CrO3 = O2 + Cr2O3

CrO_3 (chromium trioxide) ⟶ O_2 (oxygen) + Cr_2O_3 (chromium(III) oxide)

Balance the chemical equation algebraically: CrO_3 ⟶ O_2 + Cr_2O_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CrO_3 ⟶ c_2 O_2 + c_3 Cr_2O_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Cr and O: Cr: | c_1 = 2 c_3 O: | 3 c_1 = 2 c_2 + 3 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 3/2 c_3 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 4 c_2 = 3 c_3 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 CrO_3 ⟶ 3 O_2 + 2 Cr_2O_3

⟶ +

chromium trioxide ⟶ oxygen + chromium(III) oxide

| chromium trioxide | oxygen | chromium(III) oxide molecular free energy | -502 kJ/mol | 231.7 kJ/mol | -1058 kJ/mol total free energy | -2008 kJ/mol | 695.1 kJ/mol | -2116 kJ/mol | G_initial = -2008 kJ/mol | G_final = -1421 kJ/mol | ΔG_rxn^0 | -1421 kJ/mol - -2008 kJ/mol = 586.9 kJ/mol (endergonic) | |

| chromium trioxide | oxygen | chromium(III) oxide molecular entropy | 72 J/(mol K) | 205 J/(mol K) | 81 J/(mol K) total entropy | 288 J/(mol K) | 615 J/(mol K) | 162 J/(mol K) | S_initial = 288 J/(mol K) | S_final = 777 J/(mol K) | ΔS_rxn^0 | 777 J/(mol K) - 288 J/(mol K) = 489 J/(mol K) (endoentropic) | |

Construct the equilibrium constant, K, expression for: CrO_3 ⟶ O_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: 4 CrO_3 ⟶ 3 O_2 + 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 CrO_3 | 4 | -4 O_2 | 3 | 3 Cr_2O_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression CrO_3 | 4 | -4 | ([CrO3])^(-4) O_2 | 3 | 3 | ([O2])^3 Cr_2O_3 | 2 | 2 | ([Cr2O3])^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 = ([CrO3])^(-4) ([O2])^3 ([Cr2O3])^2 = (([O2])^3 ([Cr2O3])^2)/([CrO3])^4

Construct the rate of reaction expression for: CrO_3 ⟶ O_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: 4 CrO_3 ⟶ 3 O_2 + 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 CrO_3 | 4 | -4 O_2 | 3 | 3 Cr_2O_3 | 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 CrO_3 | 4 | -4 | -1/4 (Δ[CrO3])/(Δt) O_2 | 3 | 3 | 1/3 (Δ[O2])/(Δt) Cr_2O_3 | 2 | 2 | 1/2 (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 = -1/4 (Δ[CrO3])/(Δt) = 1/3 (Δ[O2])/(Δt) = 1/2 (Δ[Cr2O3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| chromium trioxide | oxygen | chromium(III) oxide formula | CrO_3 | O_2 | Cr_2O_3 name | chromium trioxide | oxygen | chromium(III) oxide IUPAC name | trioxochromium | molecular oxygen |

| chromium trioxide | oxygen | chromium(III) oxide molar mass | 99.993 g/mol | 31.998 g/mol | 151.99 g/mol phase | solid (at STP) | gas (at STP) | solid (at STP) melting point | 196 °C | -218 °C | 2435 °C boiling point | | -183 °C | 4000 °C density | | 0.001429 g/cm^3 (at 0 °C) | 4.8 g/cm^3 solubility in water | very soluble | | insoluble surface tension | | 0.01347 N/m | dynamic viscosity | | 2.055×10^-5 Pa s (at 25 °C) | odor | odorless | odorless |