HNO3 + P2O5 = N2O5 + HPO3

HNO_3 nitric acid + P2O5 ⟶ N_2O_5 dinitrogen pentoxide + HPO_3 metaphosphoric acid

Balance the chemical equation algebraically: HNO_3 + P2O5 ⟶ N_2O_5 + HPO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 P2O5 ⟶ c_3 N_2O_5 + c_4 HPO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O and P: H: | c_1 = c_4 N: | c_1 = 2 c_3 O: | 3 c_1 + 5 c_2 = 5 c_3 + 3 c_4 P: | 2 c_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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 1 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 HNO_3 + P2O5 ⟶ N_2O_5 + 2 HPO_3

+ P2O5 ⟶ +

nitric acid + P2O5 ⟶ dinitrogen pentoxide + metaphosphoric acid

Construct the equilibrium constant, K, expression for: HNO_3 + P2O5 ⟶ N_2O_5 + HPO_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 HNO_3 + P2O5 ⟶ N_2O_5 + 2 HPO_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 HNO_3 | 2 | -2 P2O5 | 1 | -1 N_2O_5 | 1 | 1 HPO_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HNO_3 | 2 | -2 | ([HNO3])^(-2) P2O5 | 1 | -1 | ([P2O5])^(-1) N_2O_5 | 1 | 1 | [N2O5] HPO_3 | 2 | 2 | ([HPO3])^2 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 = ([HNO3])^(-2) ([P2O5])^(-1) [N2O5] ([HPO3])^2 = ([N2O5] ([HPO3])^2)/(([HNO3])^2 [P2O5])

Construct the rate of reaction expression for: HNO_3 + P2O5 ⟶ N_2O_5 + HPO_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 HNO_3 + P2O5 ⟶ N_2O_5 + 2 HPO_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 HNO_3 | 2 | -2 P2O5 | 1 | -1 N_2O_5 | 1 | 1 HPO_3 | 2 | 2 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 HNO_3 | 2 | -2 | -1/2 (Δ[HNO3])/(Δt) P2O5 | 1 | -1 | -(Δ[P2O5])/(Δt) N_2O_5 | 1 | 1 | (Δ[N2O5])/(Δt) HPO_3 | 2 | 2 | 1/2 (Δ[HPO3])/(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[HNO3])/(Δt) = -(Δ[P2O5])/(Δt) = (Δ[N2O5])/(Δt) = 1/2 (Δ[HPO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitric acid | P2O5 | dinitrogen pentoxide | metaphosphoric acid formula | HNO_3 | P2O5 | N_2O_5 | HPO_3 Hill formula | HNO_3 | O5P2 | N_2O_5 | HO_3P name | nitric acid | | dinitrogen pentoxide | metaphosphoric acid IUPAC name | nitric acid | | nitro nitrate | phosphenic acid

| nitric acid | P2O5 | dinitrogen pentoxide | metaphosphoric acid molar mass | 63.012 g/mol | 141.94 g/mol | 108.01 g/mol | 79.979 g/mol phase | liquid (at STP) | | solid (at STP) | liquid (at STP) melting point | -41.6 °C | | 30 °C | 21 °C boiling point | 83 °C | | 47 °C | 260 °C density | 1.5129 g/cm^3 | | 2.05 g/cm^3 | 2.4 g/cm^3 solubility in water | miscible | | | soluble dynamic viscosity | 7.6×10^-4 Pa s (at 25 °C) | | |