H2O + Mg + CsNO2 = NH3 + Mg(OH)2 + CsOH

H_2O water + Mg magnesium + CsNO2 ⟶ NH_3 ammonia + Mg(OH)_2 magnesium hydroxide + CsOH cesium hydroxide

Balance the chemical equation algebraically: H_2O + Mg + CsNO2 ⟶ NH_3 + Mg(OH)_2 + CsOH Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 Mg + c_3 CsNO2 ⟶ c_4 NH_3 + c_5 Mg(OH)_2 + c_6 CsOH Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Mg, Cs and N: H: | 2 c_1 = 3 c_4 + 2 c_5 + c_6 O: | c_1 + 2 c_3 = 2 c_5 + c_6 Mg: | c_2 = c_5 Cs: | c_3 = c_6 N: | c_3 = 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 5 c_2 = 3 c_3 = 1 c_4 = 1 c_5 = 3 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 5 H_2O + 3 Mg + CsNO2 ⟶ NH_3 + 3 Mg(OH)_2 + CsOH

+ + CsNO2 ⟶ + +

water + magnesium + CsNO2 ⟶ ammonia + magnesium hydroxide + cesium hydroxide

Construct the equilibrium constant, K, expression for: H_2O + Mg + CsNO2 ⟶ NH_3 + Mg(OH)_2 + CsOH 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: 5 H_2O + 3 Mg + CsNO2 ⟶ NH_3 + 3 Mg(OH)_2 + CsOH 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 H_2O | 5 | -5 Mg | 3 | -3 CsNO2 | 1 | -1 NH_3 | 1 | 1 Mg(OH)_2 | 3 | 3 CsOH | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 5 | -5 | ([H2O])^(-5) Mg | 3 | -3 | ([Mg])^(-3) CsNO2 | 1 | -1 | ([CsNO2])^(-1) NH_3 | 1 | 1 | [NH3] Mg(OH)_2 | 3 | 3 | ([Mg(OH)2])^3 CsOH | 1 | 1 | [CsHO] 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 = ([H2O])^(-5) ([Mg])^(-3) ([CsNO2])^(-1) [NH3] ([Mg(OH)2])^3 [CsHO] = ([NH3] ([Mg(OH)2])^3 [CsHO])/(([H2O])^5 ([Mg])^3 [CsNO2])

Construct the rate of reaction expression for: H_2O + Mg + CsNO2 ⟶ NH_3 + Mg(OH)_2 + CsOH 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: 5 H_2O + 3 Mg + CsNO2 ⟶ NH_3 + 3 Mg(OH)_2 + CsOH 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 H_2O | 5 | -5 Mg | 3 | -3 CsNO2 | 1 | -1 NH_3 | 1 | 1 Mg(OH)_2 | 3 | 3 CsOH | 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 H_2O | 5 | -5 | -1/5 (Δ[H2O])/(Δt) Mg | 3 | -3 | -1/3 (Δ[Mg])/(Δt) CsNO2 | 1 | -1 | -(Δ[CsNO2])/(Δt) NH_3 | 1 | 1 | (Δ[NH3])/(Δt) Mg(OH)_2 | 3 | 3 | 1/3 (Δ[Mg(OH)2])/(Δt) CsOH | 1 | 1 | (Δ[CsHO])/(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 = -1/5 (Δ[H2O])/(Δt) = -1/3 (Δ[Mg])/(Δt) = -(Δ[CsNO2])/(Δt) = (Δ[NH3])/(Δt) = 1/3 (Δ[Mg(OH)2])/(Δt) = (Δ[CsHO])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | magnesium | CsNO2 | ammonia | magnesium hydroxide | cesium hydroxide formula | H_2O | Mg | CsNO2 | NH_3 | Mg(OH)_2 | CsOH Hill formula | H_2O | Mg | CsNO2 | H_3N | H_2MgO_2 | CsHO name | water | magnesium | | ammonia | magnesium hydroxide | cesium hydroxide IUPAC name | water | magnesium | | ammonia | magnesium dihydroxide | cesium;hydroxide

| water | magnesium | CsNO2 | ammonia | magnesium hydroxide | cesium hydroxide molar mass | 18.015 g/mol | 24.305 g/mol | 178.91 g/mol | 17.031 g/mol | 58.319 g/mol | 149.912 g/mol phase | liquid (at STP) | solid (at STP) | | gas (at STP) | solid (at STP) | solid (at STP) melting point | 0 °C | 648 °C | | -77.73 °C | 350 °C | 338.85 °C boiling point | 99.9839 °C | 1090 °C | | -33.33 °C | | density | 1 g/cm^3 | 1.738 g/cm^3 | | 6.96×10^-4 g/cm^3 (at 25 °C) | 2.3446 g/cm^3 | 1.72 g/cm^3 solubility in water | | reacts | | | insoluble | 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 | | | | |