Na2S2O3 = Na2SO4 + Na2S5

Na_2S_2O_3 sodium hyposulfite ⟶ Na_2SO_4 sodium sulfate + Na2S5

Balance the chemical equation algebraically: Na_2S_2O_3 ⟶ Na_2SO_4 + Na2S5 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Na_2S_2O_3 ⟶ c_2 Na_2SO_4 + c_3 Na2S5 Set the number of atoms in the reactants equal to the number of atoms in the products for Na, O and S: Na: | 2 c_1 = 2 c_2 + 2 c_3 O: | 3 c_1 = 4 c_2 S: | 2 c_1 = c_2 + 5 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 4 c_2 = 3 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 Na_2S_2O_3 ⟶ 3 Na_2SO_4 + Na2S5

⟶ + Na2S5

sodium hyposulfite ⟶ sodium sulfate + Na2S5

Construct the equilibrium constant, K, expression for: Na_2S_2O_3 ⟶ Na_2SO_4 + Na2S5 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: 4 Na_2S_2O_3 ⟶ 3 Na_2SO_4 + Na2S5 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 Na_2S_2O_3 | 4 | -4 Na_2SO_4 | 3 | 3 Na2S5 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Na_2S_2O_3 | 4 | -4 | ([Na2S2O3])^(-4) Na_2SO_4 | 3 | 3 | ([Na2SO4])^3 Na2S5 | 1 | 1 | [Na2S5] 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 = ([Na2S2O3])^(-4) ([Na2SO4])^3 [Na2S5] = (([Na2SO4])^3 [Na2S5])/([Na2S2O3])^4

Construct the rate of reaction expression for: Na_2S_2O_3 ⟶ Na_2SO_4 + Na2S5 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: 4 Na_2S_2O_3 ⟶ 3 Na_2SO_4 + Na2S5 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 Na_2S_2O_3 | 4 | -4 Na_2SO_4 | 3 | 3 Na2S5 | 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 Na_2S_2O_3 | 4 | -4 | -1/4 (Δ[Na2S2O3])/(Δt) Na_2SO_4 | 3 | 3 | 1/3 (Δ[Na2SO4])/(Δt) Na2S5 | 1 | 1 | (Δ[Na2S5])/(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 = -1/4 (Δ[Na2S2O3])/(Δt) = 1/3 (Δ[Na2SO4])/(Δt) = (Δ[Na2S5])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium hyposulfite | sodium sulfate | Na2S5 formula | Na_2S_2O_3 | Na_2SO_4 | Na2S5 Hill formula | Na_2O_3S_2 | Na_2O_4S | Na2S5 name | sodium hyposulfite | sodium sulfate | IUPAC name | | disodium sulfate |

| sodium hyposulfite | sodium sulfate | Na2S5 molar mass | 158.1 g/mol | 142.04 g/mol | 206.3 g/mol phase | solid (at STP) | solid (at STP) | melting point | 48 °C | 884 °C | boiling point | 100 °C | 1429 °C | density | 1.67 g/cm^3 | 2.68 g/cm^3 | solubility in water | | soluble | odor | odorless | |