Na2SO3 + K2Cr2O7 + H2SO4 = Na2SO4 + Cr2(SO4)3 + H2O + K2SO4

Na_2SO_3 sodium sulfite + K_2Cr_2O_7 potassium dichromate + H_2SO_4 sulfuric acid ⟶ Na_2SO_4 sodium sulfate + Cr_2(SO_4)_3 chromium sulfate + H_2O water + K_2SO_4 potassium sulfate

Balance the chemical equation algebraically: Na_2SO_3 + K_2Cr_2O_7 + H_2SO_4 ⟶ Na_2SO_4 + Cr_2(SO_4)_3 + H_2O + K_2SO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Na_2SO_3 + c_2 K_2Cr_2O_7 + c_3 H_2SO_4 ⟶ c_4 Na_2SO_4 + c_5 Cr_2(SO_4)_3 + c_6 H_2O + c_7 K_2SO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for Na, O, S, Cr, K and H: Na: | 2 c_1 = 2 c_4 O: | 3 c_1 + 7 c_2 + 4 c_3 = 4 c_4 + 12 c_5 + c_6 + 4 c_7 S: | c_1 + c_3 = c_4 + 3 c_5 + c_7 Cr: | 2 c_2 = 2 c_5 K: | 2 c_2 = 2 c_7 H: | 2 c_3 = 2 c_6 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 1 c_3 = 4 c_4 = 3 c_5 = 1 c_6 = 4 c_7 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 Na_2SO_3 + K_2Cr_2O_7 + 4 H_2SO_4 ⟶ 3 Na_2SO_4 + Cr_2(SO_4)_3 + 4 H_2O + K_2SO_4

+ + ⟶ + + +

sodium sulfite + potassium dichromate + sulfuric acid ⟶ sodium sulfate + chromium sulfate + water + potassium sulfate

Construct the equilibrium constant, K, expression for: Na_2SO_3 + K_2Cr_2O_7 + H_2SO_4 ⟶ Na_2SO_4 + Cr_2(SO_4)_3 + H_2O + K_2SO_4 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: 3 Na_2SO_3 + K_2Cr_2O_7 + 4 H_2SO_4 ⟶ 3 Na_2SO_4 + Cr_2(SO_4)_3 + 4 H_2O + K_2SO_4 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_2SO_3 | 3 | -3 K_2Cr_2O_7 | 1 | -1 H_2SO_4 | 4 | -4 Na_2SO_4 | 3 | 3 Cr_2(SO_4)_3 | 1 | 1 H_2O | 4 | 4 K_2SO_4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Na_2SO_3 | 3 | -3 | ([Na2SO3])^(-3) K_2Cr_2O_7 | 1 | -1 | ([K2Cr2O7])^(-1) H_2SO_4 | 4 | -4 | ([H2SO4])^(-4) Na_2SO_4 | 3 | 3 | ([Na2SO4])^3 Cr_2(SO_4)_3 | 1 | 1 | [Cr2(SO4)3] H_2O | 4 | 4 | ([H2O])^4 K_2SO_4 | 1 | 1 | [K2SO4] 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 = ([Na2SO3])^(-3) ([K2Cr2O7])^(-1) ([H2SO4])^(-4) ([Na2SO4])^3 [Cr2(SO4)3] ([H2O])^4 [K2SO4] = (([Na2SO4])^3 [Cr2(SO4)3] ([H2O])^4 [K2SO4])/(([Na2SO3])^3 [K2Cr2O7] ([H2SO4])^4)

Construct the rate of reaction expression for: Na_2SO_3 + K_2Cr_2O_7 + H_2SO_4 ⟶ Na_2SO_4 + Cr_2(SO_4)_3 + H_2O + K_2SO_4 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: 3 Na_2SO_3 + K_2Cr_2O_7 + 4 H_2SO_4 ⟶ 3 Na_2SO_4 + Cr_2(SO_4)_3 + 4 H_2O + K_2SO_4 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_2SO_3 | 3 | -3 K_2Cr_2O_7 | 1 | -1 H_2SO_4 | 4 | -4 Na_2SO_4 | 3 | 3 Cr_2(SO_4)_3 | 1 | 1 H_2O | 4 | 4 K_2SO_4 | 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_2SO_3 | 3 | -3 | -1/3 (Δ[Na2SO3])/(Δt) K_2Cr_2O_7 | 1 | -1 | -(Δ[K2Cr2O7])/(Δt) H_2SO_4 | 4 | -4 | -1/4 (Δ[H2SO4])/(Δt) Na_2SO_4 | 3 | 3 | 1/3 (Δ[Na2SO4])/(Δt) Cr_2(SO_4)_3 | 1 | 1 | (Δ[Cr2(SO4)3])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(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 = -1/3 (Δ[Na2SO3])/(Δt) = -(Δ[K2Cr2O7])/(Δt) = -1/4 (Δ[H2SO4])/(Δt) = 1/3 (Δ[Na2SO4])/(Δt) = (Δ[Cr2(SO4)3])/(Δt) = 1/4 (Δ[H2O])/(Δt) = (Δ[K2SO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium sulfite | potassium dichromate | sulfuric acid | sodium sulfate | chromium sulfate | water | potassium sulfate formula | Na_2SO_3 | K_2Cr_2O_7 | H_2SO_4 | Na_2SO_4 | Cr_2(SO_4)_3 | H_2O | K_2SO_4 Hill formula | Na_2O_3S | Cr_2K_2O_7 | H_2O_4S | Na_2O_4S | Cr_2O_12S_3 | H_2O | K_2O_4S name | sodium sulfite | potassium dichromate | sulfuric acid | sodium sulfate | chromium sulfate | water | potassium sulfate IUPAC name | disodium sulfite | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium | sulfuric acid | disodium sulfate | chromium(+3) cation trisulfate | water | dipotassium sulfate