MgCl2 + NH4OH = NH4Cl + Mg(OH)2

MgCl_2 magnesium chloride + NH_4OH ammonium hydroxide ⟶ NH_4Cl ammonium chloride + Mg(OH)_2 magnesium hydroxide

Balance the chemical equation algebraically: MgCl_2 + NH_4OH ⟶ NH_4Cl + Mg(OH)_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 MgCl_2 + c_2 NH_4OH ⟶ c_3 NH_4Cl + c_4 Mg(OH)_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, Mg, H, N and O: Cl: | 2 c_1 = c_3 Mg: | c_1 = c_4 H: | 5 c_2 = 4 c_3 + 2 c_4 N: | c_2 = c_3 O: | c_2 = 2 c_4 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 = 2 c_3 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | MgCl_2 + 2 NH_4OH ⟶ 2 NH_4Cl + Mg(OH)_2

+ ⟶ +

magnesium chloride + ammonium hydroxide ⟶ ammonium chloride + magnesium hydroxide

Construct the equilibrium constant, K, expression for: MgCl_2 + NH_4OH ⟶ NH_4Cl + 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: MgCl_2 + 2 NH_4OH ⟶ 2 NH_4Cl + 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 MgCl_2 | 1 | -1 NH_4OH | 2 | -2 NH_4Cl | 2 | 2 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 MgCl_2 | 1 | -1 | ([MgCl2])^(-1) NH_4OH | 2 | -2 | ([NH4OH])^(-2) NH_4Cl | 2 | 2 | ([NH4Cl])^2 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 = ([MgCl2])^(-1) ([NH4OH])^(-2) ([NH4Cl])^2 [Mg(OH)2] = (([NH4Cl])^2 [Mg(OH)2])/([MgCl2] ([NH4OH])^2)

Construct the rate of reaction expression for: MgCl_2 + NH_4OH ⟶ NH_4Cl + 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: MgCl_2 + 2 NH_4OH ⟶ 2 NH_4Cl + 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 MgCl_2 | 1 | -1 NH_4OH | 2 | -2 NH_4Cl | 2 | 2 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 MgCl_2 | 1 | -1 | -(Δ[MgCl2])/(Δt) NH_4OH | 2 | -2 | -1/2 (Δ[NH4OH])/(Δt) NH_4Cl | 2 | 2 | 1/2 (Δ[NH4Cl])/(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[MgCl2])/(Δt) = -1/2 (Δ[NH4OH])/(Δt) = 1/2 (Δ[NH4Cl])/(Δt) = (Δ[Mg(OH)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| magnesium chloride | ammonium hydroxide | ammonium chloride | magnesium hydroxide formula | MgCl_2 | NH_4OH | NH_4Cl | Mg(OH)_2 Hill formula | Cl_2Mg | H_5NO | ClH_4N | H_2MgO_2 name | magnesium chloride | ammonium hydroxide | ammonium chloride | magnesium hydroxide IUPAC name | magnesium dichloride | ammonium hydroxide | ammonium chloride | magnesium dihydroxide

| magnesium chloride | ammonium hydroxide | ammonium chloride | magnesium hydroxide molar mass | 95.2 g/mol | 35.046 g/mol | 53.49 g/mol | 58.319 g/mol phase | solid (at STP) | aqueous (at STP) | solid (at STP) | solid (at STP) melting point | 714 °C | -57.5 °C | 340 °C | 350 °C boiling point | | 36 °C | | density | 2.32 g/cm^3 | 0.9 g/cm^3 | 1.5256 g/cm^3 | 2.3446 g/cm^3 solubility in water | soluble | very soluble | soluble | insoluble