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An aqueous solution of barium hydroxide is standardized by titration with a 0.167 M solution of perchloric acid. If 12.8 mL of base are required to neutralize 25.4 mL of the acid, what is the molarity of the barium hydroxide solution?

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Answer:

  • 0.166M

Explanation:

1. Barium hidroxide

Barium hydroxide is a strong base that ionizes as per the equation:

       [tex]Ba(OH)_2\rightarrow Ba^{+2}+2OH^-[/tex]

Thus, every mole of Ba(OH)₂ yields 2 moles of OH⁻.

2. Perchloric acid

Perchloric acid is a strong acid whose ionization may be represented by the following chemical equation:

         [tex]HClO_4\rightarrow H^+ClO_4^-[/tex]

Thus, every mole of HClO₄ yields 1 mole of H⁺.

3. Calculate the number of moles of perchloric acid and H⁺:

  • #moles of HClO₄ = Molarity × Volume in liters
  • #moles HClO₄ = 0.167M × 25.4mL × 1L / 1,000m: = 0.0042418‬mol

The number of moles of H⁺ is equal to the number of moles of HClO₄

  • #moles of  H⁺ = 0.0042418 mol

4. Calculate the number of moles of Ba(OH)₂

When the solution is neutralized the number of moles of OH⁻ is equal to the number of moles of H⁺

  • #moles of OH⁻ = 0.0042418

The number of moles of Ba(OH)₂ is half of the number of moles of OH⁻:

  • #moles of Ba(OH)₂ = 0.0042418/2 = 0.0021209 mol Ba(OH)₂

5. Calculate the molarity of the Ba(OH)₂ solution:

  • Molarity = number of moles / volume in liters
  • Molarity = 0.0021209mol / 0.0128liters = 0.16569 ≈ 0.166M