HNO3 + PH3 = H2O + NO2 + H3PO4

HNO_3 nitric acid + PH_3 phosphine ⟶ H_2O water + NO_2 nitrogen dioxide + H_3PO_4 phosphoric acid

Balance the chemical equation algebraically: HNO_3 + PH_3 ⟶ H_2O + NO_2 + H_3PO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 PH_3 ⟶ c_3 H_2O + c_4 NO_2 + c_5 H_3PO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O and P: H: | c_1 + 3 c_2 = 2 c_3 + 3 c_5 N: | c_1 = c_4 O: | 3 c_1 = c_3 + 2 c_4 + 4 c_5 P: | 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 = 8 c_2 = 1 c_3 = 4 c_4 = 8 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 HNO_3 + PH_3 ⟶ 4 H_2O + 8 NO_2 + H_3PO_4

+ ⟶ + +

nitric acid + phosphine ⟶ water + nitrogen dioxide + phosphoric acid

| nitric acid | phosphine | water | nitrogen dioxide | phosphoric acid molecular free energy | -80.7 kJ/mol | 13.5 kJ/mol | -237.1 kJ/mol | 51.3 kJ/mol | -1124 kJ/mol total free energy | -645.6 kJ/mol | 13.5 kJ/mol | -948.4 kJ/mol | 410.4 kJ/mol | -1124 kJ/mol | G_initial = -632.1 kJ/mol | | G_final = -1662 kJ/mol | | ΔG_rxn^0 | -1662 kJ/mol - -632.1 kJ/mol = -1030 kJ/mol (exergonic) | | | |

Construct the equilibrium constant, K, expression for: HNO_3 + PH_3 ⟶ H_2O + NO_2 + H_3PO_4 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: 8 HNO_3 + PH_3 ⟶ 4 H_2O + 8 NO_2 + H_3PO_4 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 | 8 | -8 PH_3 | 1 | -1 H_2O | 4 | 4 NO_2 | 8 | 8 H_3PO_4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HNO_3 | 8 | -8 | ([HNO3])^(-8) PH_3 | 1 | -1 | ([PH3])^(-1) H_2O | 4 | 4 | ([H2O])^4 NO_2 | 8 | 8 | ([NO2])^8 H_3PO_4 | 1 | 1 | [H3PO4] 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])^(-8) ([PH3])^(-1) ([H2O])^4 ([NO2])^8 [H3PO4] = (([H2O])^4 ([NO2])^8 [H3PO4])/(([HNO3])^8 [PH3])

Construct the rate of reaction expression for: HNO_3 + PH_3 ⟶ H_2O + NO_2 + H_3PO_4 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: 8 HNO_3 + PH_3 ⟶ 4 H_2O + 8 NO_2 + H_3PO_4 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 | 8 | -8 PH_3 | 1 | -1 H_2O | 4 | 4 NO_2 | 8 | 8 H_3PO_4 | 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 HNO_3 | 8 | -8 | -1/8 (Δ[HNO3])/(Δt) PH_3 | 1 | -1 | -(Δ[PH3])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) NO_2 | 8 | 8 | 1/8 (Δ[NO2])/(Δt) H_3PO_4 | 1 | 1 | (Δ[H3PO4])/(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 = -1/8 (Δ[HNO3])/(Δt) = -(Δ[PH3])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/8 (Δ[NO2])/(Δt) = (Δ[H3PO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitric acid | phosphine | water | nitrogen dioxide | phosphoric acid formula | HNO_3 | PH_3 | H_2O | NO_2 | H_3PO_4 Hill formula | HNO_3 | H_3P | H_2O | NO_2 | H_3O_4P name | nitric acid | phosphine | water | nitrogen dioxide | phosphoric acid IUPAC name | nitric acid | phosphine | water | Nitrogen dioxide | phosphoric acid

| nitric acid | phosphine | water | nitrogen dioxide | phosphoric acid molar mass | 63.012 g/mol | 33.998 g/mol | 18.015 g/mol | 46.005 g/mol | 97.994 g/mol phase | liquid (at STP) | gas (at STP) | liquid (at STP) | gas (at STP) | liquid (at STP) melting point | -41.6 °C | -132.8 °C | 0 °C | -11 °C | 42.4 °C boiling point | 83 °C | -87.5 °C | 99.9839 °C | 21 °C | 158 °C density | 1.5129 g/cm^3 | 0.00139 g/cm^3 (at 25 °C) | 1 g/cm^3 | 0.00188 g/cm^3 (at 25 °C) | 1.685 g/cm^3 solubility in water | miscible | slightly soluble | | reacts | very soluble surface tension | | | 0.0728 N/m | | dynamic viscosity | 7.6×10^-4 Pa s (at 25 °C) | 1.1×10^-5 Pa s (at 0 °C) | 8.9×10^-4 Pa s (at 25 °C) | 4.02×10^-4 Pa s (at 25 °C) | odor | | | odorless | | odorless