Question

consider these compounds:
a. pbf₂
b. ni(oh)₂
c. fes
d. cas
complete the following statements by entering the letter(s) corresponding to the correct compound(s). (if more than one compound fits
the description, include all the relevant compounds by writing your answer as a string of characters without punctuation, e.g. abc.)
without doing any calculations it is possible to determine that silver cyanide is more soluble than , and silver cyanide is less
soluble than
it is not possible to determine whether silver cyanide is more or less soluble than by simply comparing ksp values.
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Explanation:

To determine if we can compare the solubility of silver cyanide (\( \text{AgCN} \)) with the given compounds, we analyze the stoichiometry of the dissolution reactions (since \( K_{sp} \) comparison for solubility requires the same ion ratio in the dissolution equilibrium).

Step 1: Analyze each compound's dissolution stoichiometry

• A. \( \text{PbF}_2 \): Dissolves as \( \text{PbF}_2(s)

ightleftharpoons \text{Pb}^{2+}(aq) + 2\text{F}^-(aq) \) (2:1 ion ratio).

• B. \( \text{Ni(OH)}_2 \): Dissolves as \( \text{Ni(OH)}_2(s)

ightleftharpoons \text{Ni}^{2+}(aq) + 2\text{OH}^-(aq) \) (2:1 ion ratio).

• C. \( \text{FeS} \): Dissolves as \( \text{FeS}(s)

ightleftharpoons \text{Fe}^{2+}(aq) + \text{S}^{2-}(aq) \) (1:1 ion ratio).

• D. \( \text{CaS} \): Dissolves as \( \text{CaS}(s)

ightleftharpoons \text{Ca}^{2+}(aq) + \text{S}^{2-}(aq) \) (1:1 ion ratio).

Step 2: Compare with \( \text{AgCN} \)’s stoichiometry

Silver cyanide dissolves as \( \text{AgCN}(s)
ightleftharpoons \text{Ag}^+(aq) + \text{CN}^-(aq) \) (1:1 ion ratio).

• For compounds with 1:1 ion ratios (C, D), we can directly compare \( K_{sp} \) to determine solubility (since \( \text{solubility} = \sqrt{K_{sp}} \) for 1:1 salts).
• For compounds with 2:1 ion ratios (A, B), the solubility formula is \( \text{solubility} = \sqrt[3]{\frac{K_{sp}}{4}} \), so \( K_{sp} \) alone cannot be used to compare solubility with 1:1 salts (different mathematical relationships).

Step 3: Determine which compounds can be compared

• With 1:1 ratio (C, D): We can compare \( \text{AgCN} \)’s solubility to \( \text{FeS} \) or \( \text{CaS} \) using \( K_{sp} \) (same ion ratio, so \( \sqrt{K_{sp}} \) directly reflects solubility).
• With 2:1 ratio (A, B): We cannot compare \( \text{AgCN} \)’s solubility to \( \text{PbF}_2 \) or \( \text{Ni(OH)}_2 \) using \( K_{sp} \) alone (different ion ratios, so \( K_{sp} \) magnitude does not directly correlate to solubility).

Final Answer

For the first blank (compounds more soluble than \( \text{AgCN} \) or less, but we focus on “possible to determine”):

• It is possible to determine if \( \text{AgCN} \) is more/less soluble than C, D (FeS, CaS) by comparing \( K_{sp} \).
• It is not possible to determine with A, B (PbF₂, Ni(OH)₂) because their ion ratios differ.

(For the first part: “Without doing any calculations...”, the answer is the 1:1 ratio compounds, so \( \boldsymbol{\text{CD}} \). For the second part, the 2:1 ratio compounds, so \( \boldsymbol{\text{AB}} \).)

Answer:

First blank: CD
Second blank: AB