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Calculate Ph of 10m Hcn That Is 0.007 Ionized

Reviewed by Calculator Editorial Team

This calculator determines the pH of a 10 molar solution of hydrogen cyanide (HCN) where 0.007 of the acid is ionized. The calculation uses the Henderson-Hasselbalch equation and assumes standard conditions.

Introduction

Hydrogen cyanide (HCN) is a weak acid with a pKa of approximately 9.21. When dissolved in water, it can partially ionize according to the equation:

HCN ⇌ H⁺ + CN⁻

For a 10 molar solution where only 0.007 of the acid is ionized, we can calculate the resulting pH using the Henderson-Hasselbalch equation.

Formula

The Henderson-Hasselbalch equation relates the pH of a buffer solution to the pKa of the acid and the ratio of conjugate base to acid:

pH = pKa + log₁₀([A⁻]/[HA])

Where:

  • pKa is the acid dissociation constant (9.21 for HCN)
  • [A⁻] is the concentration of the conjugate base (CN⁻)
  • [HA] is the concentration of the acid (HCN)

For our calculation, we'll use the given ionization ratio of 0.007.

Calculation

Given:

  • Initial concentration of HCN = 10 M
  • Fraction of HCN that is ionized = 0.007
  • pKa of HCN = 9.21

First, calculate the concentration of ionized HCN:

[H⁺] = [HCN] × fraction ionized = 10 × 0.007 = 0.07 M

Then, calculate the concentration of the conjugate base (CN⁻):

[CN⁻] = [H⁺] = 0.07 M

Now, apply the Henderson-Hasselbalch equation:

pH = pKa + log₁₀([CN⁻]/[HCN]) = 9.21 + log₁₀(0.07/10) = 9.21 + log₁₀(0.007) ≈ 9.21 - 2.15 ≈ 7.06

The calculated pH is approximately 7.06.

Interpretation

A pH of 7.06 indicates a slightly acidic solution. This result makes sense because:

  • The solution is diluted (10 M is extremely concentrated)
  • Only a small fraction (0.7%) of the HCN is ionized
  • The remaining HCN molecules are mostly unionized

Note: In reality, 10 M HCN would be extremely dangerous and would not behave as a simple weak acid due to its high concentration and potential for polymerization.

FAQ

What is the pKa of HCN?
The pKa of hydrogen cyanide is approximately 9.21 at standard conditions.
Why is the solution acidic despite the pH being near neutral?
The solution is acidic because the ionized fraction (0.7%) produces hydrogen ions, even though most HCN remains unionized.
Can this calculation be used for other weak acids?
Yes, the Henderson-Hasselbalch equation can be applied to any weak acid-base pair where the ionization ratio is known.
What happens if more HCN ionizes?
The pH would decrease further as more hydrogen ions are produced.