HNO3 + Mg = H2O + NO + MgH(NO3)2

HNO_3 nitric acid + Mg magnesium ⟶ H_2O water + NO nitric oxide + MgH(NO3)2

Balance the chemical equation algebraically: HNO_3 + Mg ⟶ H_2O + NO + MgH(NO3)2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 Mg ⟶ c_3 H_2O + c_4 NO + c_5 MgH(NO3)2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O and Mg: H: | c_1 = 2 c_3 + c_5 N: | c_1 = c_4 + 2 c_5 O: | 3 c_1 = c_3 + c_4 + 6 c_5 Mg: | c_2 = c_5 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 7 c_2 = 3 c_3 = 2 c_4 = 1 c_5 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 7 HNO_3 + 3 Mg ⟶ 2 H_2O + NO + 3 MgH(NO3)2

+ ⟶ + + MgH(NO3)2

nitric acid + magnesium ⟶ water + nitric oxide + MgH(NO3)2

Construct the equilibrium constant, K, expression for: HNO_3 + Mg ⟶ H_2O + NO + MgH(NO3)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: 7 HNO_3 + 3 Mg ⟶ 2 H_2O + NO + 3 MgH(NO3)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 HNO_3 | 7 | -7 Mg | 3 | -3 H_2O | 2 | 2 NO | 1 | 1 MgH(NO3)2 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HNO_3 | 7 | -7 | ([HNO3])^(-7) Mg | 3 | -3 | ([Mg])^(-3) H_2O | 2 | 2 | ([H2O])^2 NO | 1 | 1 | [NO] MgH(NO3)2 | 3 | 3 | ([MgH(NO3)2])^3 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 = ([HNO3])^(-7) ([Mg])^(-3) ([H2O])^2 [NO] ([MgH(NO3)2])^3 = (([H2O])^2 [NO] ([MgH(NO3)2])^3)/(([HNO3])^7 ([Mg])^3)

Construct the rate of reaction expression for: HNO_3 + Mg ⟶ H_2O + NO + MgH(NO3)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: 7 HNO_3 + 3 Mg ⟶ 2 H_2O + NO + 3 MgH(NO3)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 HNO_3 | 7 | -7 Mg | 3 | -3 H_2O | 2 | 2 NO | 1 | 1 MgH(NO3)2 | 3 | 3 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 HNO_3 | 7 | -7 | -1/7 (Δ[HNO3])/(Δt) Mg | 3 | -3 | -1/3 (Δ[Mg])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) NO | 1 | 1 | (Δ[NO])/(Δt) MgH(NO3)2 | 3 | 3 | 1/3 (Δ[MgH(NO3)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 = -1/7 (Δ[HNO3])/(Δt) = -1/3 (Δ[Mg])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[NO])/(Δt) = 1/3 (Δ[MgH(NO3)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitric acid | magnesium | water | nitric oxide | MgH(NO3)2 formula | HNO_3 | Mg | H_2O | NO | MgH(NO3)2 Hill formula | HNO_3 | Mg | H_2O | NO | HMgN2O6 name | nitric acid | magnesium | water | nitric oxide |