H2O + O2 + Na2S = NaOH + Na2S2O3

H_2O (water) + O_2 (oxygen) + Na_2S (sodium sulfide) ⟶ NaOH (sodium hydroxide) + Na_2S_2O_3 (sodium hyposulfite)

Balance the chemical equation algebraically: H_2O + O_2 + Na_2S ⟶ NaOH + Na_2S_2O_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 O_2 + c_3 Na_2S ⟶ c_4 NaOH + c_5 Na_2S_2O_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Na and S: H: | 2 c_1 = c_4 O: | c_1 + 2 c_2 = c_4 + 3 c_5 Na: | 2 c_3 = c_4 + 2 c_5 S: | c_3 = 2 c_5 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 = 2 c_3 = 2 c_4 = 2 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2O + 2 O_2 + 2 Na_2S ⟶ 2 NaOH + Na_2S_2O_3

+ + ⟶ +

water + oxygen + sodium sulfide ⟶ sodium hydroxide + sodium hyposulfite

Construct the equilibrium constant, K, expression for: H_2O + O_2 + Na_2S ⟶ NaOH + 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: H_2O + 2 O_2 + 2 Na_2S ⟶ 2 NaOH + 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 H_2O | 1 | -1 O_2 | 2 | -2 Na_2S | 2 | -2 NaOH | 2 | 2 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 H_2O | 1 | -1 | ([H2O])^(-1) O_2 | 2 | -2 | ([O2])^(-2) Na_2S | 2 | -2 | ([Na2S])^(-2) NaOH | 2 | 2 | ([NaOH])^2 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 = ([H2O])^(-1) ([O2])^(-2) ([Na2S])^(-2) ([NaOH])^2 [Na2S2O3] = (([NaOH])^2 [Na2S2O3])/([H2O] ([O2])^2 ([Na2S])^2)

Construct the rate of reaction expression for: H_2O + O_2 + Na_2S ⟶ NaOH + 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: H_2O + 2 O_2 + 2 Na_2S ⟶ 2 NaOH + 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 H_2O | 1 | -1 O_2 | 2 | -2 Na_2S | 2 | -2 NaOH | 2 | 2 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 H_2O | 1 | -1 | -(Δ[H2O])/(Δt) O_2 | 2 | -2 | -1/2 (Δ[O2])/(Δt) Na_2S | 2 | -2 | -1/2 (Δ[Na2S])/(Δt) NaOH | 2 | 2 | 1/2 (Δ[NaOH])/(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[H2O])/(Δt) = -1/2 (Δ[O2])/(Δt) = -1/2 (Δ[Na2S])/(Δt) = 1/2 (Δ[NaOH])/(Δt) = (Δ[Na2S2O3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | oxygen | sodium sulfide | sodium hydroxide | sodium hyposulfite formula | H_2O | O_2 | Na_2S | NaOH | Na_2S_2O_3 Hill formula | H_2O | O_2 | Na_2S_1 | HNaO | Na_2O_3S_2 name | water | oxygen | sodium sulfide | sodium hydroxide | sodium hyposulfite IUPAC name | water | molecular oxygen | | sodium hydroxide |

| water | oxygen | sodium sulfide | sodium hydroxide | sodium hyposulfite molar mass | 18.015 g/mol | 31.998 g/mol | 78.04 g/mol | 39.997 g/mol | 158.1 g/mol phase | liquid (at STP) | gas (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 0 °C | -218 °C | 1172 °C | 323 °C | 48 °C boiling point | 99.9839 °C | -183 °C | | 1390 °C | 100 °C density | 1 g/cm^3 | 0.001429 g/cm^3 (at 0 °C) | 1.856 g/cm^3 | 2.13 g/cm^3 | 1.67 g/cm^3 solubility in water | | | | soluble | surface tension | 0.0728 N/m | 0.01347 N/m | | 0.07435 N/m | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | 2.055×10^-5 Pa s (at 25 °C) | | 0.004 Pa s (at 350 °C) | odor | odorless | odorless | | | odorless