Skip to main content
Pearson+ LogoPearson+ Logo
Ch.17 - Aqueous Ionic Equilibrium
All textbooksTro 4th EditionCh.17 - Aqueous Ionic EquilibriumProblem 136
Chapter 17, Problem 136

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).
Determine the \(\text{pK}_a\) of HCN: Look up the \(\text{pK}_a\) value for HCN, which is approximately 9.21.
Calculate the ratio \( \frac{[\text{A}^-]}{[\text{HA}]} \) using the Henderson-Hasselbalch equation: Rearrange the equation to find \( \frac{[\text{A}^-]}{[\text{HA}]} = 10^{(\text{pH} - \text{pK}_a)} \).
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.
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.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Buffer Solutions

A buffer solution is a system that resists changes in pH upon the addition of small amounts of acid or base. It typically consists 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 can maintain a pH of 9.8.
Recommended video:
Guided course
03:02
Buffer Solutions

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation relates the pH of a buffer solution to the concentration of its acid and conjugate base. It is expressed as pH = pKa + log([A-]/[HA]), where pKa is the negative logarithm of the acid dissociation constant. This equation is essential for calculating the required concentrations of HCN and NaCN to achieve the desired pH.
Recommended video:
Guided course
02:40
Henderson-Hasselbalch Equation

Osmotic Pressure

Osmotic pressure is the pressure required to prevent the flow of solvent into a solution through a semipermeable membrane. It can be calculated using the formula π = iCRT, where π is the osmotic pressure, i is the van 't Hoff factor, C is the molarity of the solution, R is the ideal gas constant, and T is the temperature in Kelvin. Understanding osmotic pressure is crucial for determining the concentrations of HCN and NaCN needed to achieve the specified osmotic pressure of 1.35 atm.
Recommended video:
Guided course
01:13
Osmotic Pressure Formula
Related Practice
Textbook Question

A 25.0-mL volume of a sodium hydroxide solution requires 19.6 mL of a 0.189 M hydrochloric acid for neutralization. A 10.0-mL volume of a phosphoric acid solution requires 34.9 mL of the sodium hydroxide solution for complete neutralization. Calculate the concentration of the phosphoric acid solution.

Textbook Question

What should the molar concentrations of benzoic acid and sodium benzoate be in a solution that is buffered at a pH of 4.55 and has a freezing point of -2.0 °C? (Assume complete dissociation of sodium benzoate and a density of 1.01 g/mL for the solution.)