Home / AP Chemistry 7.11 Introduction to Solubility Equilibria – Exam Style questions – FRQs

AP Chemistry 7.11 Introduction to Solubility Equilibria - Exam Style questions - FRQs- New Syllabus

Question

Strontium hydroxide dissolves in water according to the following equation. The \( K_{sp} \) expression for strontium hydroxide is provided.
\( \mathrm{Sr(OH)}_{2}(s) \rightleftharpoons \mathrm{Sr}^{2+}(aq) + 2\,\mathrm{OH}^{-}(aq) \qquad K_{sp} = [\mathrm{Sr}^{2+}][\mathrm{OH}^{-}]^{2} \)
(a) A student draws the particulate diagram shown to represent the ions present in an aqueous solution of \( \mathrm{Sr(OH)}_{2} \). (Water molecules are intentionally omitted.) Identify the error in the student’s drawing.
(b) The student prepares a saturated solution by adding excess \( \mathrm{Sr(OH)}_{2}(s) \) to distilled water and stirring until no more solid dissolves. The student then determines that \( [\mathrm{Sr}^{2+}] = 0.043\ \mathrm{M} \) in the solution.
(i) Calculate the value of \( [\mathrm{OH}^{-}] \) in the solution.
(ii) Calculate the value of \( K_{sp} \) for \( \mathrm{Sr(OH)}_{2} \).
(c) The student prepares a second saturated solution of \( \mathrm{Sr(OH)}_{2} \) in aqueous \( 0.10\ \mathrm{M\ Sr(NO}_{3})_{2} \) instead of water. Will the value of \( [\mathrm{OH}^{-}] \) in the second solution be greater than, less than, or equal to the value in the first solution? Justify your answer. (Assume constant temperature.)

Most-appropriate topic codes (AP Chemistry):

• Topic \( 7.11 \) — Introduction to Solubility Equilibria (Parts \( \mathrm{(a)} \), \( \mathrm{(b)(i)} \), \( \mathrm{(b)(ii)} \))
• Topic \( 7.12 \) — Common-Ion Effect (Part \( \mathrm{(c)} \))
▶️ Answer/Explanation

(a)
For a correct answer:
Accept one of the following:

• The student’s drawing shows an incorrect ratio of \( \mathrm{Sr}^{2+} \) and \( \mathrm{OH}^{-} \) ions.
• The student’s drawing is not charge-balanced.

Since each \( \mathrm{Sr}^{2+} \) ion must be accompanied by two \( \mathrm{OH}^{-} \) ions, the diagram should show twice as many hydroxide ions as strontium ions.

(b)(i)
For the correct calculated value:
\( 0.043\ \mathrm{mol\ Sr}^{2+}\!/\mathrm{L} \times \dfrac{2\ \mathrm{mol\ OH}^{-}}{1\ \mathrm{mol\ Sr}^{2+}} = 0.086\ \mathrm{M\ OH}^{-} \)

The coefficient \( 2 \) in the dissolution equation means hydroxide concentration is twice the strontium ion concentration.
Therefore, \( \boxed{[\mathrm{OH}^{-}] = 0.086\ \mathrm{M}} \).

(b)(ii)
For the correct calculated value, consistent with part \( \mathrm{(b)(i)} \):
\( K_{sp} = [\mathrm{Sr}^{2+}][\mathrm{OH}^{-}]^{2} = (0.043)(0.086)^{2} = 3.2 \times 10^{-4} \)

Squaring \( [\mathrm{OH}^{-}] \) is important because there are \( 2 \) hydroxide ions in the balanced dissolution equation.
Thus, \( \boxed{K_{sp} = 3.2 \times 10^{-4}} \).

(c)
For the correct answer and a valid justification:
Less than. Because the \( \mathrm{Sr(NO}_{3})_{2}(aq) \) solution already contains a common ion, \( \mathrm{Sr}^{2+}(aq) \), the solubility of \( \mathrm{Sr(OH)}_{2} \) will be decreased, resulting in a lower value of \( [\mathrm{OH}^{-}] \).

Adding extra \( \mathrm{Sr}^{2+} \) shifts the dissolution equilibrium to the left, so less \( \mathrm{Sr(OH)}_{2} \) dissolves and fewer hydroxide ions are produced.

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