H2O + SO2 + Na2CO3 = CO2 + NaHSO3

H_2O water + SO_2 sulfur dioxide + Na_2CO_3 soda ash ⟶ CO_2 carbon dioxide + NaHSO_3 sodium bisulfite

Balance the chemical equation algebraically: H_2O + SO_2 + Na_2CO_3 ⟶ CO_2 + NaHSO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 SO_2 + c_3 Na_2CO_3 ⟶ c_4 CO_2 + c_5 NaHSO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, C and Na: H: | 2 c_1 = c_5 O: | c_1 + 2 c_2 + 3 c_3 = 2 c_4 + 3 c_5 S: | c_2 = c_5 C: | c_3 = c_4 Na: | 2 c_3 = 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 = 1 c_4 = 1 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2O + 2 SO_2 + Na_2CO_3 ⟶ CO_2 + 2 NaHSO_3

+ + ⟶ +

water + sulfur dioxide + soda ash ⟶ carbon dioxide + sodium bisulfite

Construct the equilibrium constant, K, expression for: H_2O + SO_2 + Na_2CO_3 ⟶ CO_2 + NaHSO_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 SO_2 + Na_2CO_3 ⟶ CO_2 + 2 NaHSO_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 SO_2 | 2 | -2 Na_2CO_3 | 1 | -1 CO_2 | 1 | 1 NaHSO_3 | 2 | 2 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) SO_2 | 2 | -2 | ([SO2])^(-2) Na_2CO_3 | 1 | -1 | ([Na2CO3])^(-1) CO_2 | 1 | 1 | [CO2] NaHSO_3 | 2 | 2 | ([NaHSO3])^2 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) ([SO2])^(-2) ([Na2CO3])^(-1) [CO2] ([NaHSO3])^2 = ([CO2] ([NaHSO3])^2)/([H2O] ([SO2])^2 [Na2CO3])

Construct the rate of reaction expression for: H_2O + SO_2 + Na_2CO_3 ⟶ CO_2 + NaHSO_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 SO_2 + Na_2CO_3 ⟶ CO_2 + 2 NaHSO_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 SO_2 | 2 | -2 Na_2CO_3 | 1 | -1 CO_2 | 1 | 1 NaHSO_3 | 2 | 2 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) SO_2 | 2 | -2 | -1/2 (Δ[SO2])/(Δt) Na_2CO_3 | 1 | -1 | -(Δ[Na2CO3])/(Δt) CO_2 | 1 | 1 | (Δ[CO2])/(Δt) NaHSO_3 | 2 | 2 | 1/2 (Δ[NaHSO3])/(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[SO2])/(Δt) = -(Δ[Na2CO3])/(Δt) = (Δ[CO2])/(Δt) = 1/2 (Δ[NaHSO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | sulfur dioxide | soda ash | carbon dioxide | sodium bisulfite formula | H_2O | SO_2 | Na_2CO_3 | CO_2 | NaHSO_3 Hill formula | H_2O | O_2S | CNa_2O_3 | CO_2 | HNaO_3S name | water | sulfur dioxide | soda ash | carbon dioxide | sodium bisulfite IUPAC name | water | sulfur dioxide | disodium carbonate | carbon dioxide |