You are asked to prepare 2.0 L of an HCN/NaCN buffer that has a pH of 9.8 and an osmotic pressure of 1.35 atm at 298 K. What masses of HCN and NaCN should you use to prepare the buffer? (Assume complete dissociation of NaCN.)

Verified step by step guidance

1. Identify the relevant equations: Use the Henderson-Hasselbalch equation for buffer solutions: \( \text{pH} = \text{pK}_a + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right) \), where \([\text{A}^-]\) is the concentration of the conjugate base (NaCN) and \([\text{HA}]\) is the concentration of the weak acid (HCN).
2. Determine the \(\text{pK}_a\) of HCN: Look up the \(\text{pK}_a\) value for HCN, which is approximately 9.21.
3. Calculate the ratio \( \frac{[\text{A}^-]}{[\text{HA}]} \) using the Henderson-Hasselbalch equation: Rearrange the equation to find \( \frac{[\text{A}^-]}{[\text{HA}]} = 10^{(\text{pH} - \text{pK}_a)} \).
4. Use the osmotic pressure equation to find the total molarity: The osmotic pressure equation is \( \Pi = iMRT \), where \( \Pi \) is the osmotic pressure, \( i \) is the van't Hoff factor (which is 2 for NaCN due to complete dissociation), \( M \) is the molarity, \( R \) is the ideal gas constant (0.0821 L·atm/mol·K), and \( T \) is the temperature in Kelvin.
5. Solve for the individual concentrations of HCN and NaCN: Use the total molarity from the osmotic pressure equation and the ratio from the Henderson-Hasselbalch equation to set up a system of equations. Solve for \([\text{HCN}]\) and \([\text{NaCN}]\), then convert these concentrations to masses using their respective molar masses.