Calculate The Ph of Each of The Following Solutions Nacn

Introduction

The pH of a solution is a measure of its acidity or alkalinity. For sodium cyanide (NaCN) solutions, the pH can be calculated using the concentration of the dissolved cyanide ions (CN⁻). Since NaCN is a strong electrolyte, it dissociates completely in water, producing Na⁺ and CN⁻ ions.

The pH of a solution containing CN⁻ ions is determined by the concentration of the cyanide ions. The cyanide ion (CN⁻) is a weak base, meaning it can accept a proton (H⁺) to form the cyanide acid (HCN), which is a weak acid. This equilibrium affects the pH of the solution.

pH Calculation Formula

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

1. Determine the concentration of the CN⁻ ions in the solution.
2. Calculate the concentration of the HCN formed by the equilibrium reaction between CN⁻ and H₂O.
3. Use the concentration of HCN to calculate the pH.

Worked Examples

Let's calculate the pH of a 0.1 M NaCN solution.

1. Since NaCN is a strong electrolyte, it dissociates completely to give [CN⁻] = 0.1 M.
2. The equilibrium reaction between CN⁻ and H₂O is:
3. CN⁻ + H₂O ⇌ HCN + OH⁻
4. The equilibrium constant (K_b) is 4.9 × 10⁻¹⁴.
5. Let x be the concentration of HCN and OH⁻ formed.
6. The equilibrium expression is:
7. K_b = [HCN][OH⁻]/[CN⁻] = x²/0.1 = 4.9 × 10⁻¹⁴
8. Solving for x:
9. x² = 4.9 × 10⁻¹⁵
10. x ≈ 7.0 × 10⁻⁸ M
11. Now, calculate the pH:
12. pH = pK_a + log([HCN]/[CN⁻]) = 9.21 + log(7.0 × 10⁻⁸ / 0.1)
13. pH = 9.21 + log(7.0 × 10⁻⁷)
14. pH = 9.21 - 6.15 = 3.06

The pH of a 0.1 M NaCN solution is approximately 3.06.