S + Na2SO3 = Na2S2O3

S mixed sulfur + Na_2SO_3 sodium sulfite ⟶ Na_2S_2O_3 sodium hyposulfite

Balance the chemical equation algebraically: S + Na_2SO_3 ⟶ Na_2S_2O_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 S + c_2 Na_2SO_3 ⟶ c_3 Na_2S_2O_3 Set the number of atoms in the reactants equal to the number of atoms in the products for S, Na and O: S: | c_1 + c_2 = 2 c_3 Na: | 2 c_2 = 2 c_3 O: | 3 c_2 = 3 c_3 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 = 1 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | S + Na_2SO_3 ⟶ Na_2S_2O_3

+ ⟶

mixed sulfur + sodium sulfite ⟶ sodium hyposulfite

Construct the equilibrium constant, K, expression for: S + Na_2SO_3 ⟶ Na_2S_2O_3 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: S + Na_2SO_3 ⟶ Na_2S_2O_3 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 S | 1 | -1 Na_2SO_3 | 1 | -1 Na_2S_2O_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression S | 1 | -1 | ([S])^(-1) Na_2SO_3 | 1 | -1 | ([Na2SO3])^(-1) Na_2S_2O_3 | 1 | 1 | [Na2S2O3] 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 = ([S])^(-1) ([Na2SO3])^(-1) [Na2S2O3] = ([Na2S2O3])/([S] [Na2SO3])

Construct the rate of reaction expression for: S + Na_2SO_3 ⟶ Na_2S_2O_3 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: S + Na_2SO_3 ⟶ Na_2S_2O_3 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 S | 1 | -1 Na_2SO_3 | 1 | -1 Na_2S_2O_3 | 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 S | 1 | -1 | -(Δ[S])/(Δt) Na_2SO_3 | 1 | -1 | -(Δ[Na2SO3])/(Δt) Na_2S_2O_3 | 1 | 1 | (Δ[Na2S2O3])/(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[S])/(Δt) = -(Δ[Na2SO3])/(Δt) = (Δ[Na2S2O3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| mixed sulfur | sodium sulfite | sodium hyposulfite formula | S | Na_2SO_3 | Na_2S_2O_3 Hill formula | S | Na_2O_3S | Na_2O_3S_2 name | mixed sulfur | sodium sulfite | sodium hyposulfite IUPAC name | sulfur | disodium sulfite |

| mixed sulfur | sodium sulfite | sodium hyposulfite molar mass | 32.06 g/mol | 126.04 g/mol | 158.1 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) melting point | 112.8 °C | 500 °C | 48 °C boiling point | 444.7 °C | | 100 °C density | 2.07 g/cm^3 | 2.63 g/cm^3 | 1.67 g/cm^3 odor | | | odorless