KOH + NO2 + P2O3 = H2O + NO + K2HPO4

KOH potassium hydroxide + NO_2 nitrogen dioxide + P_2O_3 phosphorus trioxide ⟶ H_2O water + NO nitric oxide + K_2HPO_4 dipotassium hydrogen phosphate

Balance the chemical equation algebraically: KOH + NO_2 + P_2O_3 ⟶ H_2O + NO + K_2HPO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 NO_2 + c_3 P_2O_3 ⟶ c_4 H_2O + c_5 NO + c_6 K_2HPO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, K, O, N and P: H: | c_1 = 2 c_4 + c_6 K: | c_1 = 2 c_6 O: | c_1 + 2 c_2 + 3 c_3 = c_4 + c_5 + 4 c_6 N: | c_2 = c_5 P: | 2 c_3 = 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 4 c_2 = 2 c_3 = 1 c_4 = 1 c_5 = 2 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 KOH + 2 NO_2 + P_2O_3 ⟶ H_2O + 2 NO + 2 K_2HPO_4

+ + ⟶ + +

potassium hydroxide + nitrogen dioxide + phosphorus trioxide ⟶ water + nitric oxide + dipotassium hydrogen phosphate

Construct the equilibrium constant, K, expression for: KOH + NO_2 + P_2O_3 ⟶ H_2O + NO + K_2HPO_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: 4 KOH + 2 NO_2 + P_2O_3 ⟶ H_2O + 2 NO + 2 K_2HPO_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 KOH | 4 | -4 NO_2 | 2 | -2 P_2O_3 | 1 | -1 H_2O | 1 | 1 NO | 2 | 2 K_2HPO_4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 4 | -4 | ([KOH])^(-4) NO_2 | 2 | -2 | ([NO2])^(-2) P_2O_3 | 1 | -1 | ([P2O3])^(-1) H_2O | 1 | 1 | [H2O] NO | 2 | 2 | ([NO])^2 K_2HPO_4 | 2 | 2 | ([K2HPO4])^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 = ([KOH])^(-4) ([NO2])^(-2) ([P2O3])^(-1) [H2O] ([NO])^2 ([K2HPO4])^2 = ([H2O] ([NO])^2 ([K2HPO4])^2)/(([KOH])^4 ([NO2])^2 [P2O3])

Construct the rate of reaction expression for: KOH + NO_2 + P_2O_3 ⟶ H_2O + NO + K_2HPO_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: 4 KOH + 2 NO_2 + P_2O_3 ⟶ H_2O + 2 NO + 2 K_2HPO_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 KOH | 4 | -4 NO_2 | 2 | -2 P_2O_3 | 1 | -1 H_2O | 1 | 1 NO | 2 | 2 K_2HPO_4 | 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 KOH | 4 | -4 | -1/4 (Δ[KOH])/(Δt) NO_2 | 2 | -2 | -1/2 (Δ[NO2])/(Δt) P_2O_3 | 1 | -1 | -(Δ[P2O3])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) NO | 2 | 2 | 1/2 (Δ[NO])/(Δt) K_2HPO_4 | 2 | 2 | 1/2 (Δ[K2HPO4])/(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[KOH])/(Δt) = -1/2 (Δ[NO2])/(Δt) = -(Δ[P2O3])/(Δt) = (Δ[H2O])/(Δt) = 1/2 (Δ[NO])/(Δt) = 1/2 (Δ[K2HPO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium hydroxide | nitrogen dioxide | phosphorus trioxide | water | nitric oxide | dipotassium hydrogen phosphate formula | KOH | NO_2 | P_2O_3 | H_2O | NO | K_2HPO_4 Hill formula | HKO | NO_2 | O_3P_2 | H_2O | NO | HK_2O_4P name | potassium hydroxide | nitrogen dioxide | phosphorus trioxide | water | nitric oxide | dipotassium hydrogen phosphate IUPAC name | potassium hydroxide | Nitrogen dioxide | | water | nitric oxide | dipotassium hydrogen phosphate