KNO3 + C6H12O6 = H2O + CO2 + KNO2

KNO_3 potassium nitrate + C_6H_12O_6 D-(+)-glucose ⟶ H_2O water + CO_2 carbon dioxide + KNO_2 potassium nitrite

Balance the chemical equation algebraically: KNO_3 + C_6H_12O_6 ⟶ H_2O + CO_2 + KNO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KNO_3 + c_2 C_6H_12O_6 ⟶ c_3 H_2O + c_4 CO_2 + c_5 KNO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for K, N, O, C and H: K: | c_1 = c_5 N: | c_1 = c_5 O: | 3 c_1 + 6 c_2 = c_3 + 2 c_4 + 2 c_5 C: | 6 c_2 = c_4 H: | 12 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 = 12 c_2 = 1 c_3 = 6 c_4 = 6 c_5 = 12 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 12 KNO_3 + C_6H_12O_6 ⟶ 6 H_2O + 6 CO_2 + 12 KNO_2

+ ⟶ + +

potassium nitrate + D-(+)-glucose ⟶ water + carbon dioxide + potassium nitrite

Construct the equilibrium constant, K, expression for: KNO_3 + C_6H_12O_6 ⟶ H_2O + CO_2 + KNO_2 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: 12 KNO_3 + C_6H_12O_6 ⟶ 6 H_2O + 6 CO_2 + 12 KNO_2 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 KNO_3 | 12 | -12 C_6H_12O_6 | 1 | -1 H_2O | 6 | 6 CO_2 | 6 | 6 KNO_2 | 12 | 12 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KNO_3 | 12 | -12 | ([KNO3])^(-12) C_6H_12O_6 | 1 | -1 | ([C6H12O6])^(-1) H_2O | 6 | 6 | ([H2O])^6 CO_2 | 6 | 6 | ([CO2])^6 KNO_2 | 12 | 12 | ([KNO2])^12 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 = ([KNO3])^(-12) ([C6H12O6])^(-1) ([H2O])^6 ([CO2])^6 ([KNO2])^12 = (([H2O])^6 ([CO2])^6 ([KNO2])^12)/(([KNO3])^12 [C6H12O6])

Construct the rate of reaction expression for: KNO_3 + C_6H_12O_6 ⟶ H_2O + CO_2 + KNO_2 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: 12 KNO_3 + C_6H_12O_6 ⟶ 6 H_2O + 6 CO_2 + 12 KNO_2 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 KNO_3 | 12 | -12 C_6H_12O_6 | 1 | -1 H_2O | 6 | 6 CO_2 | 6 | 6 KNO_2 | 12 | 12 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 KNO_3 | 12 | -12 | -1/12 (Δ[KNO3])/(Δt) C_6H_12O_6 | 1 | -1 | -(Δ[C6H12O6])/(Δt) H_2O | 6 | 6 | 1/6 (Δ[H2O])/(Δt) CO_2 | 6 | 6 | 1/6 (Δ[CO2])/(Δt) KNO_2 | 12 | 12 | 1/12 (Δ[KNO2])/(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 = -1/12 (Δ[KNO3])/(Δt) = -(Δ[C6H12O6])/(Δt) = 1/6 (Δ[H2O])/(Δt) = 1/6 (Δ[CO2])/(Δt) = 1/12 (Δ[KNO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium nitrate | D-(+)-glucose | water | carbon dioxide | potassium nitrite formula | KNO_3 | C_6H_12O_6 | H_2O | CO_2 | KNO_2 name | potassium nitrate | D-(+)-glucose | water | carbon dioxide | potassium nitrite IUPAC name | potassium nitrate | 6-(hydroxymethyl)oxane-2, 3, 4, 5-tetrol | water | carbon dioxide | potassium nitrite