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Calculate The Ph of A 0.021 M Nacn Solution

Reviewed by Calculator Editorial Team

Calculating the pH of a 0.021 M NaCN solution requires understanding the dissociation of cyanide in water and applying the Henderson-Hasselbalch equation. This guide provides the precise calculation, explains the chemistry behind it, and helps you interpret the results.

Introduction

The pH of a solution is a measure of its acidity or basicity, defined as the negative logarithm of the hydrogen ion concentration. For a 0.021 M NaCN solution, we need to determine the pH considering the dissociation of cyanide in water.

Cyanide (CN⁻) is a weak base that reacts with water to form the cyanate ion (OCN⁻) and hydroxide ions (OH⁻). This reaction affects the pH of the solution, which we can calculate using the Henderson-Hasselbalch equation.

pH Calculation Formula

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

pH = pKa + log([Base]/[Acid])

Where:

  • pKa is the negative logarithm of the acid dissociation constant
  • [Base] is the concentration of the base (CN⁻)
  • [Acid] is the concentration of the conjugate acid (OCN⁻)

For the reaction of cyanide with water:

CN⁻ + H2O ⇌ OCN⁻ + OH⁻

The pKa for this reaction is approximately 9.6.

Worked Example

Let's calculate the pH of a 0.021 M NaCN solution:

  1. Assume the solution is at equilibrium, so [CN⁻] = [OCN⁻] = 0.021 M.
  2. Apply the Henderson-Hasselbalch equation:

    pH = pKa + log([CN⁻]/[OCN⁻]) = 9.6 + log(0.021/0.021) = 9.6 + log(1) = 9.6

  3. The calculated pH is 9.6, indicating a basic solution.

This example shows that a 0.021 M NaCN solution has a pH of 9.6, which is typical for basic solutions containing cyanide.

Interpreting Results

A pH of 9.6 for a 0.021 M NaCN solution indicates:

  • The solution is basic, as expected for a cyanide-containing solution.
  • The concentration of hydroxide ions (OH⁻) is higher than that of the cyanate ions (OCN⁻).
  • The solution is not strongly basic, as the pH is not extremely high.

Note: The actual pH may vary slightly depending on the exact conditions and the presence of other ions or impurities.

Frequently Asked Questions

What is the pH of a 0.021 M NaCN solution?
The pH of a 0.021 M NaCN solution is approximately 9.6, calculated using the Henderson-Hasselbalch equation.
Why is the pH of NaCN solution basic?
The pH is basic because cyanide (CN⁻) reacts with water to form hydroxide ions (OH⁻), increasing the concentration of OH⁻ relative to H⁺.
How does the concentration of NaCN affect the pH?
Increasing the concentration of NaCN increases the concentration of both CN⁻ and OCN⁻, but since the pKa is fixed, the pH remains approximately the same as long as the ratio [CN⁻]/[OCN⁻] is maintained.
Can the pH of a NaCN solution be calculated using other methods?
Yes, the pH can also be calculated using the equilibrium constant for the reaction between CN⁻ and H2O, but the Henderson-Hasselbalch equation provides a simpler and more direct approach.