Cal11 calculator
Search calculator...

Calculate The Ph of A 0.400 M Hcn Solution

Reviewed by Calculator Editorial Team

Calculating the pH of a 0.400 M HCN (hydrogen cyanide) solution requires understanding the weak acid properties of HCN and applying the Henderson-Hasselbalch equation. This guide explains the chemistry behind the calculation and provides a precise method for determining the pH.

Introduction

Hydrogen cyanide (HCN) is a weak acid with a dissociation constant (Ka) of 4.9 × 10⁻¹⁰ at 25°C. When dissolved in water, it forms the cyanide ion (CN⁻) and releases hydrogen ions (H⁺). The pH of the solution depends on the concentration of these hydrogen ions.

The pH of a solution is defined as the negative logarithm (base 10) of the hydrogen ion concentration:

pH = -log[H⁺]

For weak acids, the pH can be calculated using the dissociation constant and the concentration of the acid.

pH Calculation

The pH of a solution of a weak acid can be calculated using the following steps:

  1. Determine the dissociation constant (Ka) of the acid. For HCN, Ka = 4.9 × 10⁻¹⁰.
  2. Calculate the concentration of hydrogen ions using the Ka expression.
  3. Convert the hydrogen ion concentration to pH using the formula above.

The Ka expression for HCN is:

Ka = [H⁺][CN⁻]/[HCN]

For a dilute solution, [H⁺] ≈ [CN⁻], so the equation simplifies to:

[H⁺] = √(Ka × [HCN])

Then, the pH is calculated as:

pH = -log(√(Ka × [HCN]))

For a 0.400 M HCN solution:

pH = -log(√(4.9 × 10⁻¹⁰ × 0.400)) ≈ 9.33

Worked Example

Let's calculate the pH of a 0.400 M HCN solution step by step.

  1. Given: [HCN] = 0.400 M, Ka = 4.9 × 10⁻¹⁰
  2. Calculate [H⁺]: [H⁺] = √(4.9 × 10⁻¹⁰ × 0.400) ≈ √(1.96 × 10⁻¹⁰) ≈ 1.4 × 10⁻⁵ M
  3. Calculate pH: pH = -log(1.4 × 10⁻⁵) ≈ 4.85

The calculated pH of a 0.400 M HCN solution is approximately 4.85.

Note: The actual pH may differ slightly due to the assumption that [H⁺] ≈ [CN⁻]. For more precise calculations, iterative methods or numerical solvers may be needed.

FAQ

What is the dissociation constant of HCN?
The dissociation constant (Ka) of HCN is approximately 4.9 × 10⁻¹⁰ at 25°C.
How does temperature affect the pH of an HCN solution?
The Ka value changes with temperature, which affects the pH calculation. At higher temperatures, Ka increases, and the pH of the solution decreases.
Can the pH of an HCN solution be calculated using the Henderson-Hasselbalch equation?
No, the Henderson-Hasselbalch equation is used for buffer solutions, not for calculating the pH of a pure weak acid solution.
What is the pH of a 0.100 M HCN solution?
The pH of a 0.100 M HCN solution is approximately 9.33.