Question

for each of the salts on the left, match the salts on the right that can be compared directly, using ( k_{sp} ) values, to estimate solubilities. (if more than one salt on the right can be directly compared, include all the relevant salts by writing your answer as a string of characters without punctuation, e.g. abc.)
c 1. copper(ii) sulfide
d 2. magnesium hydroxide

write the expression for ( k ) in terms of the solubility, ( s ), for each salt, when dissolved in water.
copper(ii) sulfide
( k_{sp}= )
( 8^{2} )
magnesium hydroxide
( k_{sp}= )
( 4s^{3} )

note: multiply out any number and put it first in the ( k_{sp} ) expression. combine all exponents for ( s ).

no error has been detected in your answer. check for typos,
miscalculations etc. before submitting your answer.

Answer:

Part 1: Matching Copper(II) Sulfide (CuS)

To directly compare solubilities using \( K_{sp} \), salts must have the same dissociation stoichiometry (same number of cations and anions). Copper(II) sulfide dissociates as \( \text{CuS}(s)
ightleftharpoons \text{Cu}^{2+}(aq) + \text{S}^{2-}(aq) \), so its \( K_{sp} = [\text{Cu}^{2+}][\text{S}^{2-}] = s^2 \) (where \( s \) is solubility). We need a salt with the same 1:1 cation - anion ratio.

• Option A (\( \text{Ni(CN)}_2 \)): Dissociates as \( \text{Ni(CN)}_2(s)

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

• Option B (\( \text{BaCO}_3 \)): Dissociates as \( \text{BaCO}_3(s)

ightleftharpoons \text{Ba}^{2+}(aq) + \text{CO}_3^{2-}(aq) \), ratio 1:1.

• Option C (\( \text{MnS} \)): Dissociates as \( \text{MnS}(s)

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

• Option D (\( \text{Mn(OH)}_2 \)): Dissociates as \( \text{Mn(OH)}_2(s)

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

Since \( \text{CuS} \) and \( \text{MnS} \) have the same 1:1 dissociation stoichiometry, they can be directly compared. Also, \( \text{BaCO}_3 \) has a 1:1 ratio too, but let's check the second part for magnesium hydroxide.

Part 2: Matching Magnesium Hydroxide (\( \text{Mg(OH)}_2 \))

Magnesium hydroxide dissociates as \( \text{Mg(OH)}_2(s)
ightleftharpoons \text{Mg}^{2+}(aq) + 2\text{OH}^-(aq) \), so \( K_{sp} = [\text{Mg}^{2+}][\text{OH}^-]^2 = (s)(2s)^2 = 4s^3 \) (where \( s \) is solubility). We need a salt with a 1:2 cation - anion ratio.

• Option A (\( \text{Ni(CN)}_2 \)): Dissociates as \( \text{Ni(CN)}_2(s)

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

• Option D (\( \text{Mn(OH)}_2 \)): Dissociates as \( \text{Mn(OH)}_2(s)

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

Final Answers

1. For copper(II) sulfide, the salts with the same dissociation stoichiometry (1:1) are \( \text{MnS} \) (Option C) and \( \text{BaCO}_3 \) (Option B). But from the options given and the common comparison, \( \text{MnS} \) (C) is a better match as it also has a sulfide ion. Also, \( \text{BaCO}_3 \) (B) can be included. But looking at the options, the most probable for direct comparison (same ion type and ratio) is C (MnS) and also B (BaCO₃) has the same ratio. But let's re - check:

Wait, the problem says "more than one salt on the right can be directly compared". For \( \text{CuS} \) (1:1 ratio), the salts with 1:1 ratio are B (\( \text{BaCO}_3 \)) and C (\( \text{MnS} \)).

For \( \text{Mg(OH)}_2 \) (1:2 ratio), the salts with 1:2 ratio are A (\( \text{Ni(CN)}_2 \)) and D (\( \text{Mn(OH)}_2 \)).

So:

1. Copper(II) sulfide (1) can be matched with B (BaCO₃) and C (MnS) (since they have 1:1 ratio). So the answer for 1 is BC.

1. Magnesium hydroxide (2) can be matched with A (Ni(CN)₂) and D (Mn(OH)₂) (since they have 1:2 ratio). So the answer for 2 is AD.

For the \( K_{sp} \) expressions (already given but just to confirm):

• Copper(II) sulfide: \( \text{CuS}(s)

ightleftharpoons \text{Cu}^{2+}(aq) + \text{S}^{2-}(aq) \), let solubility be \( s \), then \( [\text{Cu}^{2+}] = s \), \( [\text{S}^{2-}] = s \), so \( K_{sp}=s\times s = s^{2} \).

• Magnesium hydroxide: \( \text{Mg(OH)}_2(s)

ightleftharpoons \text{Mg}^{2+}(aq) + 2\text{OH}^-(aq) \), let solubility be \( s \), then \( [\text{Mg}^{2+}] = s \), \( [\text{OH}^-]=2s \), so \( K_{sp}=s\times(2s)^{2}=4s^{3} \).

Final Answers for Matching:

1. 1. copper(II) sulfide: BC
2. 2. magnesium hydroxide: AD

(If we consider the options strictly based on ratio:

1. Copper(II) sulfide (1:1 ratio) matches with B (BaCO₃, 1:1) and C (MnS, 1:1).

1. Magnesium hydroxide (1:2 ratio) matches with A (Ni(CN)₂, 1:2) and D (Mn(OH)₂, 1:2).)