solution is formed by the combination of a weak acid and its conjugate base (or a weak base and its conjugate acid). In this case, CH3COOH is a weak acid, and NaOH is a strong base. When a weak acid is mixed with its conjugate base, it forms a buffer solution that can resist changes in pH when small amounts of acid or base are added.
To solve this problem, we need to follow a few steps:
Step 1: Write the balanced equation for the dissociation of CH3COOH.
CH3COOH (aq) ⇌ CH3COO- (aq) + H+ (aq)
Step 2: Calculate the number of moles of CH3COOH and CH3COO-. We can use the formula n = c * V, where n is the number of moles, c is the concentration, and V is the volume in liters.
For CH3COOH:
n(CH3COOH) = c(CH3COOH) * V(CH3COOH)
= 2.0 M * 0.5 L
= 1.0 mol
For CH3COO-:
The number of moles of CH3COO- can be assumed to be the same as CH3COOH since they are present in equal concentrations in the buffer solution.
Step 3: Calculate the concentration of CH3COOH and CH3COO- in the buffer solution.
The total volume of the buffer solution is the sum of the volumes of CH3COOH and NaOH:
V(total) = V(CH3COOH) + V(NaOH)
= 0.5 L + 0.3 L
= 0.8 L
For CH3COOH:
c(CH3COOH) = n(CH3COOH) / V(total)
= 1.0 mol / 0.8 L
= 1.25 M
For CH3COO-:
c(CH3COO-) = c(CH3COOH)
= 1.25 M
Step 4: Calculate the concentration of H+ ions using the equation for the dissociation of CH3COOH.
[H+] = Ka * (c(CH3COOH) / c(CH3COO-))
= (1.8 × 10^-5) * (1.25 M / 1.25 M)
= 1.8 × 10^-5 M
Step 5: Calculate the pH using the formula pH = -log10[H+].
pH = -log10(1.8 × 10^-5)
≈ 4.74
Therefore, the pH of this buffer solution is approximately 4.74.