H2O = O2 + H2

H_2O (water) ⟶ O_2 (oxygen) + H_2 (hydrogen)

Balance the chemical equation algebraically: H_2O ⟶ O_2 + H_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O ⟶ c_2 O_2 + c_3 H_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H and O: H: | 2 c_1 = 2 c_3 O: | c_1 = 2 c_2 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 = 2 c_2 = 1 c_3 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2O ⟶ O_2 + 2 H_2

⟶ +

water ⟶ oxygen + hydrogen

| water | oxygen | hydrogen molecular enthalpy | -285.8 kJ/mol | 0 kJ/mol | 0 kJ/mol total enthalpy | -571.7 kJ/mol | 0 kJ/mol | 0 kJ/mol | H_initial = -571.7 kJ/mol | H_final = 0 kJ/mol | ΔH_rxn^0 | 0 kJ/mol - -571.7 kJ/mol = 571.7 kJ/mol (endothermic) | |

| water | oxygen | hydrogen molecular free energy | -237.1 kJ/mol | 231.7 kJ/mol | 0 kJ/mol total free energy | -474.2 kJ/mol | 231.7 kJ/mol | 0 kJ/mol | G_initial = -474.2 kJ/mol | G_final = 231.7 kJ/mol | ΔG_rxn^0 | 231.7 kJ/mol - -474.2 kJ/mol = 705.9 kJ/mol (endergonic) | |

| water | oxygen | hydrogen molecular entropy | 69.91 J/(mol K) | 205 J/(mol K) | 115 J/(mol K) total entropy | 139.8 J/(mol K) | 205 J/(mol K) | 230 J/(mol K) | S_initial = 139.8 J/(mol K) | S_final = 435 J/(mol K) | ΔS_rxn^0 | 435 J/(mol K) - 139.8 J/(mol K) = 295.2 J/(mol K) (endoentropic) | |

Construct the equilibrium constant, K, expression for: H_2O ⟶ O_2 + H_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: 2 H_2O ⟶ O_2 + 2 H_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 H_2O | 2 | -2 O_2 | 1 | 1 H_2 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 2 | -2 | ([H2O])^(-2) O_2 | 1 | 1 | [O2] H_2 | 2 | 2 | ([H2])^2 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])^(-2) [O2] ([H2])^2 = ([O2] ([H2])^2)/([H2O])^2

Construct the rate of reaction expression for: H_2O ⟶ O_2 + H_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: 2 H_2O ⟶ O_2 + 2 H_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 H_2O | 2 | -2 O_2 | 1 | 1 H_2 | 2 | 2 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 | 2 | -2 | -1/2 (Δ[H2O])/(Δt) O_2 | 1 | 1 | (Δ[O2])/(Δt) H_2 | 2 | 2 | 1/2 (Δ[H2])/(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 = -1/2 (Δ[H2O])/(Δt) = (Δ[O2])/(Δt) = 1/2 (Δ[H2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | oxygen | hydrogen formula | H_2O | O_2 | H_2 name | water | oxygen | hydrogen IUPAC name | water | molecular oxygen | molecular hydrogen

| water | oxygen | hydrogen molar mass | 18.015 g/mol | 31.998 g/mol | 2.016 g/mol phase | liquid (at STP) | gas (at STP) | gas (at STP) melting point | 0 °C | -218 °C | -259.2 °C boiling point | 99.9839 °C | -183 °C | -252.8 °C density | 1 g/cm^3 | 0.001429 g/cm^3 (at 0 °C) | 8.99×10^-5 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) | 2.055×10^-5 Pa s (at 25 °C) | 8.9×10^-6 Pa s (at 25 °C) odor | odorless | odorless | odorless