H2O + AgNO3 + P4 = HNO3 + H3PO4 + Ag

H_2O water + AgNO_3 silver nitrate + P_4 white phosphorus ⟶ HNO_3 nitric acid + H_3PO_4 phosphoric acid + Ag silver

Balance the chemical equation algebraically: H_2O + AgNO_3 + P_4 ⟶ HNO_3 + H_3PO_4 + Ag Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 AgNO_3 + c_3 P_4 ⟶ c_4 HNO_3 + c_5 H_3PO_4 + c_6 Ag Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Ag, N and P: H: | 2 c_1 = c_4 + 3 c_5 O: | c_1 + 3 c_2 = 3 c_4 + 4 c_5 Ag: | c_2 = c_6 N: | c_2 = c_4 P: | 4 c_3 = 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 16 c_2 = 20 c_3 = 1 c_4 = 20 c_5 = 4 c_6 = 20 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 16 H_2O + 20 AgNO_3 + P_4 ⟶ 20 HNO_3 + 4 H_3PO_4 + 20 Ag

+ + ⟶ + +

water + silver nitrate + white phosphorus ⟶ nitric acid + phosphoric acid + silver

Construct the equilibrium constant, K, expression for: H_2O + AgNO_3 + P_4 ⟶ HNO_3 + H_3PO_4 + Ag 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: 16 H_2O + 20 AgNO_3 + P_4 ⟶ 20 HNO_3 + 4 H_3PO_4 + 20 Ag 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 H_2O | 16 | -16 AgNO_3 | 20 | -20 P_4 | 1 | -1 HNO_3 | 20 | 20 H_3PO_4 | 4 | 4 Ag | 20 | 20 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 16 | -16 | ([H2O])^(-16) AgNO_3 | 20 | -20 | ([AgNO3])^(-20) P_4 | 1 | -1 | ([P4])^(-1) HNO_3 | 20 | 20 | ([HNO3])^20 H_3PO_4 | 4 | 4 | ([H3PO4])^4 Ag | 20 | 20 | ([Ag])^20 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 = ([H2O])^(-16) ([AgNO3])^(-20) ([P4])^(-1) ([HNO3])^20 ([H3PO4])^4 ([Ag])^20 = (([HNO3])^20 ([H3PO4])^4 ([Ag])^20)/(([H2O])^16 ([AgNO3])^20 [P4])

Construct the rate of reaction expression for: H_2O + AgNO_3 + P_4 ⟶ HNO_3 + H_3PO_4 + Ag 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: 16 H_2O + 20 AgNO_3 + P_4 ⟶ 20 HNO_3 + 4 H_3PO_4 + 20 Ag 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 H_2O | 16 | -16 AgNO_3 | 20 | -20 P_4 | 1 | -1 HNO_3 | 20 | 20 H_3PO_4 | 4 | 4 Ag | 20 | 20 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 H_2O | 16 | -16 | -1/16 (Δ[H2O])/(Δt) AgNO_3 | 20 | -20 | -1/20 (Δ[AgNO3])/(Δt) P_4 | 1 | -1 | -(Δ[P4])/(Δt) HNO_3 | 20 | 20 | 1/20 (Δ[HNO3])/(Δt) H_3PO_4 | 4 | 4 | 1/4 (Δ[H3PO4])/(Δt) Ag | 20 | 20 | 1/20 (Δ[Ag])/(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 = -1/16 (Δ[H2O])/(Δt) = -1/20 (Δ[AgNO3])/(Δt) = -(Δ[P4])/(Δt) = 1/20 (Δ[HNO3])/(Δt) = 1/4 (Δ[H3PO4])/(Δt) = 1/20 (Δ[Ag])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | silver nitrate | white phosphorus | nitric acid | phosphoric acid | silver formula | H_2O | AgNO_3 | P_4 | HNO_3 | H_3PO_4 | Ag Hill formula | H_2O | AgNO_3 | P_4 | HNO_3 | H_3O_4P | Ag name | water | silver nitrate | white phosphorus | nitric acid | phosphoric acid | silver IUPAC name | water | silver nitrate | tetraphosphorus | nitric acid | phosphoric acid | silver

| water | silver nitrate | white phosphorus | nitric acid | phosphoric acid | silver molar mass | 18.015 g/mol | 169.87 g/mol | 123.89504799 g/mol | 63.012 g/mol | 97.994 g/mol | 107.8682 g/mol phase | liquid (at STP) | solid (at STP) | solid (at STP) | liquid (at STP) | liquid (at STP) | solid (at STP) melting point | 0 °C | 212 °C | 44.15 °C | -41.6 °C | 42.4 °C | 960 °C boiling point | 99.9839 °C | | 280.5 °C | 83 °C | 158 °C | 2212 °C density | 1 g/cm^3 | | 1.823 g/cm^3 | 1.5129 g/cm^3 | 1.685 g/cm^3 | 10.49 g/cm^3 solubility in water | | soluble | insoluble | miscible | very soluble | insoluble surface tension | 0.0728 N/m | | | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | 0.00169 Pa s (at 50 °C) | 7.6×10^-4 Pa s (at 25 °C) | | odor | odorless | odorless | odorless | | odorless |