NO2 + P = NO + P2O5

NO_2 nitrogen dioxide + P red phosphorus ⟶ NO nitric oxide + P2O5

Balance the chemical equation algebraically: NO_2 + P ⟶ NO + P2O5 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NO_2 + c_2 P ⟶ c_3 NO + c_4 P2O5 Set the number of atoms in the reactants equal to the number of atoms in the products for N, O and P: N: | c_1 = c_3 O: | 2 c_1 = c_3 + 5 c_4 P: | c_2 = 2 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 = 5 c_2 = 2 c_3 = 5 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 5 NO_2 + 2 P ⟶ 5 NO + P2O5

+ ⟶ + P2O5

nitrogen dioxide + red phosphorus ⟶ nitric oxide + P2O5

Construct the equilibrium constant, K, expression for: NO_2 + P ⟶ NO + P2O5 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: 5 NO_2 + 2 P ⟶ 5 NO + P2O5 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 NO_2 | 5 | -5 P | 2 | -2 NO | 5 | 5 P2O5 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NO_2 | 5 | -5 | ([NO2])^(-5) P | 2 | -2 | ([P])^(-2) NO | 5 | 5 | ([NO])^5 P2O5 | 1 | 1 | [P2O5] 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 = ([NO2])^(-5) ([P])^(-2) ([NO])^5 [P2O5] = (([NO])^5 [P2O5])/(([NO2])^5 ([P])^2)

Construct the rate of reaction expression for: NO_2 + P ⟶ NO + P2O5 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: 5 NO_2 + 2 P ⟶ 5 NO + P2O5 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 NO_2 | 5 | -5 P | 2 | -2 NO | 5 | 5 P2O5 | 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 NO_2 | 5 | -5 | -1/5 (Δ[NO2])/(Δt) P | 2 | -2 | -1/2 (Δ[P])/(Δt) NO | 5 | 5 | 1/5 (Δ[NO])/(Δt) P2O5 | 1 | 1 | (Δ[P2O5])/(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 = -1/5 (Δ[NO2])/(Δt) = -1/2 (Δ[P])/(Δt) = 1/5 (Δ[NO])/(Δt) = (Δ[P2O5])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitrogen dioxide | red phosphorus | nitric oxide | P2O5 formula | NO_2 | P | NO | P2O5 Hill formula | NO_2 | P | NO | O5P2 name | nitrogen dioxide | red phosphorus | nitric oxide | IUPAC name | Nitrogen dioxide | phosphorus | nitric oxide |

| nitrogen dioxide | red phosphorus | nitric oxide | P2O5 molar mass | 46.005 g/mol | 30.973761998 g/mol | 30.006 g/mol | 141.94 g/mol phase | gas (at STP) | solid (at STP) | gas (at STP) | melting point | -11 °C | 579.2 °C | -163.6 °C | boiling point | 21 °C | | -151.7 °C | density | 0.00188 g/cm^3 (at 25 °C) | 2.16 g/cm^3 | 0.001226 g/cm^3 (at 25 °C) | solubility in water | reacts | insoluble | | dynamic viscosity | 4.02×10^-4 Pa s (at 25 °C) | 7.6×10^-4 Pa s (at 20.2 °C) | 1.911×10^-5 Pa s (at 25 °C) |