P + N2O = N2 + P2O3

P red phosphorus + N_2O nitrous oxide ⟶ N_2 nitrogen + P_2O_3 phosphorus trioxide

Balance the chemical equation algebraically: P + N_2O ⟶ N_2 + P_2O_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 P + c_2 N_2O ⟶ c_3 N_2 + c_4 P_2O_3 Set the number of atoms in the reactants equal to the number of atoms in the products for P, N and O: P: | c_1 = 2 c_4 N: | 2 c_2 = 2 c_3 O: | c_2 = 3 c_4 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 = 2 c_2 = 3 c_3 = 3 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 P + 3 N_2O ⟶ 3 N_2 + P_2O_3

+ ⟶ +

red phosphorus + nitrous oxide ⟶ nitrogen + phosphorus trioxide

Construct the equilibrium constant, K, expression for: P + N_2O ⟶ N_2 + P_2O_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: 2 P + 3 N_2O ⟶ 3 N_2 + P_2O_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 P | 2 | -2 N_2O | 3 | -3 N_2 | 3 | 3 P_2O_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression P | 2 | -2 | ([P])^(-2) N_2O | 3 | -3 | ([N2O])^(-3) N_2 | 3 | 3 | ([N2])^3 P_2O_3 | 1 | 1 | [P2O3] 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])^(-2) ([N2O])^(-3) ([N2])^3 [P2O3] = (([N2])^3 [P2O3])/(([P])^2 ([N2O])^3)

Construct the rate of reaction expression for: P + N_2O ⟶ N_2 + P_2O_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: 2 P + 3 N_2O ⟶ 3 N_2 + P_2O_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 P | 2 | -2 N_2O | 3 | -3 N_2 | 3 | 3 P_2O_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 P | 2 | -2 | -1/2 (Δ[P])/(Δt) N_2O | 3 | -3 | -1/3 (Δ[N2O])/(Δt) N_2 | 3 | 3 | 1/3 (Δ[N2])/(Δt) P_2O_3 | 1 | 1 | (Δ[P2O3])/(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 = -1/2 (Δ[P])/(Δt) = -1/3 (Δ[N2O])/(Δt) = 1/3 (Δ[N2])/(Δt) = (Δ[P2O3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| red phosphorus | nitrous oxide | nitrogen | phosphorus trioxide formula | P | N_2O | N_2 | P_2O_3 Hill formula | P | N_2O | N_2 | O_3P_2 name | red phosphorus | nitrous oxide | nitrogen | phosphorus trioxide IUPAC name | phosphorus | nitrous oxide | molecular nitrogen |

| red phosphorus | nitrous oxide | nitrogen | phosphorus trioxide molar mass | 30.973761998 g/mol | 44.013 g/mol | 28.014 g/mol | 109.94 g/mol phase | solid (at STP) | gas (at STP) | gas (at STP) | solid (at STP) melting point | 579.2 °C | -91 °C | -210 °C | 23.8 °C boiling point | | -88 °C | -195.79 °C | 173.1 °C density | 2.16 g/cm^3 | 0.001799 g/cm^3 (at 25 °C) | 0.001251 g/cm^3 (at 0 °C) | 2.135 g/cm^3 solubility in water | insoluble | | insoluble | decomposes surface tension | | 0.00175 N/m | 0.0066 N/m | dynamic viscosity | 7.6×10^-4 Pa s (at 20.2 °C) | 1.491×10^-5 Pa s (at 25 °C) | 1.78×10^-5 Pa s (at 25 °C) | odor | | | odorless |