PH3 + N2O = H2O + N2 + P4H10

PH_3 phosphine + N_2O nitrous oxide ⟶ H_2O water + N_2 nitrogen + P4H10

Balance the chemical equation algebraically: PH_3 + N_2O ⟶ H_2O + N_2 + P4H10 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 PH_3 + c_2 N_2O ⟶ c_3 H_2O + c_4 N_2 + c_5 P4H10 Set the number of atoms in the reactants equal to the number of atoms in the products for H, P, N and O: H: | 3 c_1 = 2 c_3 + 10 c_5 P: | c_1 = 4 c_5 N: | 2 c_2 = 2 c_4 O: | c_2 = c_3 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 = 4 c_2 = 1 c_3 = 1 c_4 = 1 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 PH_3 + N_2O ⟶ H_2O + N_2 + P4H10

+ ⟶ + + P4H10

phosphine + nitrous oxide ⟶ water + nitrogen + P4H10

Construct the equilibrium constant, K, expression for: PH_3 + N_2O ⟶ H_2O + N_2 + P4H10 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: 4 PH_3 + N_2O ⟶ H_2O + N_2 + P4H10 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 PH_3 | 4 | -4 N_2O | 1 | -1 H_2O | 1 | 1 N_2 | 1 | 1 P4H10 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression PH_3 | 4 | -4 | ([PH3])^(-4) N_2O | 1 | -1 | ([N2O])^(-1) H_2O | 1 | 1 | [H2O] N_2 | 1 | 1 | [N2] P4H10 | 1 | 1 | [P4H10] 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 = ([PH3])^(-4) ([N2O])^(-1) [H2O] [N2] [P4H10] = ([H2O] [N2] [P4H10])/(([PH3])^4 [N2O])

Construct the rate of reaction expression for: PH_3 + N_2O ⟶ H_2O + N_2 + P4H10 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: 4 PH_3 + N_2O ⟶ H_2O + N_2 + P4H10 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 PH_3 | 4 | -4 N_2O | 1 | -1 H_2O | 1 | 1 N_2 | 1 | 1 P4H10 | 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 PH_3 | 4 | -4 | -1/4 (Δ[PH3])/(Δt) N_2O | 1 | -1 | -(Δ[N2O])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) N_2 | 1 | 1 | (Δ[N2])/(Δt) P4H10 | 1 | 1 | (Δ[P4H10])/(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 = -1/4 (Δ[PH3])/(Δt) = -(Δ[N2O])/(Δt) = (Δ[H2O])/(Δt) = (Δ[N2])/(Δt) = (Δ[P4H10])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| phosphine | nitrous oxide | water | nitrogen | P4H10 formula | PH_3 | N_2O | H_2O | N_2 | P4H10 Hill formula | H_3P | N_2O | H_2O | N_2 | H10P4 name | phosphine | nitrous oxide | water | nitrogen | IUPAC name | phosphine | nitrous oxide | water | molecular nitrogen |

| phosphine | nitrous oxide | water | nitrogen | P4H10 molar mass | 33.998 g/mol | 44.013 g/mol | 18.015 g/mol | 28.014 g/mol | 133.98 g/mol phase | gas (at STP) | gas (at STP) | liquid (at STP) | gas (at STP) | melting point | -132.8 °C | -91 °C | 0 °C | -210 °C | boiling point | -87.5 °C | -88 °C | 99.9839 °C | -195.79 °C | density | 0.00139 g/cm^3 (at 25 °C) | 0.001799 g/cm^3 (at 25 °C) | 1 g/cm^3 | 0.001251 g/cm^3 (at 0 °C) | solubility in water | slightly soluble | | | insoluble | surface tension | | 0.00175 N/m | 0.0728 N/m | 0.0066 N/m | dynamic viscosity | 1.1×10^-5 Pa s (at 0 °C) | 1.491×10^-5 Pa s (at 25 °C) | 8.9×10^-4 Pa s (at 25 °C) | 1.78×10^-5 Pa s (at 25 °C) | odor | | | odorless | odorless |