H2O + CO2 = O2 + C6H12O6

H_2O (water) + CO_2 (carbon dioxide) ⟶ O_2 (oxygen) + C_6H_12O_6 (D-(+)-glucose)

Balance the chemical equation algebraically: H_2O + CO_2 ⟶ O_2 + C_6H_12O_6 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 CO_2 ⟶ c_3 O_2 + c_4 C_6H_12O_6 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O and C: H: | 2 c_1 = 12 c_4 O: | c_1 + 2 c_2 = 2 c_3 + 6 c_4 C: | c_2 = 6 c_4 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 6 c_2 = 6 c_3 = 6 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 H_2O + 6 CO_2 ⟶ 6 O_2 + C_6H_12O_6

+ ⟶ +

water + carbon dioxide ⟶ oxygen + D-(+)-glucose

Construct the equilibrium constant, K, expression for: H_2O + CO_2 ⟶ O_2 + C_6H_12O_6 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_2O + 6 CO_2 ⟶ 6 O_2 + C_6H_12O_6 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_2O | 6 | -6 CO_2 | 6 | -6 O_2 | 6 | 6 C_6H_12O_6 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 6 | -6 | ([H2O])^(-6) CO_2 | 6 | -6 | ([CO2])^(-6) O_2 | 6 | 6 | ([O2])^6 C_6H_12O_6 | 1 | 1 | [C6H12O6] 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 = ([H2O])^(-6) ([CO2])^(-6) ([O2])^6 [C6H12O6] = (([O2])^6 [C6H12O6])/(([H2O])^6 ([CO2])^6)

Construct the rate of reaction expression for: H_2O + CO_2 ⟶ O_2 + C_6H_12O_6 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_2O + 6 CO_2 ⟶ 6 O_2 + C_6H_12O_6 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_2O | 6 | -6 CO_2 | 6 | -6 O_2 | 6 | 6 C_6H_12O_6 | 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_2O | 6 | -6 | -1/6 (Δ[H2O])/(Δt) CO_2 | 6 | -6 | -1/6 (Δ[CO2])/(Δt) O_2 | 6 | 6 | 1/6 (Δ[O2])/(Δt) C_6H_12O_6 | 1 | 1 | (Δ[C6H12O6])/(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[H2O])/(Δt) = -1/6 (Δ[CO2])/(Δt) = 1/6 (Δ[O2])/(Δt) = (Δ[C6H12O6])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | carbon dioxide | oxygen | D-(+)-glucose formula | H_2O | CO_2 | O_2 | C_6H_12O_6 name | water | carbon dioxide | oxygen | D-(+)-glucose IUPAC name | water | carbon dioxide | molecular oxygen | 6-(hydroxymethyl)oxane-2, 3, 4, 5-tetrol