Calculate The Ph of A 0.300 M Hcn Solution

Introduction

The pH of a solution is a measure of its acidity or alkalinity. For a weak acid like HCN, the pH depends on the concentration of the acid and its dissociation constant. The dissociation of HCN in water can be represented by the equation:

The dissociation constant (Ka) for HCN is approximately 4.9 × 10⁻¹⁰ at 25°C. This value indicates that HCN is a very weak acid, meaning it does not dissociate completely in water.

Formula

The pH of a solution containing a weak acid can be calculated using the Henderson-Hasselbalch equation:

Where:

• pKa is the negative logarithm of the acid dissociation constant (-log(Ka))
• [CN⁻] is the concentration of the conjugate base (cyanide ion)
• [HCN] is the concentration of the weak acid (hydrocyanic acid)

For a solution where the concentration of HCN is known and assuming that the concentration of CN⁻ is negligible (since HCN is a weak acid), the pH can be approximated using the formula:

Calculation

To calculate the pH of a 0.300 M HCN solution:

1. Determine the pKa value for HCN. The pKa is -log(Ka) = -log(4.9 × 10⁻¹⁰) ≈ 9.31.
2. Take the negative logarithm of the HCN concentration: -log(0.300) ≈ 0.5229.
3. Subtract the log of the HCN concentration from the pKa: 9.31 - 0.5229 ≈ 8.7871.

The pH of the 0.300 M HCN solution is approximately 8.79.

Interpretation

A pH of 8.79 indicates that the solution is slightly basic. This is expected because HCN is a weak acid and does not fully dissociate in water. The solution contains more OH⁻ ions than H₃O⁺ ions, resulting in a basic pH.

To verify this result, you can compare it with the pH of a solution containing a stronger acid, such as hydrochloric acid (HCl), which would have a much lower pH due to complete dissociation.