H2O + Cr = H2 + Cr2O3

H_2O water + Cr chromium ⟶ H_2 hydrogen + Cr_2O_3 chromium(III) oxide

Balance the chemical equation algebraically: H_2O + Cr ⟶ H_2 + Cr_2O_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 Cr ⟶ c_3 H_2 + c_4 Cr_2O_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O and Cr: H: | 2 c_1 = 2 c_3 O: | c_1 = 3 c_4 Cr: | c_2 = 2 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 = 3 c_2 = 2 c_3 = 3 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2O + 2 Cr ⟶ 3 H_2 + Cr_2O_3

+ ⟶ +

water + chromium ⟶ hydrogen + chromium(III) oxide

| water | chromium | hydrogen | chromium(III) oxide molecular enthalpy | -285.8 kJ/mol | 0 kJ/mol | 0 kJ/mol | -1140 kJ/mol total enthalpy | -857.5 kJ/mol | 0 kJ/mol | 0 kJ/mol | -1140 kJ/mol | H_initial = -857.5 kJ/mol | | H_final = -1140 kJ/mol | ΔH_rxn^0 | -1140 kJ/mol - -857.5 kJ/mol = -282.2 kJ/mol (exothermic) | | |

| water | chromium | hydrogen | chromium(III) oxide molecular entropy | 69.91 J/(mol K) | 24 J/(mol K) | 115 J/(mol K) | 81 J/(mol K) total entropy | 209.7 J/(mol K) | 48 J/(mol K) | 345 J/(mol K) | 81 J/(mol K) | S_initial = 257.7 J/(mol K) | | S_final = 426 J/(mol K) | ΔS_rxn^0 | 426 J/(mol K) - 257.7 J/(mol K) = 168.3 J/(mol K) (endoentropic) | | |

Construct the equilibrium constant, K, expression for: H_2O + Cr ⟶ H_2 + Cr_2O_3 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: 3 H_2O + 2 Cr ⟶ 3 H_2 + Cr_2O_3 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 | 3 | -3 Cr | 2 | -2 H_2 | 3 | 3 Cr_2O_3 | 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 | 3 | -3 | ([H2O])^(-3) Cr | 2 | -2 | ([Cr])^(-2) H_2 | 3 | 3 | ([H2])^3 Cr_2O_3 | 1 | 1 | [Cr2O3] 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])^(-3) ([Cr])^(-2) ([H2])^3 [Cr2O3] = (([H2])^3 [Cr2O3])/(([H2O])^3 ([Cr])^2)

Construct the rate of reaction expression for: H_2O + Cr ⟶ H_2 + Cr_2O_3 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: 3 H_2O + 2 Cr ⟶ 3 H_2 + Cr_2O_3 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 | 3 | -3 Cr | 2 | -2 H_2 | 3 | 3 Cr_2O_3 | 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 | 3 | -3 | -1/3 (Δ[H2O])/(Δt) Cr | 2 | -2 | -1/2 (Δ[Cr])/(Δt) H_2 | 3 | 3 | 1/3 (Δ[H2])/(Δt) Cr_2O_3 | 1 | 1 | (Δ[Cr2O3])/(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 = -1/3 (Δ[H2O])/(Δt) = -1/2 (Δ[Cr])/(Δt) = 1/3 (Δ[H2])/(Δt) = (Δ[Cr2O3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | chromium | hydrogen | chromium(III) oxide formula | H_2O | Cr | H_2 | Cr_2O_3 name | water | chromium | hydrogen | chromium(III) oxide IUPAC name | water | chromium | molecular hydrogen |

| water | chromium | hydrogen | chromium(III) oxide molar mass | 18.015 g/mol | 51.9961 g/mol | 2.016 g/mol | 151.99 g/mol phase | liquid (at STP) | solid (at STP) | gas (at STP) | solid (at STP) melting point | 0 °C | 1857 °C | -259.2 °C | 2435 °C boiling point | 99.9839 °C | 2672 °C | -252.8 °C | 4000 °C density | 1 g/cm^3 | 7.14 g/cm^3 | 8.99×10^-5 g/cm^3 (at 0 °C) | 4.8 g/cm^3 solubility in water | | insoluble | | insoluble surface tension | 0.0728 N/m | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | 8.9×10^-6 Pa s (at 25 °C) | odor | odorless | odorless | odorless |