KClO3 + C12H22O11 = H2O + CO2 + KCl

KClO_3 potassium chlorate + C_12H_22O_11 sucrose ⟶ H_2O water + CO_2 carbon dioxide + KCl potassium chloride

Balance the chemical equation algebraically: KClO_3 + C_12H_22O_11 ⟶ H_2O + CO_2 + KCl Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KClO_3 + c_2 C_12H_22O_11 ⟶ c_3 H_2O + c_4 CO_2 + c_5 KCl Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, K, O, C and H: Cl: | c_1 = c_5 K: | c_1 = c_5 O: | 3 c_1 + 11 c_2 = c_3 + 2 c_4 C: | 12 c_2 = c_4 H: | 22 c_2 = 2 c_3 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 = 11 c_4 = 12 c_5 = 8 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 KClO_3 + C_12H_22O_11 ⟶ 11 H_2O + 12 CO_2 + 8 KCl

+ ⟶ + +

potassium chlorate + sucrose ⟶ water + carbon dioxide + potassium chloride

| potassium chlorate | sucrose | water | carbon dioxide | potassium chloride molecular enthalpy | -397.7 kJ/mol | -2226 kJ/mol | -285.8 kJ/mol | -393.5 kJ/mol | -436.5 kJ/mol total enthalpy | -3182 kJ/mol | -2226 kJ/mol | -3144 kJ/mol | -4722 kJ/mol | -3492 kJ/mol | H_initial = -5408 kJ/mol | | H_final = -11358 kJ/mol | | ΔH_rxn^0 | -11358 kJ/mol - -5408 kJ/mol = -5950 kJ/mol (exothermic) | | | |

Construct the equilibrium constant, K, expression for: KClO_3 + C_12H_22O_11 ⟶ H_2O + CO_2 + KCl 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 KClO_3 + C_12H_22O_11 ⟶ 11 H_2O + 12 CO_2 + 8 KCl 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 KClO_3 | 8 | -8 C_12H_22O_11 | 1 | -1 H_2O | 11 | 11 CO_2 | 12 | 12 KCl | 8 | 8 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KClO_3 | 8 | -8 | ([KClO3])^(-8) C_12H_22O_11 | 1 | -1 | ([C12H22O11])^(-1) H_2O | 11 | 11 | ([H2O])^11 CO_2 | 12 | 12 | ([CO2])^12 KCl | 8 | 8 | ([KCl])^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 = ([KClO3])^(-8) ([C12H22O11])^(-1) ([H2O])^11 ([CO2])^12 ([KCl])^8 = (([H2O])^11 ([CO2])^12 ([KCl])^8)/(([KClO3])^8 [C12H22O11])

Construct the rate of reaction expression for: KClO_3 + C_12H_22O_11 ⟶ H_2O + CO_2 + KCl 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 KClO_3 + C_12H_22O_11 ⟶ 11 H_2O + 12 CO_2 + 8 KCl 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 KClO_3 | 8 | -8 C_12H_22O_11 | 1 | -1 H_2O | 11 | 11 CO_2 | 12 | 12 KCl | 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 KClO_3 | 8 | -8 | -1/8 (Δ[KClO3])/(Δt) C_12H_22O_11 | 1 | -1 | -(Δ[C12H22O11])/(Δt) H_2O | 11 | 11 | 1/11 (Δ[H2O])/(Δt) CO_2 | 12 | 12 | 1/12 (Δ[CO2])/(Δt) KCl | 8 | 8 | 1/8 (Δ[KCl])/(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[KClO3])/(Δt) = -(Δ[C12H22O11])/(Δt) = 1/11 (Δ[H2O])/(Δt) = 1/12 (Δ[CO2])/(Δt) = 1/8 (Δ[KCl])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium chlorate | sucrose | water | carbon dioxide | potassium chloride formula | KClO_3 | C_12H_22O_11 | H_2O | CO_2 | KCl Hill formula | ClKO_3 | C_12H_22O_11 | H_2O | CO_2 | ClK name | potassium chlorate | sucrose | water | carbon dioxide | potassium chloride IUPAC name | potassium chlorate | (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 | potassium chloride