KNO3 + Cr2O3 + K2CO3 = CO2 + K2CrO4 + KNO2

KNO_3 (potassium nitrate) + Cr_2O_3 (chromium(III) oxide) + K_2CO_3 (pearl ash) ⟶ CO_2 (carbon dioxide) + K_2CrO_4 (potassium chromate) + KNO_2 (potassium nitrite)

Balance the chemical equation algebraically: KNO_3 + Cr_2O_3 + K_2CO_3 ⟶ CO_2 + K_2CrO_4 + KNO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KNO_3 + c_2 Cr_2O_3 + c_3 K_2CO_3 ⟶ c_4 CO_2 + c_5 K_2CrO_4 + c_6 KNO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for K, N, O, Cr and C: K: | c_1 + 2 c_3 = 2 c_5 + c_6 N: | c_1 = c_6 O: | 3 c_1 + 3 c_2 + 3 c_3 = 2 c_4 + 4 c_5 + 2 c_6 Cr: | 2 c_2 = c_5 C: | c_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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 1 c_3 = 2 c_4 = 2 c_5 = 2 c_6 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 KNO_3 + Cr_2O_3 + 2 K_2CO_3 ⟶ 2 CO_2 + 2 K_2CrO_4 + 3 KNO_2

+ + ⟶ + +

potassium nitrate + chromium(III) oxide + pearl ash ⟶ carbon dioxide + potassium chromate + potassium nitrite

Construct the equilibrium constant, K, expression for: KNO_3 + Cr_2O_3 + K_2CO_3 ⟶ CO_2 + K_2CrO_4 + KNO_2 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 KNO_3 + Cr_2O_3 + 2 K_2CO_3 ⟶ 2 CO_2 + 2 K_2CrO_4 + 3 KNO_2 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 KNO_3 | 3 | -3 Cr_2O_3 | 1 | -1 K_2CO_3 | 2 | -2 CO_2 | 2 | 2 K_2CrO_4 | 2 | 2 KNO_2 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KNO_3 | 3 | -3 | ([KNO3])^(-3) Cr_2O_3 | 1 | -1 | ([Cr2O3])^(-1) K_2CO_3 | 2 | -2 | ([K2CO3])^(-2) CO_2 | 2 | 2 | ([CO2])^2 K_2CrO_4 | 2 | 2 | ([K2CrO4])^2 KNO_2 | 3 | 3 | ([KNO2])^3 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 = ([KNO3])^(-3) ([Cr2O3])^(-1) ([K2CO3])^(-2) ([CO2])^2 ([K2CrO4])^2 ([KNO2])^3 = (([CO2])^2 ([K2CrO4])^2 ([KNO2])^3)/(([KNO3])^3 [Cr2O3] ([K2CO3])^2)

Construct the rate of reaction expression for: KNO_3 + Cr_2O_3 + K_2CO_3 ⟶ CO_2 + K_2CrO_4 + KNO_2 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 KNO_3 + Cr_2O_3 + 2 K_2CO_3 ⟶ 2 CO_2 + 2 K_2CrO_4 + 3 KNO_2 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 KNO_3 | 3 | -3 Cr_2O_3 | 1 | -1 K_2CO_3 | 2 | -2 CO_2 | 2 | 2 K_2CrO_4 | 2 | 2 KNO_2 | 3 | 3 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 KNO_3 | 3 | -3 | -1/3 (Δ[KNO3])/(Δt) Cr_2O_3 | 1 | -1 | -(Δ[Cr2O3])/(Δt) K_2CO_3 | 2 | -2 | -1/2 (Δ[K2CO3])/(Δt) CO_2 | 2 | 2 | 1/2 (Δ[CO2])/(Δt) K_2CrO_4 | 2 | 2 | 1/2 (Δ[K2CrO4])/(Δt) KNO_2 | 3 | 3 | 1/3 (Δ[KNO2])/(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[KNO3])/(Δt) = -(Δ[Cr2O3])/(Δt) = -1/2 (Δ[K2CO3])/(Δt) = 1/2 (Δ[CO2])/(Δt) = 1/2 (Δ[K2CrO4])/(Δt) = 1/3 (Δ[KNO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium nitrate | chromium(III) oxide | pearl ash | carbon dioxide | potassium chromate | potassium nitrite formula | KNO_3 | Cr_2O_3 | K_2CO_3 | CO_2 | K_2CrO_4 | KNO_2 Hill formula | KNO_3 | Cr_2O_3 | CK_2O_3 | CO_2 | CrK_2O_4 | KNO_2 name | potassium nitrate | chromium(III) oxide | pearl ash | carbon dioxide | potassium chromate | potassium nitrite IUPAC name | potassium nitrate | | dipotassium carbonate | carbon dioxide | dipotassium dioxido-dioxochromium | potassium nitrite

| potassium nitrate | chromium(III) oxide | pearl ash | carbon dioxide | potassium chromate | potassium nitrite molar mass | 101.1 g/mol | 151.99 g/mol | 138.2 g/mol | 44.009 g/mol | 194.19 g/mol | 85.103 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | gas (at STP) | solid (at STP) | solid (at STP) melting point | 334 °C | 2435 °C | 891 °C | -56.56 °C (at triple point) | 971 °C | 350 °C boiling point | | 4000 °C | | -78.5 °C (at sublimation point) | | density | | 4.8 g/cm^3 | 2.43 g/cm^3 | 0.00184212 g/cm^3 (at 20 °C) | 2.73 g/cm^3 | 1.915 g/cm^3 solubility in water | soluble | insoluble | soluble | | soluble | dynamic viscosity | | | | 1.491×10^-5 Pa s (at 25 °C) | | odor | odorless | | | odorless | odorless |