H2O + CO2 = O2 + C6H11O6

H_2O water + CO_2 carbon dioxide ⟶ O_2 oxygen + C6H11O6

Balance the chemical equation algebraically: H_2O + CO_2 ⟶ O_2 + C6H11O6 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 CO_2 ⟶ c_3 O_2 + c_4 C6H11O6 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 = 11 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 = 11/2 c_2 = 6 c_3 = 23/4 c_4 = 1 Multiply by the least common denominator, 4, to eliminate fractional coefficients: c_1 = 22 c_2 = 24 c_3 = 23 c_4 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 22 H_2O + 24 CO_2 ⟶ 23 O_2 + 4 C6H11O6

+ ⟶ + C6H11O6

water + carbon dioxide ⟶ oxygen + C6H11O6

Construct the equilibrium constant, K, expression for: H_2O + CO_2 ⟶ O_2 + C6H11O6 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: 22 H_2O + 24 CO_2 ⟶ 23 O_2 + 4 C6H11O6 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 | 22 | -22 CO_2 | 24 | -24 O_2 | 23 | 23 C6H11O6 | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 22 | -22 | ([H2O])^(-22) CO_2 | 24 | -24 | ([CO2])^(-24) O_2 | 23 | 23 | ([O2])^23 C6H11O6 | 4 | 4 | ([C6H11O6])^4 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])^(-22) ([CO2])^(-24) ([O2])^23 ([C6H11O6])^4 = (([O2])^23 ([C6H11O6])^4)/(([H2O])^22 ([CO2])^24)

Construct the rate of reaction expression for: H_2O + CO_2 ⟶ O_2 + C6H11O6 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: 22 H_2O + 24 CO_2 ⟶ 23 O_2 + 4 C6H11O6 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 | 22 | -22 CO_2 | 24 | -24 O_2 | 23 | 23 C6H11O6 | 4 | 4 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 | 22 | -22 | -1/22 (Δ[H2O])/(Δt) CO_2 | 24 | -24 | -1/24 (Δ[CO2])/(Δt) O_2 | 23 | 23 | 1/23 (Δ[O2])/(Δt) C6H11O6 | 4 | 4 | 1/4 (Δ[C6H11O6])/(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 = -1/22 (Δ[H2O])/(Δt) = -1/24 (Δ[CO2])/(Δt) = 1/23 (Δ[O2])/(Δt) = 1/4 (Δ[C6H11O6])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | carbon dioxide | oxygen | C6H11O6 formula | H_2O | CO_2 | O_2 | C6H11O6 name | water | carbon dioxide | oxygen | IUPAC name | water | carbon dioxide | molecular oxygen |

| water | carbon dioxide | oxygen | C6H11O6 molar mass | 18.015 g/mol | 44.009 g/mol | 31.998 g/mol | 179.15 g/mol phase | liquid (at STP) | gas (at STP) | gas (at STP) | melting point | 0 °C | -56.56 °C (at triple point) | -218 °C | boiling point | 99.9839 °C | -78.5 °C (at sublimation point) | -183 °C | density | 1 g/cm^3 | 0.00184212 g/cm^3 (at 20 °C) | 0.001429 g/cm^3 (at 0 °C) | surface tension | 0.0728 N/m | | 0.01347 N/m | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | 1.491×10^-5 Pa s (at 25 °C) | 2.055×10^-5 Pa s (at 25 °C) | odor | odorless | odorless | odorless |