P + NH4ClO4 = H2O + Cl2 + N2 + H3PO4

P red phosphorus + NH_4ClO_4 ammonium perchlorate ⟶ H_2O water + Cl_2 chlorine + N_2 nitrogen + H_3PO_4 phosphoric acid

Balance the chemical equation algebraically: P + NH_4ClO_4 ⟶ H_2O + Cl_2 + N_2 + H_3PO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 P + c_2 NH_4ClO_4 ⟶ c_3 H_2O + c_4 Cl_2 + c_5 N_2 + c_6 H_3PO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for P, Cl, H, N and O: P: | c_1 = c_6 Cl: | c_2 = 2 c_4 H: | 4 c_2 = 2 c_3 + 3 c_6 N: | c_2 = 2 c_5 O: | 4 c_2 = c_3 + 4 c_6 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 8/5 c_2 = 2 c_3 = 8/5 c_4 = 1 c_5 = 1 c_6 = 8/5 Multiply by the least common denominator, 5, to eliminate fractional coefficients: c_1 = 8 c_2 = 10 c_3 = 8 c_4 = 5 c_5 = 5 c_6 = 8 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 P + 10 NH_4ClO_4 ⟶ 8 H_2O + 5 Cl_2 + 5 N_2 + 8 H_3PO_4

+ ⟶ + + +

red phosphorus + ammonium perchlorate ⟶ water + chlorine + nitrogen + phosphoric acid

Construct the equilibrium constant, K, expression for: P + NH_4ClO_4 ⟶ H_2O + Cl_2 + N_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 P + 10 NH_4ClO_4 ⟶ 8 H_2O + 5 Cl_2 + 5 N_2 + 8 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 P | 8 | -8 NH_4ClO_4 | 10 | -10 H_2O | 8 | 8 Cl_2 | 5 | 5 N_2 | 5 | 5 H_3PO_4 | 8 | 8 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression P | 8 | -8 | ([P])^(-8) NH_4ClO_4 | 10 | -10 | ([NH4ClO4])^(-10) H_2O | 8 | 8 | ([H2O])^8 Cl_2 | 5 | 5 | ([Cl2])^5 N_2 | 5 | 5 | ([N2])^5 H_3PO_4 | 8 | 8 | ([H3PO4])^8 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 = ([P])^(-8) ([NH4ClO4])^(-10) ([H2O])^8 ([Cl2])^5 ([N2])^5 ([H3PO4])^8 = (([H2O])^8 ([Cl2])^5 ([N2])^5 ([H3PO4])^8)/(([P])^8 ([NH4ClO4])^10)

Construct the rate of reaction expression for: P + NH_4ClO_4 ⟶ H_2O + Cl_2 + N_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 P + 10 NH_4ClO_4 ⟶ 8 H_2O + 5 Cl_2 + 5 N_2 + 8 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 P | 8 | -8 NH_4ClO_4 | 10 | -10 H_2O | 8 | 8 Cl_2 | 5 | 5 N_2 | 5 | 5 H_3PO_4 | 8 | 8 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 P | 8 | -8 | -1/8 (Δ[P])/(Δt) NH_4ClO_4 | 10 | -10 | -1/10 (Δ[NH4ClO4])/(Δt) H_2O | 8 | 8 | 1/8 (Δ[H2O])/(Δt) Cl_2 | 5 | 5 | 1/5 (Δ[Cl2])/(Δt) N_2 | 5 | 5 | 1/5 (Δ[N2])/(Δt) H_3PO_4 | 8 | 8 | 1/8 (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[P])/(Δt) = -1/10 (Δ[NH4ClO4])/(Δt) = 1/8 (Δ[H2O])/(Δt) = 1/5 (Δ[Cl2])/(Δt) = 1/5 (Δ[N2])/(Δt) = 1/8 (Δ[H3PO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| red phosphorus | ammonium perchlorate | water | chlorine | nitrogen | phosphoric acid formula | P | NH_4ClO_4 | H_2O | Cl_2 | N_2 | H_3PO_4 Hill formula | P | ClH_4NO_4 | H_2O | Cl_2 | N_2 | H_3O_4P name | red phosphorus | ammonium perchlorate | water | chlorine | nitrogen | phosphoric acid IUPAC name | phosphorus | | water | molecular chlorine | molecular nitrogen | phosphoric acid

| red phosphorus | ammonium perchlorate | water | chlorine | nitrogen | phosphoric acid molar mass | 30.973761998 g/mol | 117.5 g/mol | 18.015 g/mol | 70.9 g/mol | 28.014 g/mol | 97.994 g/mol phase | solid (at STP) | | liquid (at STP) | gas (at STP) | gas (at STP) | liquid (at STP) melting point | 579.2 °C | | 0 °C | -101 °C | -210 °C | 42.4 °C boiling point | | | 99.9839 °C | -34 °C | -195.79 °C | 158 °C density | 2.16 g/cm^3 | 1.95 g/cm^3 | 1 g/cm^3 | 0.003214 g/cm^3 (at 0 °C) | 0.001251 g/cm^3 (at 0 °C) | 1.685 g/cm^3 solubility in water | insoluble | soluble | | | insoluble | very soluble surface tension | | | 0.0728 N/m | | 0.0066 N/m | dynamic viscosity | 7.6×10^-4 Pa s (at 20.2 °C) | | 8.9×10^-4 Pa s (at 25 °C) | | 1.78×10^-5 Pa s (at 25 °C) | odor | | | odorless | | odorless | odorless