H2SO4 + K2Cr2O7 + C12H22O11 = H2O + CO2 + K2SO4 + Cr2(SO4)3

H_2SO_4 sulfuric acid + K_2Cr_2O_7 potassium dichromate + C_12H_22O_11 sucrose ⟶ H_2O water + CO_2 carbon dioxide + K_2SO_4 potassium sulfate + Cr_2(SO_4)_3 chromium sulfate

Balance the chemical equation algebraically: H_2SO_4 + K_2Cr_2O_7 + C_12H_22O_11 ⟶ H_2O + CO_2 + K_2SO_4 + 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 C_12H_22O_11 ⟶ c_4 H_2O + c_5 CO_2 + c_6 K_2SO_4 + c_7 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 and C: H: | 2 c_1 + 22 c_3 = 2 c_4 O: | 4 c_1 + 7 c_2 + 11 c_3 = c_4 + 2 c_5 + 4 c_6 + 12 c_7 S: | c_1 = c_6 + 3 c_7 Cr: | 2 c_2 = 2 c_7 K: | 2 c_2 = 2 c_6 C: | 12 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 32 c_2 = 8 c_3 = 1 c_4 = 43 c_5 = 12 c_6 = 8 c_7 = 8 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 32 H_2SO_4 + 8 K_2Cr_2O_7 + C_12H_22O_11 ⟶ 43 H_2O + 12 CO_2 + 8 K_2SO_4 + 8 Cr_2(SO_4)_3

+ + ⟶ + + +

sulfuric acid + potassium dichromate + sucrose ⟶ water + carbon dioxide + potassium sulfate + chromium sulfate

Construct the equilibrium constant, K, expression for: H_2SO_4 + K_2Cr_2O_7 + C_12H_22O_11 ⟶ H_2O + CO_2 + K_2SO_4 + 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: 32 H_2SO_4 + 8 K_2Cr_2O_7 + C_12H_22O_11 ⟶ 43 H_2O + 12 CO_2 + 8 K_2SO_4 + 8 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 | 32 | -32 K_2Cr_2O_7 | 8 | -8 C_12H_22O_11 | 1 | -1 H_2O | 43 | 43 CO_2 | 12 | 12 K_2SO_4 | 8 | 8 Cr_2(SO_4)_3 | 8 | 8 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 32 | -32 | ([H2SO4])^(-32) K_2Cr_2O_7 | 8 | -8 | ([K2Cr2O7])^(-8) C_12H_22O_11 | 1 | -1 | ([C12H22O11])^(-1) H_2O | 43 | 43 | ([H2O])^43 CO_2 | 12 | 12 | ([CO2])^12 K_2SO_4 | 8 | 8 | ([K2SO4])^8 Cr_2(SO_4)_3 | 8 | 8 | ([Cr2(SO4)3])^8 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])^(-32) ([K2Cr2O7])^(-8) ([C12H22O11])^(-1) ([H2O])^43 ([CO2])^12 ([K2SO4])^8 ([Cr2(SO4)3])^8 = (([H2O])^43 ([CO2])^12 ([K2SO4])^8 ([Cr2(SO4)3])^8)/(([H2SO4])^32 ([K2Cr2O7])^8 [C12H22O11])

Construct the rate of reaction expression for: H_2SO_4 + K_2Cr_2O_7 + C_12H_22O_11 ⟶ H_2O + CO_2 + K_2SO_4 + 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: 32 H_2SO_4 + 8 K_2Cr_2O_7 + C_12H_22O_11 ⟶ 43 H_2O + 12 CO_2 + 8 K_2SO_4 + 8 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 | 32 | -32 K_2Cr_2O_7 | 8 | -8 C_12H_22O_11 | 1 | -1 H_2O | 43 | 43 CO_2 | 12 | 12 K_2SO_4 | 8 | 8 Cr_2(SO_4)_3 | 8 | 8 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 | 32 | -32 | -1/32 (Δ[H2SO4])/(Δt) K_2Cr_2O_7 | 8 | -8 | -1/8 (Δ[K2Cr2O7])/(Δt) C_12H_22O_11 | 1 | -1 | -(Δ[C12H22O11])/(Δt) H_2O | 43 | 43 | 1/43 (Δ[H2O])/(Δt) CO_2 | 12 | 12 | 1/12 (Δ[CO2])/(Δt) K_2SO_4 | 8 | 8 | 1/8 (Δ[K2SO4])/(Δt) Cr_2(SO_4)_3 | 8 | 8 | 1/8 (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 = -1/32 (Δ[H2SO4])/(Δt) = -1/8 (Δ[K2Cr2O7])/(Δt) = -(Δ[C12H22O11])/(Δt) = 1/43 (Δ[H2O])/(Δt) = 1/12 (Δ[CO2])/(Δt) = 1/8 (Δ[K2SO4])/(Δt) = 1/8 (Δ[Cr2(SO4)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | potassium dichromate | sucrose | water | carbon dioxide | potassium sulfate | chromium sulfate formula | H_2SO_4 | K_2Cr_2O_7 | C_12H_22O_11 | H_2O | CO_2 | K_2SO_4 | Cr_2(SO_4)_3 Hill formula | H_2O_4S | Cr_2K_2O_7 | C_12H_22O_11 | H_2O | CO_2 | K_2O_4S | Cr_2O_12S_3 name | sulfuric acid | potassium dichromate | sucrose | water | carbon dioxide | potassium sulfate | chromium sulfate IUPAC name | sulfuric acid | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium | (2R, 3S, 4S, 5S, 6R)-2-[(2S, 3S, 4S, 5R)-3, 4-dihydroxy-2, 5-bis(hydroxymethyl)oxolan-2-yl]oxy-6-(hydroxymethyl)oxane-3, 4, 5-triol | water | carbon dioxide | dipotassium sulfate | chromium(+3) cation trisulfate