H2SO4 + C12H22O11 = H2O + SO2 + C + C2O2

H_2SO_4 sulfuric acid + C_12H_22O_11 sucrose ⟶ H_2O water + SO_2 sulfur dioxide + C activated charcoal + C2O2

Balance the chemical equation algebraically: H_2SO_4 + C_12H_22O_11 ⟶ H_2O + SO_2 + C + C2O2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 C_12H_22O_11 ⟶ c_3 H_2O + c_4 SO_2 + c_5 C + c_6 C2O2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S and C: H: | 2 c_1 + 22 c_2 = 2 c_3 O: | 4 c_1 + 11 c_2 = c_3 + 2 c_4 + 2 c_6 S: | c_1 = c_4 C: | 12 c_2 = c_5 + 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_2 = 1 c_3 = c_1 + 11 c_4 = c_1 c_5 = 12 - c_1 c_6 = c_1/2 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 6 and solve for the remaining coefficients: c_1 = 6 c_2 = 1 c_3 = 17 c_4 = 6 c_5 = 6 c_6 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 H_2SO_4 + C_12H_22O_11 ⟶ 17 H_2O + 6 SO_2 + 6 C + 3 C2O2

+ ⟶ + + + C2O2

sulfuric acid + sucrose ⟶ water + sulfur dioxide + activated charcoal + C2O2

Construct the equilibrium constant, K, expression for: H_2SO_4 + C_12H_22O_11 ⟶ H_2O + SO_2 + C + C2O2 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: 6 H_2SO_4 + C_12H_22O_11 ⟶ 17 H_2O + 6 SO_2 + 6 C + 3 C2O2 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 | 6 | -6 C_12H_22O_11 | 1 | -1 H_2O | 17 | 17 SO_2 | 6 | 6 C | 6 | 6 C2O2 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 6 | -6 | ([H2SO4])^(-6) C_12H_22O_11 | 1 | -1 | ([C12H22O11])^(-1) H_2O | 17 | 17 | ([H2O])^17 SO_2 | 6 | 6 | ([SO2])^6 C | 6 | 6 | ([C])^6 C2O2 | 3 | 3 | ([C2O2])^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])^(-6) ([C12H22O11])^(-1) ([H2O])^17 ([SO2])^6 ([C])^6 ([C2O2])^3 = (([H2O])^17 ([SO2])^6 ([C])^6 ([C2O2])^3)/(([H2SO4])^6 [C12H22O11])

Construct the rate of reaction expression for: H_2SO_4 + C_12H_22O_11 ⟶ H_2O + SO_2 + C + C2O2 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: 6 H_2SO_4 + C_12H_22O_11 ⟶ 17 H_2O + 6 SO_2 + 6 C + 3 C2O2 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 | 6 | -6 C_12H_22O_11 | 1 | -1 H_2O | 17 | 17 SO_2 | 6 | 6 C | 6 | 6 C2O2 | 3 | 3 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 | 6 | -6 | -1/6 (Δ[H2SO4])/(Δt) C_12H_22O_11 | 1 | -1 | -(Δ[C12H22O11])/(Δt) H_2O | 17 | 17 | 1/17 (Δ[H2O])/(Δt) SO_2 | 6 | 6 | 1/6 (Δ[SO2])/(Δt) C | 6 | 6 | 1/6 (Δ[C])/(Δt) C2O2 | 3 | 3 | 1/3 (Δ[C2O2])/(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 = -1/6 (Δ[H2SO4])/(Δt) = -(Δ[C12H22O11])/(Δt) = 1/17 (Δ[H2O])/(Δt) = 1/6 (Δ[SO2])/(Δt) = 1/6 (Δ[C])/(Δt) = 1/3 (Δ[C2O2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | sucrose | water | sulfur dioxide | activated charcoal | C2O2 formula | H_2SO_4 | C_12H_22O_11 | H_2O | SO_2 | C | C2O2 Hill formula | H_2O_4S | C_12H_22O_11 | H_2O | O_2S | C | C2O2 name | sulfuric acid | sucrose | water | sulfur dioxide | activated charcoal | IUPAC name | sulfuric acid | (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 | sulfur dioxide | carbon |