H2S2O4 = H2O + S + SO2

H2S2O4 ⟶ H_2O water + S mixed sulfur + SO_2 sulfur dioxide

Balance the chemical equation algebraically: H2S2O4 ⟶ H_2O + S + SO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H2S2O4 ⟶ c_2 H_2O + c_3 S + c_4 SO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, S and O: H: | 2 c_1 = 2 c_2 S: | 2 c_1 = c_3 + c_4 O: | 4 c_1 = c_2 + 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 2 c_3 = 1 c_4 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H2S2O4 ⟶ 2 H_2O + S + 3 SO_2

H2S2O4 ⟶ + +

H2S2O4 ⟶ water + mixed sulfur + sulfur dioxide

Construct the equilibrium constant, K, expression for: H2S2O4 ⟶ H_2O + S + SO_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 H2S2O4 ⟶ 2 H_2O + S + 3 SO_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 H2S2O4 | 2 | -2 H_2O | 2 | 2 S | 1 | 1 SO_2 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H2S2O4 | 2 | -2 | ([H2S2O4])^(-2) H_2O | 2 | 2 | ([H2O])^2 S | 1 | 1 | [S] SO_2 | 3 | 3 | ([SO2])^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 = ([H2S2O4])^(-2) ([H2O])^2 [S] ([SO2])^3 = (([H2O])^2 [S] ([SO2])^3)/([H2S2O4])^2

Construct the rate of reaction expression for: H2S2O4 ⟶ H_2O + S + SO_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 H2S2O4 ⟶ 2 H_2O + S + 3 SO_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 H2S2O4 | 2 | -2 H_2O | 2 | 2 S | 1 | 1 SO_2 | 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 H2S2O4 | 2 | -2 | -1/2 (Δ[H2S2O4])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) S | 1 | 1 | (Δ[S])/(Δt) SO_2 | 3 | 3 | 1/3 (Δ[SO2])/(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[H2S2O4])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[S])/(Δt) = 1/3 (Δ[SO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| H2S2O4 | water | mixed sulfur | sulfur dioxide formula | H2S2O4 | H_2O | S | SO_2 Hill formula | H2O4S2 | H_2O | S | O_2S name | | water | mixed sulfur | sulfur dioxide IUPAC name | | water | sulfur | sulfur dioxide

| H2S2O4 | water | mixed sulfur | sulfur dioxide molar mass | 130.1 g/mol | 18.015 g/mol | 32.06 g/mol | 64.06 g/mol phase | | liquid (at STP) | solid (at STP) | gas (at STP) melting point | | 0 °C | 112.8 °C | -73 °C boiling point | | 99.9839 °C | 444.7 °C | -10 °C density | | 1 g/cm^3 | 2.07 g/cm^3 | 0.002619 g/cm^3 (at 25 °C) surface tension | | 0.0728 N/m | | 0.02859 N/m dynamic viscosity | | 8.9×10^-4 Pa s (at 25 °C) | | 1.282×10^-5 Pa s (at 25 °C) odor | | odorless | |