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Difficulty: HardpH and pOH Scale and Calculations

What mass of calcium hydroxide, Ca(OH)2\text{Ca(OH)}_2, must be dissolved in distilled water to make 250 cm3250\text{ cm}^3 of an aqueous solution with a pH of 12.0012.00 at 25∘C25^\circ\text{C}? [Molar mass of Ca(OH)2=74.0 g mol−1][\text{Molar mass of Ca(OH)}_2 = 74.0\text{ g mol}^{-1}]

  1. 0.0925 g0.0925\text{ g}Answer
  2. B
    0.185 g0.185\text{ g}
  3. C
    0.370 g0.370\text{ g}
  4. D
    0.740 g0.740\text{ g}

Answer

0.0925 g0.0925\text{ g}
At 25∘C25^\circ\text{C}, pOH=14−12=2\text{pOH} = 14 - 12 = 2, giving [OH−]=10−2=0.01 mol dm−3[\text{OH}^-] = 10^{-2} = 0.01\text{ mol dm}^{-3}. Because Ca(OH)2\text{Ca(OH)}_2 produces two OH−\text{OH}^- ions per formula unit upon dissociation, the molar concentration of Ca(OH)2\text{Ca(OH)}_2 is 0.005 mol dm−30.005\text{ mol dm}^{-3}. In 250 cm3250\text{ cm}^3 (0.25 dm30.25\text{ dm}^3), the number of moles is 0.005×0.25=0.00125 mol0.005 \times 0.25 = 0.00125\text{ mol}. Multiplying by the molar mass (74.0 g mol−174.0\text{ g mol}^{-1}) gives 0.0925 g0.0925\text{ g}.

Step-by-Step Solution

1
Calculate the pOH and hydroxide ion concentration [OH−][\text{OH}^-] from the given pH.
pOH=14.00−12.00=2.00  ⟹  [OH−]=10−2.00=0.01 mol dm−3\text{pOH} = 14.00 - 12.00 = 2.00 \implies [\text{OH}^-] = 10^{-2.00} = 0.01\text{ mol dm}^{-3}.
Water ion product relationship pH+pOH=14.00\text{pH} + \text{pOH} = 14.00 at 25∘C25^\circ\text{C} connects pH to hydroxide ion concentration.
2
Determine the molar concentration of Ca(OH)2\text{Ca(OH)}_2.
[Ca(OH)2]=[OH−]2=0.01 mol dm−32=0.005 mol dm−3[\text{Ca(OH)}_2] = \frac{[\text{OH}^-]}{2} = \frac{0.01\text{ mol dm}^{-3}}{2} = 0.005\text{ mol dm}^{-3}.
Calcium hydroxide dissociates completely according to Ca(OH)2(aq)→Ca2+(aq)+2OH−(aq)\text{Ca(OH)}_2(aq) \rightarrow \text{Ca}^{2+}(aq) + 2\text{OH}^-(aq), yielding two moles of OH−\text{OH}^- per mole of base.
3
Calculate the number of moles of Ca(OH)2\text{Ca(OH)}_2 required for 250 cm3250\text{ cm}^3 of solution.
\text{Moles} = 0.005\text{ mol dm}^{-3} \times 0.25\text{ dm}^3 = 0.00125\text{ mol}.
Volume must be converted from cm3\text{cm}^3 to dm3\text{dm}^3 by dividing by 1000.
4
Calculate the required mass of Ca(OH)2\text{Ca(OH)}_2.
\text{Mass} = 0.00125\text{ mol} \times 74.0\text{ g mol}^{-1} = 0.0925\text{ g}.
Mass equals number of moles multiplied by molar mass.

Key Concept

Calculating required solute mass from pH for a dibasic base by converting pH to pOH, adjusting for stoichiometry, and scaling by volume and molar mass.
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Topics

pH and pOH Scale and Calculations

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