HNO3 + Mg = H2O + NH4NO3 + Mg(NO3)2

HNO_3 (nitric acid) + Mg (magnesium) ⟶ H_2O (water) + NH_4NO_3 (ammonium nitrate) + Mg(NO_3)_2 (magnesium nitrate)

Balance the chemical equation algebraically: HNO_3 + Mg ⟶ H_2O + NH_4NO_3 + Mg(NO_3)_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 Mg ⟶ c_3 H_2O + c_4 NH_4NO_3 + c_5 Mg(NO_3)_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 + 4 c_4 N: | c_1 = 2 c_4 + 2 c_5 O: | 3 c_1 = c_3 + 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 = 10 c_2 = 4 c_3 = 3 c_4 = 1 c_5 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 10 HNO_3 + 4 Mg ⟶ 3 H_2O + NH_4NO_3 + 4 Mg(NO_3)_2

+ ⟶ + +

nitric acid + magnesium ⟶ water + ammonium nitrate + magnesium nitrate

Construct the equilibrium constant, K, expression for: HNO_3 + Mg ⟶ H_2O + NH_4NO_3 + Mg(NO_3)_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: 10 HNO_3 + 4 Mg ⟶ 3 H_2O + NH_4NO_3 + 4 Mg(NO_3)_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 | 10 | -10 Mg | 4 | -4 H_2O | 3 | 3 NH_4NO_3 | 1 | 1 Mg(NO_3)_2 | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HNO_3 | 10 | -10 | ([HNO3])^(-10) Mg | 4 | -4 | ([Mg])^(-4) H_2O | 3 | 3 | ([H2O])^3 NH_4NO_3 | 1 | 1 | [NH4NO3] Mg(NO_3)_2 | 4 | 4 | ([Mg(NO3)2])^4 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])^(-10) ([Mg])^(-4) ([H2O])^3 [NH4NO3] ([Mg(NO3)2])^4 = (([H2O])^3 [NH4NO3] ([Mg(NO3)2])^4)/(([HNO3])^10 ([Mg])^4)

Construct the rate of reaction expression for: HNO_3 + Mg ⟶ H_2O + NH_4NO_3 + Mg(NO_3)_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: 10 HNO_3 + 4 Mg ⟶ 3 H_2O + NH_4NO_3 + 4 Mg(NO_3)_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 | 10 | -10 Mg | 4 | -4 H_2O | 3 | 3 NH_4NO_3 | 1 | 1 Mg(NO_3)_2 | 4 | 4 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 | 10 | -10 | -1/10 (Δ[HNO3])/(Δt) Mg | 4 | -4 | -1/4 (Δ[Mg])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) NH_4NO_3 | 1 | 1 | (Δ[NH4NO3])/(Δt) Mg(NO_3)_2 | 4 | 4 | 1/4 (Δ[Mg(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 = -1/10 (Δ[HNO3])/(Δt) = -1/4 (Δ[Mg])/(Δt) = 1/3 (Δ[H2O])/(Δt) = (Δ[NH4NO3])/(Δt) = 1/4 (Δ[Mg(NO3)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitric acid | magnesium | water | ammonium nitrate | magnesium nitrate formula | HNO_3 | Mg | H_2O | NH_4NO_3 | Mg(NO_3)_2 Hill formula | HNO_3 | Mg | H_2O | H_4N_2O_3 | MgN_2O_6 name | nitric acid | magnesium | water | ammonium nitrate | magnesium nitrate IUPAC name | nitric acid | magnesium | water | | magnesium dinitrate