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Calculate Ph of The Solution Containing 0.1m Hcn and Ka

Reviewed by Calculator Editorial Team

This calculator determines the pH of a solution containing 0.1M HCN (hydrocyanic acid) using the acid dissociation constant Kₐ. The calculation follows standard weak acid equilibrium principles.

Introduction

Hydrocyanic acid (HCN) is a weak acid that dissociates in water according to the equilibrium:

HCN ⇌ H⁺ + CN⁻

The pH of a solution containing HCN can be calculated using the acid dissociation constant (Kₐ) and the initial concentration of HCN. This guide explains the calculation process and provides an interactive calculator.

Formula

The pH of a weak acid solution is calculated using the Henderson-Hasselbalch equation:

pH = pKₐ + log10([A⁻]/[HA])

Where:

  • pKₐ is the negative logarithm of the acid dissociation constant
  • [A⁻] is the concentration of the conjugate base (CN⁻)
  • [HA] is the concentration of the weak acid (HCN)

For a solution where the initial concentration of HCN is 0.1M, the calculation simplifies to:

pH = pKₐ + log10(x/(0.1 - x))

Where x is the concentration of H⁺ ions at equilibrium.

Calculation Process

The calculation involves these steps:

  1. Determine the initial concentration of HCN (0.1M)
  2. Find the acid dissociation constant (Kₐ) for HCN
  3. Calculate the equilibrium concentration of H⁺ ions
  4. Compute the pH from the H⁺ concentration

The acid dissociation constant (Kₐ) for HCN is approximately 4.9 × 10⁻¹⁰ at 25°C.

Example Calculation

Let's calculate the pH of a 0.1M HCN solution with Kₐ = 4.9 × 10⁻¹⁰:

  1. Initial [HCN] = 0.1M
  2. Assume x = [H⁺] = [CN⁻] at equilibrium
  3. Set up the equilibrium equation: Kₐ = (x²)/(0.1 - x)
  4. Solve for x using the quadratic formula
  5. Calculate pH = -log10(x)

The result for this example is approximately pH 8.31.

FAQ

What is the pKₐ value for HCN?
The pKₐ for HCN is approximately 9.31 at 25°C, which corresponds to Kₐ = 4.9 × 10⁻¹⁰.
How does temperature affect the pH calculation?
The Kₐ value changes with temperature. For more precise calculations, use temperature-adjusted Kₐ values.
Can this calculator handle different concentrations of HCN?
Yes, the calculator accepts any initial concentration of HCN and uses the provided Kₐ value.
What is the significance of the pH result?
The pH indicates the acidity or basicity of the solution. Values below 7 are acidic, above 7 are basic.