HNO3 + Mg3P2 = H2O + NO2 + H3PO4 + Mg(NO3)2

HNO_3 nitric acid + Mg_3P_2 magnesium phosphide ⟶ H_2O water + NO_2 nitrogen dioxide + H_3PO_4 phosphoric acid + Mg(NO_3)_2 magnesium nitrate

Balance the chemical equation algebraically: HNO_3 + Mg_3P_2 ⟶ H_2O + NO_2 + H_3PO_4 + Mg(NO_3)_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 Mg_3P_2 ⟶ c_3 H_2O + c_4 NO_2 + c_5 H_3PO_4 + c_6 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, Mg and P: H: | c_1 = 2 c_3 + 3 c_5 N: | c_1 = c_4 + 2 c_6 O: | 3 c_1 = c_3 + 2 c_4 + 4 c_5 + 6 c_6 Mg: | 3 c_2 = c_6 P: | 2 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 22 c_2 = 1 c_3 = 8 c_4 = 16 c_5 = 2 c_6 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 22 HNO_3 + Mg_3P_2 ⟶ 8 H_2O + 16 NO_2 + 2 H_3PO_4 + 3 Mg(NO_3)_2

+ ⟶ + + +

nitric acid + magnesium phosphide ⟶ water + nitrogen dioxide + phosphoric acid + magnesium nitrate

Construct the equilibrium constant, K, expression for: HNO_3 + Mg_3P_2 ⟶ H_2O + NO_2 + H_3PO_4 + 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: 22 HNO_3 + Mg_3P_2 ⟶ 8 H_2O + 16 NO_2 + 2 H_3PO_4 + 3 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 | 22 | -22 Mg_3P_2 | 1 | -1 H_2O | 8 | 8 NO_2 | 16 | 16 H_3PO_4 | 2 | 2 Mg(NO_3)_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 | 22 | -22 | ([HNO3])^(-22) Mg_3P_2 | 1 | -1 | ([Mg3P2])^(-1) H_2O | 8 | 8 | ([H2O])^8 NO_2 | 16 | 16 | ([NO2])^16 H_3PO_4 | 2 | 2 | ([H3PO4])^2 Mg(NO_3)_2 | 3 | 3 | ([Mg(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])^(-22) ([Mg3P2])^(-1) ([H2O])^8 ([NO2])^16 ([H3PO4])^2 ([Mg(NO3)2])^3 = (([H2O])^8 ([NO2])^16 ([H3PO4])^2 ([Mg(NO3)2])^3)/(([HNO3])^22 [Mg3P2])

Construct the rate of reaction expression for: HNO_3 + Mg_3P_2 ⟶ H_2O + NO_2 + H_3PO_4 + 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: 22 HNO_3 + Mg_3P_2 ⟶ 8 H_2O + 16 NO_2 + 2 H_3PO_4 + 3 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 | 22 | -22 Mg_3P_2 | 1 | -1 H_2O | 8 | 8 NO_2 | 16 | 16 H_3PO_4 | 2 | 2 Mg(NO_3)_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 | 22 | -22 | -1/22 (Δ[HNO3])/(Δt) Mg_3P_2 | 1 | -1 | -(Δ[Mg3P2])/(Δt) H_2O | 8 | 8 | 1/8 (Δ[H2O])/(Δt) NO_2 | 16 | 16 | 1/16 (Δ[NO2])/(Δt) H_3PO_4 | 2 | 2 | 1/2 (Δ[H3PO4])/(Δt) Mg(NO_3)_2 | 3 | 3 | 1/3 (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 = -1/22 (Δ[HNO3])/(Δt) = -(Δ[Mg3P2])/(Δt) = 1/8 (Δ[H2O])/(Δt) = 1/16 (Δ[NO2])/(Δt) = 1/2 (Δ[H3PO4])/(Δt) = 1/3 (Δ[Mg(NO3)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitric acid | magnesium phosphide | water | nitrogen dioxide | phosphoric acid | magnesium nitrate formula | HNO_3 | Mg_3P_2 | H_2O | NO_2 | H_3PO_4 | Mg(NO_3)_2 Hill formula | HNO_3 | Mg_3P_2 | H_2O | NO_2 | H_3O_4P | MgN_2O_6 name | nitric acid | magnesium phosphide | water | nitrogen dioxide | phosphoric acid | magnesium nitrate IUPAC name | nitric acid | trimagnesium phosphorus(-3) anion | water | Nitrogen dioxide | phosphoric acid | magnesium dinitrate

| nitric acid | magnesium phosphide | water | nitrogen dioxide | phosphoric acid | magnesium nitrate molar mass | 63.012 g/mol | 134.86 g/mol | 18.015 g/mol | 46.005 g/mol | 97.994 g/mol | 148.31 g/mol phase | liquid (at STP) | solid (at STP) | liquid (at STP) | gas (at STP) | liquid (at STP) | solid (at STP) melting point | -41.6 °C | 750 °C | 0 °C | -11 °C | 42.4 °C | 88.9 °C boiling point | 83 °C | | 99.9839 °C | 21 °C | 158 °C | 330 °C density | 1.5129 g/cm^3 | 2.055 g/cm^3 | 1 g/cm^3 | 0.00188 g/cm^3 (at 25 °C) | 1.685 g/cm^3 | 1.2051 g/cm^3 solubility in water | miscible | reacts | | reacts | very soluble | surface tension | | | 0.0728 N/m | | | dynamic viscosity | 7.6×10^-4 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | 4.02×10^-4 Pa s (at 25 °C) | | odor | | | odorless | | odorless |