O2 + Na2CO3 + Cr2O3 = CO2 + Na2CrO4

O_2 (oxygen) + Na_2CO_3 (soda ash) + Cr_2O_3 (chromium(III) oxide) ⟶ CO_2 (carbon dioxide) + Na_2CrO_4 (sodium chromate)

Balance the chemical equation algebraically: O_2 + Na_2CO_3 + Cr_2O_3 ⟶ CO_2 + Na_2CrO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 O_2 + c_2 Na_2CO_3 + c_3 Cr_2O_3 ⟶ c_4 CO_2 + c_5 Na_2CrO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for O, C, Na and Cr: O: | 2 c_1 + 3 c_2 + 3 c_3 = 2 c_4 + 4 c_5 C: | c_2 = c_4 Na: | 2 c_2 = 2 c_5 Cr: | 2 c_3 = c_5 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 = 3/2 c_2 = 2 c_3 = 1 c_4 = 2 c_5 = 2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 3 c_2 = 4 c_3 = 2 c_4 = 4 c_5 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 O_2 + 4 Na_2CO_3 + 2 Cr_2O_3 ⟶ 4 CO_2 + 4 Na_2CrO_4

+ + ⟶ +

oxygen + soda ash + chromium(III) oxide ⟶ carbon dioxide + sodium chromate

Construct the equilibrium constant, K, expression for: O_2 + Na_2CO_3 + Cr_2O_3 ⟶ CO_2 + Na_2CrO_4 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 O_2 + 4 Na_2CO_3 + 2 Cr_2O_3 ⟶ 4 CO_2 + 4 Na_2CrO_4 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 O_2 | 3 | -3 Na_2CO_3 | 4 | -4 Cr_2O_3 | 2 | -2 CO_2 | 4 | 4 Na_2CrO_4 | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression O_2 | 3 | -3 | ([O2])^(-3) Na_2CO_3 | 4 | -4 | ([Na2CO3])^(-4) Cr_2O_3 | 2 | -2 | ([Cr2O3])^(-2) CO_2 | 4 | 4 | ([CO2])^4 Na_2CrO_4 | 4 | 4 | ([Na2CrO4])^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 = ([O2])^(-3) ([Na2CO3])^(-4) ([Cr2O3])^(-2) ([CO2])^4 ([Na2CrO4])^4 = (([CO2])^4 ([Na2CrO4])^4)/(([O2])^3 ([Na2CO3])^4 ([Cr2O3])^2)

Construct the rate of reaction expression for: O_2 + Na_2CO_3 + Cr_2O_3 ⟶ CO_2 + Na_2CrO_4 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 O_2 + 4 Na_2CO_3 + 2 Cr_2O_3 ⟶ 4 CO_2 + 4 Na_2CrO_4 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 O_2 | 3 | -3 Na_2CO_3 | 4 | -4 Cr_2O_3 | 2 | -2 CO_2 | 4 | 4 Na_2CrO_4 | 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 O_2 | 3 | -3 | -1/3 (Δ[O2])/(Δt) Na_2CO_3 | 4 | -4 | -1/4 (Δ[Na2CO3])/(Δt) Cr_2O_3 | 2 | -2 | -1/2 (Δ[Cr2O3])/(Δt) CO_2 | 4 | 4 | 1/4 (Δ[CO2])/(Δt) Na_2CrO_4 | 4 | 4 | 1/4 (Δ[Na2CrO4])/(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[O2])/(Δt) = -1/4 (Δ[Na2CO3])/(Δt) = -1/2 (Δ[Cr2O3])/(Δt) = 1/4 (Δ[CO2])/(Δt) = 1/4 (Δ[Na2CrO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| oxygen | soda ash | chromium(III) oxide | carbon dioxide | sodium chromate formula | O_2 | Na_2CO_3 | Cr_2O_3 | CO_2 | Na_2CrO_4 Hill formula | O_2 | CNa_2O_3 | Cr_2O_3 | CO_2 | CrNa_2O_4 name | oxygen | soda ash | chromium(III) oxide | carbon dioxide | sodium chromate IUPAC name | molecular oxygen | disodium carbonate | | carbon dioxide | disodium dioxido(dioxo)chromium

| oxygen | soda ash | chromium(III) oxide | carbon dioxide | sodium chromate molar mass | 31.998 g/mol | 105.99 g/mol | 151.99 g/mol | 44.009 g/mol | 161.97 g/mol phase | gas (at STP) | solid (at STP) | solid (at STP) | gas (at STP) | solid (at STP) melting point | -218 °C | 851 °C | 2435 °C | -56.56 °C (at triple point) | 780 °C boiling point | -183 °C | 1600 °C | 4000 °C | -78.5 °C (at sublimation point) | density | 0.001429 g/cm^3 (at 0 °C) | | 4.8 g/cm^3 | 0.00184212 g/cm^3 (at 20 °C) | 2.698 g/cm^3 solubility in water | | soluble | insoluble | | surface tension | 0.01347 N/m | | | | dynamic viscosity | 2.055×10^-5 Pa s (at 25 °C) | 0.00355 Pa s (at 900 °C) | | 1.491×10^-5 Pa s (at 25 °C) | odor | odorless | | | odorless |