NO + H2S = H2O + S + N2

NO nitric oxide + H_2S hydrogen sulfide ⟶ H_2O water + S mixed sulfur + N_2 nitrogen

Balance the chemical equation algebraically: NO + H_2S ⟶ H_2O + S + N_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NO + c_2 H_2S ⟶ c_3 H_2O + c_4 S + c_5 N_2 Set the number of atoms in the reactants equal to the number of atoms in the products for N, O, H and S: N: | c_1 = 2 c_5 O: | c_1 = c_3 H: | 2 c_2 = 2 c_3 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 = 2 c_2 = 2 c_3 = 2 c_4 = 2 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 NO + 2 H_2S ⟶ 2 H_2O + 2 S + N_2

+ ⟶ + +

nitric oxide + hydrogen sulfide ⟶ water + mixed sulfur + nitrogen

Construct the equilibrium constant, K, expression for: NO + H_2S ⟶ H_2O + S + N_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 NO + 2 H_2S ⟶ 2 H_2O + 2 S + N_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 NO | 2 | -2 H_2S | 2 | -2 H_2O | 2 | 2 S | 2 | 2 N_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NO | 2 | -2 | ([NO])^(-2) H_2S | 2 | -2 | ([H2S])^(-2) H_2O | 2 | 2 | ([H2O])^2 S | 2 | 2 | ([S])^2 N_2 | 1 | 1 | [N2] 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 = ([NO])^(-2) ([H2S])^(-2) ([H2O])^2 ([S])^2 [N2] = (([H2O])^2 ([S])^2 [N2])/(([NO])^2 ([H2S])^2)

Construct the rate of reaction expression for: NO + H_2S ⟶ H_2O + S + N_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 NO + 2 H_2S ⟶ 2 H_2O + 2 S + N_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 NO | 2 | -2 H_2S | 2 | -2 H_2O | 2 | 2 S | 2 | 2 N_2 | 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 NO | 2 | -2 | -1/2 (Δ[NO])/(Δt) H_2S | 2 | -2 | -1/2 (Δ[H2S])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) S | 2 | 2 | 1/2 (Δ[S])/(Δt) N_2 | 1 | 1 | (Δ[N2])/(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[NO])/(Δt) = -1/2 (Δ[H2S])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/2 (Δ[S])/(Δt) = (Δ[N2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitric oxide | hydrogen sulfide | water | mixed sulfur | nitrogen formula | NO | H_2S | H_2O | S | N_2 name | nitric oxide | hydrogen sulfide | water | mixed sulfur | nitrogen IUPAC name | nitric oxide | hydrogen sulfide | water | sulfur | molecular nitrogen