HNO3 + P = H2O + NO2 + HPO3

HNO_3 nitric acid + P red phosphorus ⟶ H_2O water + NO_2 nitrogen dioxide + HPO_3 metaphosphoric acid

Balance the chemical equation algebraically: HNO_3 + P ⟶ H_2O + NO_2 + HPO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 P ⟶ c_3 H_2O + c_4 NO_2 + c_5 HPO_3 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 = 2 c_3 + c_5 N: | c_1 = c_4 O: | 3 c_1 = c_3 + 2 c_4 + 3 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 = 5 c_2 = 1 c_3 = 2 c_4 = 5 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 5 HNO_3 + P ⟶ 2 H_2O + 5 NO_2 + HPO_3

+ ⟶ + +

nitric acid + red phosphorus ⟶ water + nitrogen dioxide + metaphosphoric acid

Construct the equilibrium constant, K, expression for: HNO_3 + P ⟶ H_2O + NO_2 + HPO_3 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 HNO_3 + P ⟶ 2 H_2O + 5 NO_2 + HPO_3 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 | 5 | -5 P | 1 | -1 H_2O | 2 | 2 NO_2 | 5 | 5 HPO_3 | 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 | 5 | -5 | ([HNO3])^(-5) P | 1 | -1 | ([P])^(-1) H_2O | 2 | 2 | ([H2O])^2 NO_2 | 5 | 5 | ([NO2])^5 HPO_3 | 1 | 1 | [HPO3] 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])^(-5) ([P])^(-1) ([H2O])^2 ([NO2])^5 [HPO3] = (([H2O])^2 ([NO2])^5 [HPO3])/(([HNO3])^5 [P])

Construct the rate of reaction expression for: HNO_3 + P ⟶ H_2O + NO_2 + HPO_3 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 HNO_3 + P ⟶ 2 H_2O + 5 NO_2 + HPO_3 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 | 5 | -5 P | 1 | -1 H_2O | 2 | 2 NO_2 | 5 | 5 HPO_3 | 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 | 5 | -5 | -1/5 (Δ[HNO3])/(Δt) P | 1 | -1 | -(Δ[P])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) NO_2 | 5 | 5 | 1/5 (Δ[NO2])/(Δt) HPO_3 | 1 | 1 | (Δ[HPO3])/(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[HNO3])/(Δt) = -(Δ[P])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/5 (Δ[NO2])/(Δt) = (Δ[HPO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitric acid | red phosphorus | water | nitrogen dioxide | metaphosphoric acid formula | HNO_3 | P | H_2O | NO_2 | HPO_3 Hill formula | HNO_3 | P | H_2O | NO_2 | HO_3P name | nitric acid | red phosphorus | water | nitrogen dioxide | metaphosphoric acid IUPAC name | nitric acid | phosphorus | water | Nitrogen dioxide | phosphenic acid

| nitric acid | red phosphorus | water | nitrogen dioxide | metaphosphoric acid molar mass | 63.012 g/mol | 30.973761998 g/mol | 18.015 g/mol | 46.005 g/mol | 79.979 g/mol phase | liquid (at STP) | solid (at STP) | liquid (at STP) | gas (at STP) | liquid (at STP) melting point | -41.6 °C | 579.2 °C | 0 °C | -11 °C | 21 °C boiling point | 83 °C | | 99.9839 °C | 21 °C | 260 °C density | 1.5129 g/cm^3 | 2.16 g/cm^3 | 1 g/cm^3 | 0.00188 g/cm^3 (at 25 °C) | 2.4 g/cm^3 solubility in water | miscible | insoluble | | reacts | soluble surface tension | | | 0.0728 N/m | | dynamic viscosity | 7.6×10^-4 Pa s (at 25 °C) | 7.6×10^-4 Pa s (at 20.2 °C) | 8.9×10^-4 Pa s (at 25 °C) | 4.02×10^-4 Pa s (at 25 °C) | odor | | | odorless | |