NH4Cl + Mg(OH)2 = H2O + NH3 + MgCl2

NH_4Cl ammonium chloride + Mg(OH)_2 magnesium hydroxide ⟶ H_2O water + NH_3 ammonia + MgCl_2 magnesium chloride

Balance the chemical equation algebraically: NH_4Cl + Mg(OH)_2 ⟶ H_2O + NH_3 + MgCl_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NH_4Cl + c_2 Mg(OH)_2 ⟶ c_3 H_2O + c_4 NH_3 + c_5 MgCl_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, N, Mg and O: Cl: | c_1 = 2 c_5 H: | 4 c_1 + 2 c_2 = 2 c_3 + 3 c_4 N: | c_1 = c_4 Mg: | c_2 = c_5 O: | 2 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 2 c_4 = 2 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 NH_4Cl + Mg(OH)_2 ⟶ 2 H_2O + 2 NH_3 + MgCl_2

+ ⟶ + +

ammonium chloride + magnesium hydroxide ⟶ water + ammonia + magnesium chloride

| ammonium chloride | magnesium hydroxide | water | ammonia | magnesium chloride molecular enthalpy | -314.4 kJ/mol | -924.5 kJ/mol | -285.8 kJ/mol | -45.9 kJ/mol | -641.3 kJ/mol total enthalpy | -628.8 kJ/mol | -924.5 kJ/mol | -571.7 kJ/mol | -91.8 kJ/mol | -641.3 kJ/mol | H_initial = -1553 kJ/mol | | H_final = -1305 kJ/mol | | ΔH_rxn^0 | -1305 kJ/mol - -1553 kJ/mol = 248.5 kJ/mol (endothermic) | | | |

| ammonium chloride | magnesium hydroxide | water | ammonia | magnesium chloride molecular free energy | -202.9 kJ/mol | -833.5 kJ/mol | -237.1 kJ/mol | -16.4 kJ/mol | -591.8 kJ/mol total free energy | -405.8 kJ/mol | -833.5 kJ/mol | -474.2 kJ/mol | -32.8 kJ/mol | -591.8 kJ/mol | G_initial = -1239 kJ/mol | | G_final = -1099 kJ/mol | | ΔG_rxn^0 | -1099 kJ/mol - -1239 kJ/mol = 140.5 kJ/mol (endergonic) | | | |

Construct the equilibrium constant, K, expression for: NH_4Cl + Mg(OH)_2 ⟶ H_2O + NH_3 + MgCl_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: 2 NH_4Cl + Mg(OH)_2 ⟶ 2 H_2O + 2 NH_3 + MgCl_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 NH_4Cl | 2 | -2 Mg(OH)_2 | 1 | -1 H_2O | 2 | 2 NH_3 | 2 | 2 MgCl_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NH_4Cl | 2 | -2 | ([NH4Cl])^(-2) Mg(OH)_2 | 1 | -1 | ([Mg(OH)2])^(-1) H_2O | 2 | 2 | ([H2O])^2 NH_3 | 2 | 2 | ([NH3])^2 MgCl_2 | 1 | 1 | [MgCl2] 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 = ([NH4Cl])^(-2) ([Mg(OH)2])^(-1) ([H2O])^2 ([NH3])^2 [MgCl2] = (([H2O])^2 ([NH3])^2 [MgCl2])/(([NH4Cl])^2 [Mg(OH)2])

Construct the rate of reaction expression for: NH_4Cl + Mg(OH)_2 ⟶ H_2O + NH_3 + MgCl_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: 2 NH_4Cl + Mg(OH)_2 ⟶ 2 H_2O + 2 NH_3 + MgCl_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 NH_4Cl | 2 | -2 Mg(OH)_2 | 1 | -1 H_2O | 2 | 2 NH_3 | 2 | 2 MgCl_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 NH_4Cl | 2 | -2 | -1/2 (Δ[NH4Cl])/(Δt) Mg(OH)_2 | 1 | -1 | -(Δ[Mg(OH)2])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) NH_3 | 2 | 2 | 1/2 (Δ[NH3])/(Δt) MgCl_2 | 1 | 1 | (Δ[MgCl2])/(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 = -1/2 (Δ[NH4Cl])/(Δt) = -(Δ[Mg(OH)2])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/2 (Δ[NH3])/(Δt) = (Δ[MgCl2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| ammonium chloride | magnesium hydroxide | water | ammonia | magnesium chloride formula | NH_4Cl | Mg(OH)_2 | H_2O | NH_3 | MgCl_2 Hill formula | ClH_4N | H_2MgO_2 | H_2O | H_3N | Cl_2Mg name | ammonium chloride | magnesium hydroxide | water | ammonia | magnesium chloride IUPAC name | ammonium chloride | magnesium dihydroxide | water | ammonia | magnesium dichloride

| ammonium chloride | magnesium hydroxide | water | ammonia | magnesium chloride molar mass | 53.49 g/mol | 58.319 g/mol | 18.015 g/mol | 17.031 g/mol | 95.2 g/mol phase | solid (at STP) | solid (at STP) | liquid (at STP) | gas (at STP) | solid (at STP) melting point | 340 °C | 350 °C | 0 °C | -77.73 °C | 714 °C boiling point | | | 99.9839 °C | -33.33 °C | density | 1.5256 g/cm^3 | 2.3446 g/cm^3 | 1 g/cm^3 | 6.96×10^-4 g/cm^3 (at 25 °C) | 2.32 g/cm^3 solubility in water | soluble | insoluble | | | soluble surface tension | | | 0.0728 N/m | 0.0234 N/m | dynamic viscosity | | | 8.9×10^-4 Pa s (at 25 °C) | 1.009×10^-5 Pa s (at 25 °C) | odor | | | odorless | |