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Math  /  Algebra

QuestionWhich of the following is the correct expression for the concentration based equilibrium constant for the reaction: Mg(OH)2( s)⇌Mg2+(aq)+2OH−(aq)\mathrm{Mg}(\mathrm{OH})_{2}(\mathrm{~s}) \rightleftharpoons \mathrm{Mg}^{2+}(\mathrm{aq})+2 \mathrm{OH}^{-}(\mathrm{aq}) I. KC=[Mg2+][OH−]2\mathrm{K}_{\mathrm{C}}=\left[\mathrm{Mg}^{2+}\right]\left[\mathrm{OH}^{-}\right]^{2}
A II. KC=[Mg2+][OH−][Mg(OH)2]\mathrm{K}_{\mathrm{C}}=\frac{\left[\mathrm{Mg}^{2+}\right]\left[\mathrm{OH}^{-}\right]}{\left[\mathrm{Mg}(\mathrm{OH})_{2}\right]} III. KC=[Mg2+][OH−]2[Mg(OH)2]\mathrm{K}_{\mathrm{C}}=\frac{\left[\mathrm{Mg}^{2+}\right]\left[\mathrm{OH}^{-}\right]^{2}}{\left[\mathrm{Mg}(\mathrm{OH})_{2}\right]}
B c IV. KC=[Mg2+][OH−]\mathrm{K}_{\mathrm{C}}=\left[\mathrm{Mg}^{2+}\right]\left[\mathrm{OH}^{-}\right]
D

Studdy Solution

STEP 1

1. The reaction is at equilibrium.
2. The equilibrium constant expression KC K_C is based on concentrations of aqueous species.
3. Solids do not appear in the equilibrium constant expression.

STEP 2

1. Identify the phases of each species in the reaction.
2. Determine which species are included in the equilibrium constant expression.
3. Write the correct expression for KC K_C .

STEP 3

Identify the phases of each species: - Mg(OH)2(s)\mathrm{Mg}(\mathrm{OH})_{2}(\mathrm{s}) is a solid. - Mg2+(aq)\mathrm{Mg}^{2+}(\mathrm{aq}) is aqueous. - OH−(aq)\mathrm{OH}^{-}(\mathrm{aq}) is aqueous.

STEP 4

Since Mg(OH)2\mathrm{Mg}(\mathrm{OH})_{2} is a solid, it is not included in the equilibrium constant expression.
Only aqueous species Mg2+\mathrm{Mg}^{2+} and OH−\mathrm{OH}^{-} are included.

STEP 5

Write the expression for KC K_C using only the aqueous species: KC=[Mg2+][OH−]2 K_C = [\mathrm{Mg}^{2+}][\mathrm{OH}^{-}]^2
The correct expression for the concentration-based equilibrium constant is:
KC=[Mg2+][OH−]2 \boxed{\mathrm{K}_{\mathrm{C}}=\left[\mathrm{Mg}^{2+}\right]\left[\mathrm{OH}^{-}\right]^{2}}
This corresponds to option I.

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