H2SO4 + H2S + KNO2 = H2O + K2SO4 + S + NO

H_2SO_4 sulfuric acid + H_2S hydrogen sulfide + KNO_2 potassium nitrite ⟶ H_2O water + K_2SO_4 potassium sulfate + S mixed sulfur + NO nitric oxide

Balance the chemical equation algebraically: H_2SO_4 + H_2S + KNO_2 ⟶ H_2O + K_2SO_4 + S + NO Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 H_2S + c_3 KNO_2 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 S + c_7 NO Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, K and N: H: | 2 c_1 + 2 c_2 = 2 c_4 O: | 4 c_1 + 2 c_3 = c_4 + 4 c_5 + c_7 S: | c_1 + c_2 = c_5 + c_6 K: | c_3 = 2 c_5 N: | c_3 = c_7 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_3 = 3 - c_2 c_4 = c_2 + 1 c_5 = 3/2 - c_2/2 c_6 = (3 c_2)/2 - 1/2 c_7 = 3 - c_2 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_2 = 1 and solve for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 2 c_4 = 2 c_5 = 1 c_6 = 1 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2SO_4 + H_2S + 2 KNO_2 ⟶ 2 H_2O + K_2SO_4 + S + 2 NO

+ + ⟶ + + +

sulfuric acid + hydrogen sulfide + potassium nitrite ⟶ water + potassium sulfate + mixed sulfur + nitric oxide

Construct the equilibrium constant, K, expression for: H_2SO_4 + H_2S + KNO_2 ⟶ H_2O + K_2SO_4 + S + NO 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: H_2SO_4 + H_2S + 2 KNO_2 ⟶ 2 H_2O + K_2SO_4 + S + 2 NO 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 H_2SO_4 | 1 | -1 H_2S | 1 | -1 KNO_2 | 2 | -2 H_2O | 2 | 2 K_2SO_4 | 1 | 1 S | 1 | 1 NO | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 1 | -1 | ([H2SO4])^(-1) H_2S | 1 | -1 | ([H2S])^(-1) KNO_2 | 2 | -2 | ([KNO2])^(-2) H_2O | 2 | 2 | ([H2O])^2 K_2SO_4 | 1 | 1 | [K2SO4] S | 1 | 1 | [S] NO | 2 | 2 | ([NO])^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 = ([H2SO4])^(-1) ([H2S])^(-1) ([KNO2])^(-2) ([H2O])^2 [K2SO4] [S] ([NO])^2 = (([H2O])^2 [K2SO4] [S] ([NO])^2)/([H2SO4] [H2S] ([KNO2])^2)

Construct the rate of reaction expression for: H_2SO_4 + H_2S + KNO_2 ⟶ H_2O + K_2SO_4 + S + NO 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: H_2SO_4 + H_2S + 2 KNO_2 ⟶ 2 H_2O + K_2SO_4 + S + 2 NO 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 H_2SO_4 | 1 | -1 H_2S | 1 | -1 KNO_2 | 2 | -2 H_2O | 2 | 2 K_2SO_4 | 1 | 1 S | 1 | 1 NO | 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 H_2SO_4 | 1 | -1 | -(Δ[H2SO4])/(Δt) H_2S | 1 | -1 | -(Δ[H2S])/(Δt) KNO_2 | 2 | -2 | -1/2 (Δ[KNO2])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) S | 1 | 1 | (Δ[S])/(Δt) NO | 2 | 2 | 1/2 (Δ[NO])/(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 = -(Δ[H2SO4])/(Δt) = -(Δ[H2S])/(Δt) = -1/2 (Δ[KNO2])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[K2SO4])/(Δt) = (Δ[S])/(Δt) = 1/2 (Δ[NO])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | hydrogen sulfide | potassium nitrite | water | potassium sulfate | mixed sulfur | nitric oxide formula | H_2SO_4 | H_2S | KNO_2 | H_2O | K_2SO_4 | S | NO Hill formula | H_2O_4S | H_2S | KNO_2 | H_2O | K_2O_4S | S | NO name | sulfuric acid | hydrogen sulfide | potassium nitrite | water | potassium sulfate | mixed sulfur | nitric oxide IUPAC name | sulfuric acid | hydrogen sulfide | potassium nitrite | water | dipotassium sulfate | sulfur | nitric oxide