HNO3 + CoS = H2O + S + NO + Co(NO3)2

HNO_3 nitric acid + CoS cobaltous sulfide ⟶ H_2O water + S mixed sulfur + NO nitric oxide + CoN_2O_6 cobaltous nitrate

Balance the chemical equation algebraically: HNO_3 + CoS ⟶ H_2O + S + NO + CoN_2O_6 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 CoS ⟶ c_3 H_2O + c_4 S + c_5 NO + c_6 CoN_2O_6 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O, Co and S: H: | c_1 = 2 c_3 N: | c_1 = c_5 + 2 c_6 O: | 3 c_1 = c_3 + c_5 + 6 c_6 Co: | c_2 = c_6 S: | 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_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 4 c_2 = 3/2 c_3 = 2 c_4 = 3/2 c_5 = 1 c_6 = 3/2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 8 c_2 = 3 c_3 = 4 c_4 = 3 c_5 = 2 c_6 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 HNO_3 + 3 CoS ⟶ 4 H_2O + 3 S + 2 NO + 3 CoN_2O_6

+ ⟶ + + +

nitric acid + cobaltous sulfide ⟶ water + mixed sulfur + nitric oxide + cobaltous nitrate

Construct the equilibrium constant, K, expression for: HNO_3 + CoS ⟶ H_2O + S + NO + CoN_2O_6 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: 8 HNO_3 + 3 CoS ⟶ 4 H_2O + 3 S + 2 NO + 3 CoN_2O_6 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 | 8 | -8 CoS | 3 | -3 H_2O | 4 | 4 S | 3 | 3 NO | 2 | 2 CoN_2O_6 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HNO_3 | 8 | -8 | ([HNO3])^(-8) CoS | 3 | -3 | ([CoS])^(-3) H_2O | 4 | 4 | ([H2O])^4 S | 3 | 3 | ([S])^3 NO | 2 | 2 | ([NO])^2 CoN_2O_6 | 3 | 3 | ([CoN2O6])^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 = ([HNO3])^(-8) ([CoS])^(-3) ([H2O])^4 ([S])^3 ([NO])^2 ([CoN2O6])^3 = (([H2O])^4 ([S])^3 ([NO])^2 ([CoN2O6])^3)/(([HNO3])^8 ([CoS])^3)

Construct the rate of reaction expression for: HNO_3 + CoS ⟶ H_2O + S + NO + CoN_2O_6 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: 8 HNO_3 + 3 CoS ⟶ 4 H_2O + 3 S + 2 NO + 3 CoN_2O_6 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 | 8 | -8 CoS | 3 | -3 H_2O | 4 | 4 S | 3 | 3 NO | 2 | 2 CoN_2O_6 | 3 | 3 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 | 8 | -8 | -1/8 (Δ[HNO3])/(Δt) CoS | 3 | -3 | -1/3 (Δ[CoS])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) S | 3 | 3 | 1/3 (Δ[S])/(Δt) NO | 2 | 2 | 1/2 (Δ[NO])/(Δt) CoN_2O_6 | 3 | 3 | 1/3 (Δ[CoN2O6])/(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 = -1/8 (Δ[HNO3])/(Δt) = -1/3 (Δ[CoS])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/3 (Δ[S])/(Δt) = 1/2 (Δ[NO])/(Δt) = 1/3 (Δ[CoN2O6])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitric acid | cobaltous sulfide | water | mixed sulfur | nitric oxide | cobaltous nitrate formula | HNO_3 | CoS | H_2O | S | NO | CoN_2O_6 name | nitric acid | cobaltous sulfide | water | mixed sulfur | nitric oxide | cobaltous nitrate IUPAC name | nitric acid | | water | sulfur | nitric oxide | cobalt(+2) cation dinitrate