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kobusy [5.1K]
2 years ago
7

The generic metal hydroxide M(OH)2 has Ksp = 8.05×10−12. (NOTE: In this particular problem, because of the magnitude of the Ksp

and the stoichiometry of the compound, the contribution of OH− from water can be ignored. However, this may not always be the case.)
a) What is the solubility of M(OH)2 in pure water?
b) What is the solubility of M(OH)2 in a 0.202 M solution of M(NO3)2?
Chemistry
1 answer:
vodka [1.7K]2 years ago
6 0

Answer:

a. in pure water Solubility (x) = 1.26 x 10⁻⁴M

b. in 0.202M M⁺² Solubility (x) = 9.963 x 10⁻¹²M

The large drop in solubility is consistent with the common ion effect.

Explanation:

a. Solubility in pure water

Given:       M(OH)₂ ⇄ M⁺² + 2OH⁻

            I       ---            0          0

           C      ---             x          2x

           E       ---            x           2x

Ksp = [M⁺²][OH⁻]² = (x)(2x)² = 4x³ => x = CubeRt(Ksp/4)

solubility in pure water = x = CubeRt(8.05 x 10⁻¹²/4) = 1.26 x 10⁻⁴M

b. Solubility in presence of 0.202M M⁺² as common ion.

Given:       M(OH)₂ ⇄       M⁺²      +     2OH⁻

            I       ---            0.202M              0

           C      ---                 +x                 +2x

           E       ---           0.202M + x         2x

                                   ≈ 0.202M

Ksp = [M⁺²][2x]² = (0.202)(2x)² = (0.202)(4x²) = 8.05 x 10⁻¹²

=> x = (8.05 x 10⁻¹²)/(0.202)(4) = 9.963 x 10⁻¹²M

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The question is incomplete, here is the complete question:

The equilibrium constant for the reaction

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If each yellow sphere represents 1 mol of N₂O₄(g) and each gray sphere 1 mol of NO₂ which of the following 1.0 L containers represents the equilibrium mixture at 2°C?

The image is attached below.

<u>Answer:</u> The system which represents the equilibrium having value of K_c=2.0 is system (b)

<u>Explanation:</u>

Equilibrium constant in terms of concentration is defined as the ratio of concentration of products to the concentration of reactants each raised to the power their stoichiometric ratios. It is expressed as K_c

For a general chemical reaction:

aA+bB\rightarrow cC+dD

The expression for K_{c} is written as:

K_{c}=\frac{[C]^c[D]^d}{[A]^a[B]^b}

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The expression of K_c for above equation follows:

K_c=\frac{[NO_2]^2}{[N_2O_4]}      .......(1)

We are given:

Volume of the container = 1.0 L

Value of K_c = 2.0

Molarity of the substance is calculated by using the equation:

\text{Molarity}=\frac{\text{Number of moles}}{\text{Volume}}

For the given images:

  • <u>For a:</u>

Number of Gray spheres = 8 moles

Number of yellow spheres = 4 moles

Putting values in expression 1, we get:

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  • <u>For b:</u>

Number of Gray spheres = 4 moles

Number of yellow spheres = 8 moles

Putting values in expression 1, we get:

K_c=\frac{(4/1)^2}{(8/1)}\\\\K_c=2

  • <u>For c:</u>

Number of Gray spheres = 6 moles

Number of yellow spheres = 6 moles

Putting values in expression 1, we get:

K_c=\frac{(6/1)^2}{(6/1)}\\\\K_c=6

  • <u>For d:</u>

Number of Gray spheres = 2 moles

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Putting values in expression 1, we get:

K_c=\frac{(2/1)^2}{(8/1)}\\\\K_c=\frac{1}{2}

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