H2SO4 + K2Cr2O7 + KSCN = H2O + CO2 + K2SO4 + SO2 + NO2 + Cr2(SO4)3

H_2SO_4 sulfuric acid + K_2Cr_2O_7 potassium dichromate + KSCN potassium thiocyanate ⟶ H_2O water + CO_2 carbon dioxide + K_2SO_4 potassium sulfate + SO_2 sulfur dioxide + NO_2 nitrogen dioxide + Cr_2(SO_4)_3 chromium sulfate

Balance the chemical equation algebraically: H_2SO_4 + K_2Cr_2O_7 + KSCN ⟶ H_2O + CO_2 + K_2SO_4 + SO_2 + NO_2 + Cr_2(SO_4)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 K_2Cr_2O_7 + c_3 KSCN ⟶ c_4 H_2O + c_5 CO_2 + c_6 K_2SO_4 + c_7 SO_2 + c_8 NO_2 + c_9 Cr_2(SO_4)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Cr, K, C and N: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 7 c_2 = c_4 + 2 c_5 + 4 c_6 + 2 c_7 + 2 c_8 + 12 c_9 S: | c_1 + c_3 = c_6 + c_7 + 3 c_9 Cr: | 2 c_2 = 2 c_9 K: | 2 c_2 + c_3 = 2 c_6 C: | c_3 = c_5 N: | c_3 = c_8 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_2 = 1 c_3 = c_1/7 - 1/7 c_4 = c_1 c_5 = c_1/7 - 1/7 c_6 = c_1/14 + 13/14 c_7 = (15 c_1)/14 - 57/14 c_8 = c_1/7 - 1/7 c_9 = 1 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 15 and solve for the remaining coefficients: c_1 = 15 c_2 = 1 c_3 = 2 c_4 = 15 c_5 = 2 c_6 = 2 c_7 = 12 c_8 = 2 c_9 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 15 H_2SO_4 + K_2Cr_2O_7 + 2 KSCN ⟶ 15 H_2O + 2 CO_2 + 2 K_2SO_4 + 12 SO_2 + 2 NO_2 + Cr_2(SO_4)_3

+ + ⟶ + + + + +

sulfuric acid + potassium dichromate + potassium thiocyanate ⟶ water + carbon dioxide + potassium sulfate + sulfur dioxide + nitrogen dioxide + chromium sulfate

Construct the equilibrium constant, K, expression for: H_2SO_4 + K_2Cr_2O_7 + KSCN ⟶ H_2O + CO_2 + K_2SO_4 + SO_2 + NO_2 + Cr_2(SO_4)_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: 15 H_2SO_4 + K_2Cr_2O_7 + 2 KSCN ⟶ 15 H_2O + 2 CO_2 + 2 K_2SO_4 + 12 SO_2 + 2 NO_2 + Cr_2(SO_4)_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 | 15 | -15 K_2Cr_2O_7 | 1 | -1 KSCN | 2 | -2 H_2O | 15 | 15 CO_2 | 2 | 2 K_2SO_4 | 2 | 2 SO_2 | 12 | 12 NO_2 | 2 | 2 Cr_2(SO_4)_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 | 15 | -15 | ([H2SO4])^(-15) K_2Cr_2O_7 | 1 | -1 | ([K2Cr2O7])^(-1) KSCN | 2 | -2 | ([KSCN])^(-2) H_2O | 15 | 15 | ([H2O])^15 CO_2 | 2 | 2 | ([CO2])^2 K_2SO_4 | 2 | 2 | ([K2SO4])^2 SO_2 | 12 | 12 | ([SO2])^12 NO_2 | 2 | 2 | ([NO2])^2 Cr_2(SO_4)_3 | 1 | 1 | [Cr2(SO4)3] 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])^(-15) ([K2Cr2O7])^(-1) ([KSCN])^(-2) ([H2O])^15 ([CO2])^2 ([K2SO4])^2 ([SO2])^12 ([NO2])^2 [Cr2(SO4)3] = (([H2O])^15 ([CO2])^2 ([K2SO4])^2 ([SO2])^12 ([NO2])^2 [Cr2(SO4)3])/(([H2SO4])^15 [K2Cr2O7] ([KSCN])^2)

Construct the rate of reaction expression for: H_2SO_4 + K_2Cr_2O_7 + KSCN ⟶ H_2O + CO_2 + K_2SO_4 + SO_2 + NO_2 + Cr_2(SO_4)_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: 15 H_2SO_4 + K_2Cr_2O_7 + 2 KSCN ⟶ 15 H_2O + 2 CO_2 + 2 K_2SO_4 + 12 SO_2 + 2 NO_2 + Cr_2(SO_4)_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 | 15 | -15 K_2Cr_2O_7 | 1 | -1 KSCN | 2 | -2 H_2O | 15 | 15 CO_2 | 2 | 2 K_2SO_4 | 2 | 2 SO_2 | 12 | 12 NO_2 | 2 | 2 Cr_2(SO_4)_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 | 15 | -15 | -1/15 (Δ[H2SO4])/(Δt) K_2Cr_2O_7 | 1 | -1 | -(Δ[K2Cr2O7])/(Δt) KSCN | 2 | -2 | -1/2 (Δ[KSCN])/(Δt) H_2O | 15 | 15 | 1/15 (Δ[H2O])/(Δt) CO_2 | 2 | 2 | 1/2 (Δ[CO2])/(Δt) K_2SO_4 | 2 | 2 | 1/2 (Δ[K2SO4])/(Δt) SO_2 | 12 | 12 | 1/12 (Δ[SO2])/(Δt) NO_2 | 2 | 2 | 1/2 (Δ[NO2])/(Δt) Cr_2(SO_4)_3 | 1 | 1 | (Δ[Cr2(SO4)3])/(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 = -1/15 (Δ[H2SO4])/(Δt) = -(Δ[K2Cr2O7])/(Δt) = -1/2 (Δ[KSCN])/(Δt) = 1/15 (Δ[H2O])/(Δt) = 1/2 (Δ[CO2])/(Δt) = 1/2 (Δ[K2SO4])/(Δt) = 1/12 (Δ[SO2])/(Δt) = 1/2 (Δ[NO2])/(Δt) = (Δ[Cr2(SO4)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | potassium dichromate | potassium thiocyanate | water | carbon dioxide | potassium sulfate | sulfur dioxide | nitrogen dioxide | chromium sulfate formula | H_2SO_4 | K_2Cr_2O_7 | KSCN | H_2O | CO_2 | K_2SO_4 | SO_2 | NO_2 | Cr_2(SO_4)_3 Hill formula | H_2O_4S | Cr_2K_2O_7 | CKNS | H_2O | CO_2 | K_2O_4S | O_2S | NO_2 | Cr_2O_12S_3 name | sulfuric acid | potassium dichromate | potassium thiocyanate | water | carbon dioxide | potassium sulfate | sulfur dioxide | nitrogen dioxide | chromium sulfate IUPAC name | sulfuric acid | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium | potassium isothiocyanate | water | carbon dioxide | dipotassium sulfate | sulfur dioxide | Nitrogen dioxide | chromium(+3) cation trisulfate