HNO3 + P4 = H2O + NO2 + H3PO4

HNO_3 (nitric acid) + P_4 (white phosphorus) ⟶ H_2O (water) + NO_2 (nitrogen dioxide) + H_3PO_4 (phosphoric acid)

Balance the chemical equation algebraically: HNO_3 + P_4 ⟶ H_2O + NO_2 + H_3PO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 P_4 ⟶ 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 = 2 c_3 + 3 c_5 N: | c_1 = c_4 O: | 3 c_1 = c_3 + 2 c_4 + 4 c_5 P: | 4 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 = 20 c_2 = 1 c_3 = 4 c_4 = 20 c_5 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 20 HNO_3 + P_4 ⟶ 4 H_2O + 20 NO_2 + 4 H_3PO_4

+ ⟶ + +

nitric acid + white phosphorus ⟶ water + nitrogen dioxide + phosphoric acid

K_c = ([H2O]^4 [NO2]^20 [H3PO4]^4)/([HNO3]^20 [P4])

rate = -1/20 (Δ[HNO3])/(Δt) = -(Δ[P4])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/20 (Δ[NO2])/(Δt) = 1/4 (Δ[H3PO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitric acid | white phosphorus | water | nitrogen dioxide | phosphoric acid formula | HNO_3 | P_4 | H_2O | NO_2 | H_3PO_4 Hill formula | HNO_3 | P_4 | H_2O | NO_2 | H_3O_4P name | nitric acid | white phosphorus | water | nitrogen dioxide | phosphoric acid IUPAC name | nitric acid | tetraphosphorus | water | Nitrogen dioxide | phosphoric acid

| nitric acid | white phosphorus | water | nitrogen dioxide | phosphoric acid molar mass | 63.012 g/mol | 123.89504799 g/mol | 18.015 g/mol | 46.005 g/mol | 97.994 g/mol phase | liquid (at STP) | solid (at STP) | liquid (at STP) | gas (at STP) | liquid (at STP) melting point | -41.6 °C | 44.15 °C | 0 °C | -11 °C | 42.4 °C boiling point | 83 °C | 280.5 °C | 99.9839 °C | 21 °C | 158 °C density | 1.5129 g/cm^3 | 1.823 g/cm^3 | 1 g/cm^3 | 0.00188 g/cm^3 (at 25 °C) | 1.685 g/cm^3 solubility in water | miscible | insoluble | | reacts | very soluble surface tension | | | 0.0728 N/m | | dynamic viscosity | 7.6×10^-4 Pa s (at 25 °C) | 0.00169 Pa s (at 50 °C) | 8.9×10^-4 Pa s (at 25 °C) | 4.02×10^-4 Pa s (at 25 °C) | odor | | odorless | odorless | | odorless