HNO2 + Co(NO3)2 = H2O + NO + Co(NO3)3

HNO_2 nitrous acid + CoN_2O_6 cobaltous nitrate ⟶ H_2O water + NO nitric oxide + Co(NO_3)_3 cobalt(III) nitrate

Balance the chemical equation algebraically: HNO_2 + CoN_2O_6 ⟶ H_2O + NO + Co(NO_3)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_2 + c_2 CoN_2O_6 ⟶ c_3 H_2O + c_4 NO + c_5 Co(NO_3)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O and Co: H: | c_1 = 2 c_3 N: | c_1 + 2 c_2 = c_4 + 3 c_5 O: | 2 c_1 + 6 c_2 = c_3 + c_4 + 9 c_5 Co: | c_2 = 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 = 4 c_2 = 1 c_3 = 2 c_4 = 3 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 HNO_2 + CoN_2O_6 ⟶ 2 H_2O + 3 NO + Co(NO_3)_3

+ ⟶ + +

nitrous acid + cobaltous nitrate ⟶ water + nitric oxide + cobalt(III) nitrate

Construct the equilibrium constant, K, expression for: HNO_2 + CoN_2O_6 ⟶ H_2O + NO + Co(NO_3)_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: 4 HNO_2 + CoN_2O_6 ⟶ 2 H_2O + 3 NO + Co(NO_3)_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_2 | 4 | -4 CoN_2O_6 | 1 | -1 H_2O | 2 | 2 NO | 3 | 3 Co(NO_3)_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HNO_2 | 4 | -4 | ([HNO2])^(-4) CoN_2O_6 | 1 | -1 | ([CoN2O6])^(-1) H_2O | 2 | 2 | ([H2O])^2 NO | 3 | 3 | ([NO])^3 Co(NO_3)_3 | 1 | 1 | [Co(NO3)3] 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 = ([HNO2])^(-4) ([CoN2O6])^(-1) ([H2O])^2 ([NO])^3 [Co(NO3)3] = (([H2O])^2 ([NO])^3 [Co(NO3)3])/(([HNO2])^4 [CoN2O6])

Construct the rate of reaction expression for: HNO_2 + CoN_2O_6 ⟶ H_2O + NO + Co(NO_3)_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: 4 HNO_2 + CoN_2O_6 ⟶ 2 H_2O + 3 NO + Co(NO_3)_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_2 | 4 | -4 CoN_2O_6 | 1 | -1 H_2O | 2 | 2 NO | 3 | 3 Co(NO_3)_3 | 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 HNO_2 | 4 | -4 | -1/4 (Δ[HNO2])/(Δt) CoN_2O_6 | 1 | -1 | -(Δ[CoN2O6])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) NO | 3 | 3 | 1/3 (Δ[NO])/(Δt) Co(NO_3)_3 | 1 | 1 | (Δ[Co(NO3)3])/(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[HNO2])/(Δt) = -(Δ[CoN2O6])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/3 (Δ[NO])/(Δt) = (Δ[Co(NO3)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitrous acid | cobaltous nitrate | water | nitric oxide | cobalt(III) nitrate formula | HNO_2 | CoN_2O_6 | H_2O | NO | Co(NO_3)_3 Hill formula | HNO_2 | CoN_2O_6 | H_2O | NO | CoN_3O_9 name | nitrous acid | cobaltous nitrate | water | nitric oxide | cobalt(III) nitrate IUPAC name | nitrous acid | cobalt(+2) cation dinitrate | water | nitric oxide |