Calculate the pH of a buffer solution that is 0.20 M in HCN and 0.12 M in NaCN. Will the pH change if the solution is diluted by a factor of 2? Explain.

Verified step by step guidance

1. First, identify the acid and its conjugate base in the buffer solution. In this case, HCN is the weak acid and CN- (from NaCN) is the conjugate base.
2. Next, use the Henderson-Hasselbalch equation to calculate the pH of the buffer solution. The equation is pH = pKa + log([A-]/[HA]), where [A-] is the concentration of the base (CN-) and [HA] is the concentration of the acid (HCN). The pKa of HCN can be found in a table of acid dissociation constants.
3. Substitute the given concentrations into the Henderson-Hasselbalch equation and solve for pH.
4. To determine if the pH will change when the solution is diluted by a factor of 2, consider that the ratio of [A-]/[HA] will remain the same because both the acid and its conjugate base are being diluted by the same factor. Therefore, the pH of the solution will not change.
5. Finally, remember that the effectiveness of a buffer is determined by its capacity, which is the amount of acid or base the buffer can neutralize before the pH begins to change significantly. Diluting the buffer will decrease its buffer capacity, meaning it will be less able to resist changes in pH when an acid or base is added.

Key Concepts

Buffer Solutions

Buffer solutions are mixtures that resist changes in pH when small amounts of acid or base are added. They typically consist of a weak acid and its conjugate base, or a weak base and its conjugate acid. In this case, HCN (a weak acid) and NaCN (its conjugate base) form a buffer that helps maintain a stable pH.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is a mathematical formula used to calculate the pH of a buffer solution. It is expressed as pH = pKa + log([A-]/[HA]), where [A-] is the concentration of the conjugate base and [HA] is the concentration of the weak acid. This equation highlights the relationship between the concentrations of the acid and its conjugate base in determining the pH.

Dilution and pH Stability

When a buffer solution is diluted, the concentrations of both the weak acid and its conjugate base decrease proportionally. However, the ratio of [A-] to [HA] remains constant, which means the pH of the buffer does not change significantly upon dilution. This property is what makes buffers effective in maintaining pH levels in various chemical and biological processes.