Calculate The Ph of A 0.200 M Hcn Solution
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Hydrogen cyanide (HCN) is a weak acid that dissociates in water to form the cyanide ion (CN⁻) and a hydrogen ion (H⁺). The pH of an HCN solution can be calculated using the Henderson-Hasselbalch equation, which relates the pH to the concentration of the acid and its conjugate base.
Introduction
The pH of a solution is a measure of its acidity or basicity. For weak acids like hydrogen cyanide (HCN), the pH can be calculated using the Henderson-Hasselbalch equation when the solution contains both the undissociated acid and its conjugate base.
HCN is a toxic compound that dissociates in water according to the following equilibrium:
HCN(aq) ⇌ H⁺(aq) + CN⁻(aq)
The dissociation constant (Ka) for HCN is approximately 6.2 × 10⁻¹⁰ at 25°C. This value indicates that HCN is a very weak acid.
pH Calculation Formula
The pH of an HCN solution can be calculated using the Henderson-Hasselbalch equation:
pH = pKa + log10([CN⁻]/[HCN])
Where:
- pKa is the negative logarithm of the acid dissociation constant (-log10(Ka))
- [CN⁻] is the concentration of the cyanide ion
- [HCN] is the concentration of the undissociated HCN
For a 0.200 M HCN solution, the concentration of HCN is 0.200 M. The concentration of CN⁻ can be calculated using the dissociation constant.
Worked Example
Let's calculate the pH of a 0.200 M HCN solution.
- First, determine the concentration of CN⁻ using the dissociation constant (Ka = 6.2 × 10⁻¹⁰).
- For a weak acid, the concentration of the conjugate base is approximately equal to the square root of the product of the acid dissociation constant and the initial concentration of the acid.
- Calculate [CN⁻] = √(Ka × [HCN]) = √(6.2 × 10⁻¹⁰ × 0.200) ≈ 0.00000249 M
- Calculate the pKa = -log10(6.2 × 10⁻¹⁰) ≈ 9.21
- Now apply the Henderson-Hasselbalch equation: pH = pKa + log10([CN⁻]/[HCN]) ≈ 9.21 + log10(0.00000249/0.200) ≈ 9.21 - 4.61 ≈ 4.60
The calculated pH of a 0.200 M HCN solution is approximately 4.60.
Interpreting Results
A pH of 4.60 indicates that the solution is acidic. This is expected because HCN is a weak acid. The pH value tells us that the solution contains more hydrogen ions (H⁺) than hydroxide ions (OH⁻).
It's important to note that the pH calculation assumes that the solution is at equilibrium and that the activity coefficients are close to 1. For more accurate results, especially at higher concentrations, activity coefficients should be considered.