KOH + N2O + KClO = H2O + KCl + KNO2

KOH potassium hydroxide + N_2O nitrous oxide + KClO ⟶ H_2O water + KCl potassium chloride + KNO_2 potassium nitrite

Balance the chemical equation algebraically: KOH + N_2O + KClO ⟶ H_2O + KCl + KNO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 N_2O + c_3 KClO ⟶ c_4 H_2O + c_5 KCl + c_6 KNO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, K, O, N and Cl: H: | c_1 = 2 c_4 K: | c_1 + c_3 = c_5 + c_6 O: | c_1 + c_2 + c_3 = c_4 + 2 c_6 N: | 2 c_2 = c_6 Cl: | c_3 = c_5 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 = 2 c_4 = 1 c_5 = 2 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 KOH + N_2O + 2 KClO ⟶ H_2O + 2 KCl + 2 KNO_2

+ + KClO ⟶ + +

potassium hydroxide + nitrous oxide + KClO ⟶ water + potassium chloride + potassium nitrite

Construct the equilibrium constant, K, expression for: KOH + N_2O + KClO ⟶ H_2O + KCl + KNO_2 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 KOH + N_2O + 2 KClO ⟶ H_2O + 2 KCl + 2 KNO_2 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 | 2 | -2 N_2O | 1 | -1 KClO | 2 | -2 H_2O | 1 | 1 KCl | 2 | 2 KNO_2 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 2 | -2 | ([KOH])^(-2) N_2O | 1 | -1 | ([N2O])^(-1) KClO | 2 | -2 | ([KClO])^(-2) H_2O | 1 | 1 | [H2O] KCl | 2 | 2 | ([KCl])^2 KNO_2 | 2 | 2 | ([KNO2])^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])^(-2) ([N2O])^(-1) ([KClO])^(-2) [H2O] ([KCl])^2 ([KNO2])^2 = ([H2O] ([KCl])^2 ([KNO2])^2)/(([KOH])^2 [N2O] ([KClO])^2)

Construct the rate of reaction expression for: KOH + N_2O + KClO ⟶ H_2O + KCl + KNO_2 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 KOH + N_2O + 2 KClO ⟶ H_2O + 2 KCl + 2 KNO_2 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 | 2 | -2 N_2O | 1 | -1 KClO | 2 | -2 H_2O | 1 | 1 KCl | 2 | 2 KNO_2 | 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 | 2 | -2 | -1/2 (Δ[KOH])/(Δt) N_2O | 1 | -1 | -(Δ[N2O])/(Δt) KClO | 2 | -2 | -1/2 (Δ[KClO])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) KCl | 2 | 2 | 1/2 (Δ[KCl])/(Δt) KNO_2 | 2 | 2 | 1/2 (Δ[KNO2])/(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[KOH])/(Δt) = -(Δ[N2O])/(Δt) = -1/2 (Δ[KClO])/(Δt) = (Δ[H2O])/(Δt) = 1/2 (Δ[KCl])/(Δt) = 1/2 (Δ[KNO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium hydroxide | nitrous oxide | KClO | water | potassium chloride | potassium nitrite formula | KOH | N_2O | KClO | H_2O | KCl | KNO_2 Hill formula | HKO | N_2O | ClKO | H_2O | ClK | KNO_2 name | potassium hydroxide | nitrous oxide | | water | potassium chloride | potassium nitrite