HNO3 + K2Cr2O7 + K2SO3 = H2O + K2SO4 + KNO3 + Cr(NO3)3

HNO_3 nitric acid + K_2Cr_2O_7 potassium dichromate + K_2SO_3 potassium sulfite ⟶ H_2O water + K_2SO_4 potassium sulfate + KNO_3 potassium nitrate + CrN_3O_9 chromium nitrate

Balance the chemical equation algebraically: HNO_3 + K_2Cr_2O_7 + K_2SO_3 ⟶ H_2O + K_2SO_4 + KNO_3 + CrN_3O_9 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 K_2Cr_2O_7 + c_3 K_2SO_3 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 KNO_3 + c_7 CrN_3O_9 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O, Cr, K and S: H: | c_1 = 2 c_4 N: | c_1 = c_6 + 3 c_7 O: | 3 c_1 + 7 c_2 + 3 c_3 = c_4 + 4 c_5 + 3 c_6 + 9 c_7 Cr: | 2 c_2 = c_7 K: | 2 c_2 + 2 c_3 = 2 c_5 + c_6 S: | 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 8 c_2 = 1 c_3 = 3 c_4 = 4 c_5 = 3 c_6 = 2 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 HNO_3 + K_2Cr_2O_7 + 3 K_2SO_3 ⟶ 4 H_2O + 3 K_2SO_4 + 2 KNO_3 + 2 CrN_3O_9

+ + ⟶ + + +

nitric acid + potassium dichromate + potassium sulfite ⟶ water + potassium sulfate + potassium nitrate + chromium nitrate

Construct the equilibrium constant, K, expression for: HNO_3 + K_2Cr_2O_7 + K_2SO_3 ⟶ H_2O + K_2SO_4 + KNO_3 + CrN_3O_9 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: 8 HNO_3 + K_2Cr_2O_7 + 3 K_2SO_3 ⟶ 4 H_2O + 3 K_2SO_4 + 2 KNO_3 + 2 CrN_3O_9 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 HNO_3 | 8 | -8 K_2Cr_2O_7 | 1 | -1 K_2SO_3 | 3 | -3 H_2O | 4 | 4 K_2SO_4 | 3 | 3 KNO_3 | 2 | 2 CrN_3O_9 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HNO_3 | 8 | -8 | ([HNO3])^(-8) K_2Cr_2O_7 | 1 | -1 | ([K2Cr2O7])^(-1) K_2SO_3 | 3 | -3 | ([K2SO3])^(-3) H_2O | 4 | 4 | ([H2O])^4 K_2SO_4 | 3 | 3 | ([K2SO4])^3 KNO_3 | 2 | 2 | ([KNO3])^2 CrN_3O_9 | 2 | 2 | ([CrN3O9])^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 = ([HNO3])^(-8) ([K2Cr2O7])^(-1) ([K2SO3])^(-3) ([H2O])^4 ([K2SO4])^3 ([KNO3])^2 ([CrN3O9])^2 = (([H2O])^4 ([K2SO4])^3 ([KNO3])^2 ([CrN3O9])^2)/(([HNO3])^8 [K2Cr2O7] ([K2SO3])^3)

Construct the rate of reaction expression for: HNO_3 + K_2Cr_2O_7 + K_2SO_3 ⟶ H_2O + K_2SO_4 + KNO_3 + CrN_3O_9 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: 8 HNO_3 + K_2Cr_2O_7 + 3 K_2SO_3 ⟶ 4 H_2O + 3 K_2SO_4 + 2 KNO_3 + 2 CrN_3O_9 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 HNO_3 | 8 | -8 K_2Cr_2O_7 | 1 | -1 K_2SO_3 | 3 | -3 H_2O | 4 | 4 K_2SO_4 | 3 | 3 KNO_3 | 2 | 2 CrN_3O_9 | 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 HNO_3 | 8 | -8 | -1/8 (Δ[HNO3])/(Δt) K_2Cr_2O_7 | 1 | -1 | -(Δ[K2Cr2O7])/(Δt) K_2SO_3 | 3 | -3 | -1/3 (Δ[K2SO3])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) K_2SO_4 | 3 | 3 | 1/3 (Δ[K2SO4])/(Δt) KNO_3 | 2 | 2 | 1/2 (Δ[KNO3])/(Δt) CrN_3O_9 | 2 | 2 | 1/2 (Δ[CrN3O9])/(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 = -1/8 (Δ[HNO3])/(Δt) = -(Δ[K2Cr2O7])/(Δt) = -1/3 (Δ[K2SO3])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/3 (Δ[K2SO4])/(Δt) = 1/2 (Δ[KNO3])/(Δt) = 1/2 (Δ[CrN3O9])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitric acid | potassium dichromate | potassium sulfite | water | potassium sulfate | potassium nitrate | chromium nitrate formula | HNO_3 | K_2Cr_2O_7 | K_2SO_3 | H_2O | K_2SO_4 | KNO_3 | CrN_3O_9 Hill formula | HNO_3 | Cr_2K_2O_7 | K_2O_3S | H_2O | K_2O_4S | KNO_3 | CrN_3O_9 name | nitric acid | potassium dichromate | potassium sulfite | water | potassium sulfate | potassium nitrate | chromium nitrate IUPAC name | nitric acid | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium | dipotassium sulfite | water | dipotassium sulfate | potassium nitrate | chromium(+3) cation trinitrate