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Calculate The Ph of A 0.021 M Nacn Solution

Reviewed by Calculator Editorial Team

Calculating the pH of a sodium cyanide (NaCN) solution involves understanding the dissociation of the weak acid HCN and the common ion effect. This guide provides a step-by-step explanation of the calculation process, including the formula, assumptions, and interpretation of results.

Introduction

Sodium cyanide (NaCN) is a strong electrolyte that dissociates completely in water, producing Na⁺ and CN⁻ ions. The cyanide ion (CN⁻) reacts with water to form the weak acid HCN and hydroxide ions (OH⁻), which affects the pH of the solution.

To calculate the pH of a 0.021 M NaCN solution, we need to consider the dissociation of HCN and the common ion effect. The calculation involves determining the concentration of HCN and OH⁻, then using the concentration of OH⁻ to find the pH.

Formula

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

  1. Determine the concentration of HCN formed from the dissociation of CN⁻.
  2. Calculate the concentration of OH⁻ using the dissociation constant of HCN.
  3. Use the concentration of OH⁻ to find the pH.
pH = 14 - pOH pOH = -log[OH⁻] [OH⁻] = √(Kw × Kb / Ka) Where: Kw = 1.0 × 10⁻¹⁴ (ion product of water) Kb = 4.9 × 10⁻¹⁰ (dissociation constant of CN⁻) Ka = 4.9 × 10⁻¹⁰ (dissociation constant of HCN)

Calculation

For a 0.021 M NaCN solution:

  1. The concentration of HCN is equal to the concentration of CN⁻, which is 0.021 M.
  2. The concentration of OH⁻ is calculated using the formula:
    [OH⁻] = √(1.0 × 10⁻¹⁴ × 4.9 × 10⁻¹⁰ / 4.9 × 10⁻¹⁰) = √(1.0 × 10⁻¹⁴) = 1.0 × 10⁻⁷ M
  3. The pOH is calculated as:
    pOH = -log(1.0 × 10⁻⁷) = 7
  4. The pH is calculated as:
    pH = 14 - 7 = 7

The pH of a 0.021 M NaCN solution is 7.

Interpretation

A pH of 7 indicates that the solution is neutral. This result is expected because the dissociation of HCN and the formation of OH⁻ are balanced by the common ion effect, resulting in equal concentrations of H⁺ and OH⁻.

In practical terms, a neutral pH means that the solution does not have a significant excess of either acid or base. This is important in applications where precise pH control is required, such as in chemical synthesis or environmental monitoring.

FAQ

Why is the pH of a 0.021 M NaCN solution 7?
The pH is 7 because the dissociation of HCN and the formation of OH⁻ are balanced, resulting in equal concentrations of H⁺ and OH⁻.
What factors affect the pH of a NaCN solution?
The pH is primarily affected by the dissociation of HCN and the common ion effect, which balances the concentrations of H⁺ and OH⁻.
How does the concentration of NaCN affect the pH?
The pH remains neutral (7) regardless of the NaCN concentration because the common ion effect balances the dissociation of HCN.
Can the pH of a NaCN solution be adjusted?
Yes, the pH can be adjusted by adding acid or base to the solution, which will disrupt the balance between H⁺ and OH⁻.
What are the safety considerations when working with NaCN solutions?
NaCN is highly toxic and should be handled with appropriate protective equipment. Proper disposal procedures must be followed to prevent environmental contamination.