H2 + SO2 = H2O + S

H_2 hydrogen + SO_2 sulfur dioxide ⟶ H_2O water + S mixed sulfur

Balance the chemical equation algebraically: H_2 + SO_2 ⟶ H_2O + S Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2 + c_2 SO_2 ⟶ c_3 H_2O + c_4 S Set the number of atoms in the reactants equal to the number of atoms in the products for H, O and S: H: | 2 c_1 = 2 c_3 O: | 2 c_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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2 + SO_2 ⟶ 2 H_2O + S

+ ⟶ +

hydrogen + sulfur dioxide ⟶ water + mixed sulfur

Construct the equilibrium constant, K, expression for: H_2 + SO_2 ⟶ H_2O + S 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 H_2 + SO_2 ⟶ 2 H_2O + S 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_2 | 2 | -2 SO_2 | 1 | -1 H_2O | 2 | 2 S | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2 | 2 | -2 | ([H2])^(-2) SO_2 | 1 | -1 | ([SO2])^(-1) H_2O | 2 | 2 | ([H2O])^2 S | 1 | 1 | [S] 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 = ([H2])^(-2) ([SO2])^(-1) ([H2O])^2 [S] = (([H2O])^2 [S])/(([H2])^2 [SO2])

Construct the rate of reaction expression for: H_2 + SO_2 ⟶ H_2O + S 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 H_2 + SO_2 ⟶ 2 H_2O + S 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_2 | 2 | -2 SO_2 | 1 | -1 H_2O | 2 | 2 S | 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 H_2 | 2 | -2 | -1/2 (Δ[H2])/(Δt) SO_2 | 1 | -1 | -(Δ[SO2])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) S | 1 | 1 | (Δ[S])/(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[H2])/(Δt) = -(Δ[SO2])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[S])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen | sulfur dioxide | water | mixed sulfur formula | H_2 | SO_2 | H_2O | S Hill formula | H_2 | O_2S | H_2O | S name | hydrogen | sulfur dioxide | water | mixed sulfur IUPAC name | molecular hydrogen | sulfur dioxide | water | sulfur