Na2CO3 + Cr2O3 + KBrO3O3 = CO2 + KBr + Na2CrO4

Na_2CO_3 soda ash + Cr_2O_3 chromium(III) oxide + KBrO3O3 ⟶ CO_2 carbon dioxide + KBr potassium bromide + Na_2CrO_4 sodium chromate

Balance the chemical equation algebraically: Na_2CO_3 + Cr_2O_3 + KBrO3O3 ⟶ CO_2 + KBr + Na_2CrO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Na_2CO_3 + c_2 Cr_2O_3 + c_3 KBrO3O3 ⟶ c_4 CO_2 + c_5 KBr + c_6 Na_2CrO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for C, Na, O, Cr, K and Br: C: | c_1 = c_4 Na: | 2 c_1 = 2 c_6 O: | 3 c_1 + 3 c_2 + 6 c_3 = 2 c_4 + 4 c_6 Cr: | 2 c_2 = c_6 K: | c_3 = c_5 Br: | 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 = 4 c_2 = 2 c_3 = 1 c_4 = 4 c_5 = 1 c_6 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 Na_2CO_3 + 2 Cr_2O_3 + KBrO3O3 ⟶ 4 CO_2 + KBr + 4 Na_2CrO_4

+ + KBrO3O3 ⟶ + +

soda ash + chromium(III) oxide + KBrO3O3 ⟶ carbon dioxide + potassium bromide + sodium chromate

Construct the equilibrium constant, K, expression for: Na_2CO_3 + Cr_2O_3 + KBrO3O3 ⟶ CO_2 + KBr + 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: 4 Na_2CO_3 + 2 Cr_2O_3 + KBrO3O3 ⟶ 4 CO_2 + KBr + 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 Na_2CO_3 | 4 | -4 Cr_2O_3 | 2 | -2 KBrO3O3 | 1 | -1 CO_2 | 4 | 4 KBr | 1 | 1 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 Na_2CO_3 | 4 | -4 | ([Na2CO3])^(-4) Cr_2O_3 | 2 | -2 | ([Cr2O3])^(-2) KBrO3O3 | 1 | -1 | ([KBrO3O3])^(-1) CO_2 | 4 | 4 | ([CO2])^4 KBr | 1 | 1 | [KBr] 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 = ([Na2CO3])^(-4) ([Cr2O3])^(-2) ([KBrO3O3])^(-1) ([CO2])^4 [KBr] ([Na2CrO4])^4 = (([CO2])^4 [KBr] ([Na2CrO4])^4)/(([Na2CO3])^4 ([Cr2O3])^2 [KBrO3O3])

Construct the rate of reaction expression for: Na_2CO_3 + Cr_2O_3 + KBrO3O3 ⟶ CO_2 + KBr + 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: 4 Na_2CO_3 + 2 Cr_2O_3 + KBrO3O3 ⟶ 4 CO_2 + KBr + 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 Na_2CO_3 | 4 | -4 Cr_2O_3 | 2 | -2 KBrO3O3 | 1 | -1 CO_2 | 4 | 4 KBr | 1 | 1 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 Na_2CO_3 | 4 | -4 | -1/4 (Δ[Na2CO3])/(Δt) Cr_2O_3 | 2 | -2 | -1/2 (Δ[Cr2O3])/(Δt) KBrO3O3 | 1 | -1 | -(Δ[KBrO3O3])/(Δt) CO_2 | 4 | 4 | 1/4 (Δ[CO2])/(Δt) KBr | 1 | 1 | (Δ[KBr])/(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 = -1/4 (Δ[Na2CO3])/(Δt) = -1/2 (Δ[Cr2O3])/(Δt) = -(Δ[KBrO3O3])/(Δt) = 1/4 (Δ[CO2])/(Δt) = (Δ[KBr])/(Δt) = 1/4 (Δ[Na2CrO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| soda ash | chromium(III) oxide | KBrO3O3 | carbon dioxide | potassium bromide | sodium chromate formula | Na_2CO_3 | Cr_2O_3 | KBrO3O3 | CO_2 | KBr | Na_2CrO_4 Hill formula | CNa_2O_3 | Cr_2O_3 | BrKO6 | CO_2 | BrK | CrNa_2O_4 name | soda ash | chromium(III) oxide | | carbon dioxide | potassium bromide | sodium chromate IUPAC name | disodium carbonate | | | carbon dioxide | potassium bromide | disodium dioxido(dioxo)chromium

| soda ash | chromium(III) oxide | KBrO3O3 | carbon dioxide | potassium bromide | sodium chromate molar mass | 105.99 g/mol | 151.99 g/mol | 215 g/mol | 44.009 g/mol | 119 g/mol | 161.97 g/mol phase | solid (at STP) | solid (at STP) | | gas (at STP) | solid (at STP) | solid (at STP) melting point | 851 °C | 2435 °C | | -56.56 °C (at triple point) | 734 °C | 780 °C boiling point | 1600 °C | 4000 °C | | -78.5 °C (at sublimation point) | 1435 °C | density | | 4.8 g/cm^3 | | 0.00184212 g/cm^3 (at 20 °C) | 2.75 g/cm^3 | 2.698 g/cm^3 solubility in water | soluble | insoluble | | | soluble | dynamic viscosity | 0.00355 Pa s (at 900 °C) | | | 1.491×10^-5 Pa s (at 25 °C) | | odor | | | | odorless | |