Calculate the pH of a buffer solution prepared by dissolving 4.2 g of NaHCO3 and 5.3 g of Na2CO3 in 0.20 L of water. Will the pH change if the solution volume is increased by a factor of 10? Explain.

Verified step by step guidance

1. Step 1: Calculate the moles of NaHCO3 and Na2CO3. Use the molar mass of each compound to convert grams to moles. For NaHCO3, the molar mass is approximately 84.01 g/mol, and for Na2CO3, it is approximately 105.99 g/mol.
2. Step 2: Determine the concentrations of NaHCO3 and Na2CO3 in the buffer solution. Divide the moles of each compound by the initial volume of the solution (0.20 L) to find their molar concentrations.
3. Step 3: Use the Henderson-Hasselbalch equation to calculate the pH of the buffer solution. The equation is: \( \text{pH} = \text{pK}_a + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right) \), where \( \text{pK}_a \) is the negative logarithm of the acid dissociation constant for HCO3⁻, \([\text{A}^-]\) is the concentration of the base (CO3²⁻), and \([\text{HA}]\) is the concentration of the acid (HCO3⁻).
4. Step 4: Consider the effect of increasing the solution volume by a factor of 10. Since both the concentrations of the acid and base will decrease by the same factor, the ratio \( \frac{[\text{A}^-]}{[\text{HA}]} \) remains constant, and thus the pH of the buffer solution will not change.
5. Step 5: Conclude that the pH of the buffer solution is independent of dilution, as long as the ratio of the concentrations of the conjugate base and acid remains constant. This is a characteristic property of buffer solutions.