Cr(NO3)3 = O2 + NO2 + Cr2O3

CrN_3O_9 chromium nitrate ⟶ O_2 oxygen + NO_2 nitrogen dioxide + Cr_2O_3 chromium(III) oxide

Balance the chemical equation algebraically: CrN_3O_9 ⟶ O_2 + NO_2 + Cr_2O_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CrN_3O_9 ⟶ c_2 O_2 + c_3 NO_2 + c_4 Cr_2O_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Cr, N and O: Cr: | c_1 = 2 c_4 N: | 3 c_1 = c_3 O: | 9 c_1 = 2 c_2 + 2 c_3 + 3 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 = 2 c_2 = 3/2 c_3 = 6 c_4 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 4 c_2 = 3 c_3 = 12 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 CrN_3O_9 ⟶ 3 O_2 + 12 NO_2 + 2 Cr_2O_3

⟶ + +

chromium nitrate ⟶ oxygen + nitrogen dioxide + chromium(III) oxide

Construct the equilibrium constant, K, expression for: CrN_3O_9 ⟶ O_2 + NO_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 CrN_3O_9 ⟶ 3 O_2 + 12 NO_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 CrN_3O_9 | 4 | -4 O_2 | 3 | 3 NO_2 | 12 | 12 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 CrN_3O_9 | 4 | -4 | ([CrN3O9])^(-4) O_2 | 3 | 3 | ([O2])^3 NO_2 | 12 | 12 | ([NO2])^12 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 = ([CrN3O9])^(-4) ([O2])^3 ([NO2])^12 ([Cr2O3])^2 = (([O2])^3 ([NO2])^12 ([Cr2O3])^2)/([CrN3O9])^4

Construct the rate of reaction expression for: CrN_3O_9 ⟶ O_2 + NO_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 CrN_3O_9 ⟶ 3 O_2 + 12 NO_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 CrN_3O_9 | 4 | -4 O_2 | 3 | 3 NO_2 | 12 | 12 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 CrN_3O_9 | 4 | -4 | -1/4 (Δ[CrN3O9])/(Δt) O_2 | 3 | 3 | 1/3 (Δ[O2])/(Δt) NO_2 | 12 | 12 | 1/12 (Δ[NO2])/(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[CrN3O9])/(Δt) = 1/3 (Δ[O2])/(Δt) = 1/12 (Δ[NO2])/(Δt) = 1/2 (Δ[Cr2O3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| chromium nitrate | oxygen | nitrogen dioxide | chromium(III) oxide formula | CrN_3O_9 | O_2 | NO_2 | Cr_2O_3 name | chromium nitrate | oxygen | nitrogen dioxide | chromium(III) oxide IUPAC name | chromium(+3) cation trinitrate | molecular oxygen | Nitrogen dioxide |

| chromium nitrate | oxygen | nitrogen dioxide | chromium(III) oxide molar mass | 238.01 g/mol | 31.998 g/mol | 46.005 g/mol | 151.99 g/mol phase | solid (at STP) | gas (at STP) | gas (at STP) | solid (at STP) melting point | 66 °C | -218 °C | -11 °C | 2435 °C boiling point | | -183 °C | 21 °C | 4000 °C density | 1.8 g/cm^3 | 0.001429 g/cm^3 (at 0 °C) | 0.00188 g/cm^3 (at 25 °C) | 4.8 g/cm^3 solubility in water | soluble | | reacts | insoluble surface tension | | 0.01347 N/m | | dynamic viscosity | | 2.055×10^-5 Pa s (at 25 °C) | 4.02×10^-4 Pa s (at 25 °C) | odor | | odorless | |