SO2 + Zn + NaHSO3 = H2O + Na2S2O3 + ZnSO3

SO_2 sulfur dioxide + Zn zinc + NaHSO_3 sodium bisulfite ⟶ H_2O water + Na_2S_2O_3 sodium hyposulfite + ZnSO3

Balance the chemical equation algebraically: SO_2 + Zn + NaHSO_3 ⟶ H_2O + Na_2S_2O_3 + ZnSO3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 SO_2 + c_2 Zn + c_3 NaHSO_3 ⟶ c_4 H_2O + c_5 Na_2S_2O_3 + c_6 ZnSO3 Set the number of atoms in the reactants equal to the number of atoms in the products for O, S, Zn, H and Na: O: | 2 c_1 + 3 c_3 = c_4 + 3 c_5 + 3 c_6 S: | c_1 + c_3 = 2 c_5 + c_6 Zn: | c_2 = c_6 H: | c_3 = 2 c_4 Na: | 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 2 c_3 = 2 c_4 = 1 c_5 = 1 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 SO_2 + 2 Zn + 2 NaHSO_3 ⟶ H_2O + Na_2S_2O_3 + 2 ZnSO3

+ + ⟶ + + ZnSO3

sulfur dioxide + zinc + sodium bisulfite ⟶ water + sodium hyposulfite + ZnSO3

Construct the equilibrium constant, K, expression for: SO_2 + Zn + NaHSO_3 ⟶ H_2O + Na_2S_2O_3 + ZnSO3 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 SO_2 + 2 Zn + 2 NaHSO_3 ⟶ H_2O + Na_2S_2O_3 + 2 ZnSO3 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 SO_2 | 2 | -2 Zn | 2 | -2 NaHSO_3 | 2 | -2 H_2O | 1 | 1 Na_2S_2O_3 | 1 | 1 ZnSO3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression SO_2 | 2 | -2 | ([SO2])^(-2) Zn | 2 | -2 | ([Zn])^(-2) NaHSO_3 | 2 | -2 | ([NaHSO3])^(-2) H_2O | 1 | 1 | [H2O] Na_2S_2O_3 | 1 | 1 | [Na2S2O3] ZnSO3 | 2 | 2 | ([ZnSO3])^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 = ([SO2])^(-2) ([Zn])^(-2) ([NaHSO3])^(-2) [H2O] [Na2S2O3] ([ZnSO3])^2 = ([H2O] [Na2S2O3] ([ZnSO3])^2)/(([SO2])^2 ([Zn])^2 ([NaHSO3])^2)

Construct the rate of reaction expression for: SO_2 + Zn + NaHSO_3 ⟶ H_2O + Na_2S_2O_3 + ZnSO3 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 SO_2 + 2 Zn + 2 NaHSO_3 ⟶ H_2O + Na_2S_2O_3 + 2 ZnSO3 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 SO_2 | 2 | -2 Zn | 2 | -2 NaHSO_3 | 2 | -2 H_2O | 1 | 1 Na_2S_2O_3 | 1 | 1 ZnSO3 | 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 SO_2 | 2 | -2 | -1/2 (Δ[SO2])/(Δt) Zn | 2 | -2 | -1/2 (Δ[Zn])/(Δt) NaHSO_3 | 2 | -2 | -1/2 (Δ[NaHSO3])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) Na_2S_2O_3 | 1 | 1 | (Δ[Na2S2O3])/(Δt) ZnSO3 | 2 | 2 | 1/2 (Δ[ZnSO3])/(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[SO2])/(Δt) = -1/2 (Δ[Zn])/(Δt) = -1/2 (Δ[NaHSO3])/(Δt) = (Δ[H2O])/(Δt) = (Δ[Na2S2O3])/(Δt) = 1/2 (Δ[ZnSO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfur dioxide | zinc | sodium bisulfite | water | sodium hyposulfite | ZnSO3 formula | SO_2 | Zn | NaHSO_3 | H_2O | Na_2S_2O_3 | ZnSO3 Hill formula | O_2S | Zn | HNaO_3S | H_2O | Na_2O_3S_2 | O3SZn name | sulfur dioxide | zinc | sodium bisulfite | water | sodium hyposulfite |