H2SO4 + Na2S2O3 = S + Na2SO4 + H2SO3

Input interpretation

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H_2SO_4 sulfuric acid + Na_2S_2O_3 sodium hyposulfite ⟶ S mixed sulfur + Na_2SO_4 sodium sulfate + H_2SO_3 sulfurous acid

Balanced equation

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Balance the chemical equation algebraically: H_2SO_4 + Na_2S_2O_3 ⟶ S + Na_2SO_4 + H_2SO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 Na_2S_2O_3 ⟶ c_3 S + c_4 Na_2SO_4 + c_5 H_2SO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S and Na: H: | 2 c_1 = 2 c_5 O: | 4 c_1 + 3 c_2 = 4 c_4 + 3 c_5 S: | c_1 + 2 c_2 = c_3 + c_4 + c_5 Na: | 2 c_2 = 2 c_4 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 c_4 = 1 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2SO_4 + Na_2S_2O_3 ⟶ S + Na_2SO_4 + H_2SO_3

+ ⟶ + +

Names

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sulfuric acid + sodium hyposulfite ⟶ mixed sulfur + sodium sulfate + sulfurous acid

Equilibrium constant

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Construct the equilibrium constant, K, expression for: H_2SO_4 + Na_2S_2O_3 ⟶ S + Na_2SO_4 + H_2SO_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_2SO_4 + Na_2S_2O_3 ⟶ S + Na_2SO_4 + H_2SO_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_2SO_4 | 1 | -1 Na_2S_2O_3 | 1 | -1 S | 1 | 1 Na_2SO_4 | 1 | 1 H_2SO_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_2SO_4 | 1 | -1 | ([H2SO4])^(-1) Na_2S_2O_3 | 1 | -1 | ([Na2S2O3])^(-1) S | 1 | 1 | [S] Na_2SO_4 | 1 | 1 | [Na2SO4] H_2SO_3 | 1 | 1 | [H2SO3] 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 = ([H2SO4])^(-1) ([Na2S2O3])^(-1) [S] [Na2SO4] [H2SO3] = ([S] [Na2SO4] [H2SO3])/([H2SO4] [Na2S2O3])

Rate of reaction

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Construct the rate of reaction expression for: H_2SO_4 + Na_2S_2O_3 ⟶ S + Na_2SO_4 + H_2SO_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_2SO_4 + Na_2S_2O_3 ⟶ S + Na_2SO_4 + H_2SO_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_2SO_4 | 1 | -1 Na_2S_2O_3 | 1 | -1 S | 1 | 1 Na_2SO_4 | 1 | 1 H_2SO_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_2SO_4 | 1 | -1 | -(Δ[H2SO4])/(Δt) Na_2S_2O_3 | 1 | -1 | -(Δ[Na2S2O3])/(Δt) S | 1 | 1 | (Δ[S])/(Δt) Na_2SO_4 | 1 | 1 | (Δ[Na2SO4])/(Δt) H_2SO_3 | 1 | 1 | (Δ[H2SO3])/(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[H2SO4])/(Δt) = -(Δ[Na2S2O3])/(Δt) = (Δ[S])/(Δt) = (Δ[Na2SO4])/(Δt) = (Δ[H2SO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)