H2S + NaClO = H2O + SO2 + NaCl

H_2S hydrogen sulfide + NaOCl sodium hypochlorite ⟶ H_2O water + SO_2 sulfur dioxide + NaCl sodium chloride

Balance the chemical equation algebraically: H_2S + NaOCl ⟶ H_2O + SO_2 + NaCl Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2S + c_2 NaOCl ⟶ c_3 H_2O + c_4 SO_2 + c_5 NaCl Set the number of atoms in the reactants equal to the number of atoms in the products for H, S, Cl, Na and O: H: | 2 c_1 = 2 c_3 S: | c_1 = c_4 Cl: | c_2 = c_5 Na: | c_2 = c_5 O: | c_2 = c_3 + 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 3 c_3 = 1 c_4 = 1 c_5 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2S + 3 NaOCl ⟶ H_2O + SO_2 + 3 NaCl

+ ⟶ + +

hydrogen sulfide + sodium hypochlorite ⟶ water + sulfur dioxide + sodium chloride

Construct the equilibrium constant, K, expression for: H_2S + NaOCl ⟶ H_2O + SO_2 + NaCl 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_2S + 3 NaOCl ⟶ H_2O + SO_2 + 3 NaCl 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_2S | 1 | -1 NaOCl | 3 | -3 H_2O | 1 | 1 SO_2 | 1 | 1 NaCl | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2S | 1 | -1 | ([H2S])^(-1) NaOCl | 3 | -3 | ([NaOCl])^(-3) H_2O | 1 | 1 | [H2O] SO_2 | 1 | 1 | [SO2] NaCl | 3 | 3 | ([NaCl])^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 = ([H2S])^(-1) ([NaOCl])^(-3) [H2O] [SO2] ([NaCl])^3 = ([H2O] [SO2] ([NaCl])^3)/([H2S] ([NaOCl])^3)

Construct the rate of reaction expression for: H_2S + NaOCl ⟶ H_2O + SO_2 + NaCl 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_2S + 3 NaOCl ⟶ H_2O + SO_2 + 3 NaCl 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_2S | 1 | -1 NaOCl | 3 | -3 H_2O | 1 | 1 SO_2 | 1 | 1 NaCl | 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 H_2S | 1 | -1 | -(Δ[H2S])/(Δt) NaOCl | 3 | -3 | -1/3 (Δ[NaOCl])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) SO_2 | 1 | 1 | (Δ[SO2])/(Δt) NaCl | 3 | 3 | 1/3 (Δ[NaCl])/(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[H2S])/(Δt) = -1/3 (Δ[NaOCl])/(Δt) = (Δ[H2O])/(Δt) = (Δ[SO2])/(Δt) = 1/3 (Δ[NaCl])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen sulfide | sodium hypochlorite | water | sulfur dioxide | sodium chloride formula | H_2S | NaOCl | H_2O | SO_2 | NaCl Hill formula | H_2S | ClNaO | H_2O | O_2S | ClNa name | hydrogen sulfide | sodium hypochlorite | water | sulfur dioxide | sodium chloride