MgSO4 + Zn(OH)2 = ZnSO4 + Mg(OH)2

Input interpretation

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MgSO_4 magnesium sulfate + Zn(OH)_2 zinc hydroxide ⟶ ZnSO_4 zinc sulfate + Mg(OH)_2 magnesium hydroxide

Balanced equation

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Balance the chemical equation algebraically: MgSO_4 + Zn(OH)_2 ⟶ ZnSO_4 + Mg(OH)_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 MgSO_4 + c_2 Zn(OH)_2 ⟶ c_3 ZnSO_4 + c_4 Mg(OH)_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Mg, O, S, H and Zn: Mg: | c_1 = c_4 O: | 4 c_1 + 2 c_2 = 4 c_3 + 2 c_4 S: | c_1 = c_3 H: | 2 c_2 = 2 c_4 Zn: | c_2 = c_3 Since the coefficients are relative quantities and underdetermined, choose a coefficient to set arbitrarily. To keep the coefficients small, the arbitrary value is ordinarily one. For instance, set c_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | MgSO_4 + Zn(OH)_2 ⟶ ZnSO_4 + Mg(OH)_2

+ ⟶ +

Names

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magnesium sulfate + zinc hydroxide ⟶ zinc sulfate + magnesium hydroxide

Equilibrium constant

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Construct the equilibrium constant, K, expression for: MgSO_4 + Zn(OH)_2 ⟶ ZnSO_4 + Mg(OH)_2 Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the activity expression for each chemical species. • Use the activity expressions to build the equilibrium constant expression. Write the balanced chemical equation: MgSO_4 + Zn(OH)_2 ⟶ ZnSO_4 + Mg(OH)_2 Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i MgSO_4 | 1 | -1 Zn(OH)_2 | 1 | -1 ZnSO_4 | 1 | 1 Mg(OH)_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression MgSO_4 | 1 | -1 | ([MgSO4])^(-1) Zn(OH)_2 | 1 | -1 | ([Zn(OH)2])^(-1) ZnSO_4 | 1 | 1 | [ZnSO4] Mg(OH)_2 | 1 | 1 | [Mg(OH)2] The equilibrium constant symbol in the concentration basis is: K_c Mulitply the activity expressions to arrive at the K_c expression: Answer: | | K_c = ([MgSO4])^(-1) ([Zn(OH)2])^(-1) [ZnSO4] [Mg(OH)2] = ([ZnSO4] [Mg(OH)2])/([MgSO4] [Zn(OH)2])

Rate of reaction

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Construct the rate of reaction expression for: MgSO_4 + Zn(OH)_2 ⟶ ZnSO_4 + Mg(OH)_2 Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the rate term for each chemical species. • Write the rate of reaction expression. Write the balanced chemical equation: MgSO_4 + Zn(OH)_2 ⟶ ZnSO_4 + Mg(OH)_2 Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i MgSO_4 | 1 | -1 Zn(OH)_2 | 1 | -1 ZnSO_4 | 1 | 1 Mg(OH)_2 | 1 | 1 The rate term for each chemical species, B_i, is 1/ν_i(Δ[B_i])/(Δt) where [B_i] is the amount concentration and t is time: chemical species | c_i | ν_i | rate term MgSO_4 | 1 | -1 | -(Δ[MgSO4])/(Δt) Zn(OH)_2 | 1 | -1 | -(Δ[Zn(OH)2])/(Δt) ZnSO_4 | 1 | 1 | (Δ[ZnSO4])/(Δt) Mg(OH)_2 | 1 | 1 | (Δ[Mg(OH)2])/(Δt) (for infinitesimal rate of change, replace Δ with d) Set the rate terms equal to each other to arrive at the rate expression: Answer: | | rate = -(Δ[MgSO4])/(Δt) = -(Δ[Zn(OH)2])/(Δt) = (Δ[ZnSO4])/(Δt) = (Δ[Mg(OH)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)