CO + Cr2O3 = CO2 + Cr

CO carbon monoxide + Cr_2O_3 chromium(III) oxide ⟶ CO_2 carbon dioxide + Cr chromium

Balance the chemical equation algebraically: CO + Cr_2O_3 ⟶ CO_2 + Cr Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CO + c_2 Cr_2O_3 ⟶ c_3 CO_2 + c_4 Cr Set the number of atoms in the reactants equal to the number of atoms in the products for C, O and Cr: C: | c_1 = c_3 O: | c_1 + 3 c_2 = 2 c_3 Cr: | 2 c_2 = 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 = 3 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 CO + Cr_2O_3 ⟶ 3 CO_2 + 2 Cr

+ ⟶ +

carbon monoxide + chromium(III) oxide ⟶ carbon dioxide + chromium

| carbon monoxide | chromium(III) oxide | carbon dioxide | chromium molecular enthalpy | -110.5 kJ/mol | -1140 kJ/mol | -393.5 kJ/mol | 0 kJ/mol total enthalpy | -331.5 kJ/mol | -1140 kJ/mol | -1181 kJ/mol | 0 kJ/mol | H_initial = -1471 kJ/mol | | H_final = -1181 kJ/mol | ΔH_rxn^0 | -1181 kJ/mol - -1471 kJ/mol = 290.7 kJ/mol (endothermic) | | |

| carbon monoxide | chromium(III) oxide | carbon dioxide | chromium molecular entropy | 198 J/(mol K) | 81 J/(mol K) | 214 J/(mol K) | 24 J/(mol K) total entropy | 594 J/(mol K) | 81 J/(mol K) | 642 J/(mol K) | 48 J/(mol K) | S_initial = 675 J/(mol K) | | S_final = 690 J/(mol K) | ΔS_rxn^0 | 690 J/(mol K) - 675 J/(mol K) = 15 J/(mol K) (endoentropic) | | |

Construct the equilibrium constant, K, expression for: CO + Cr_2O_3 ⟶ CO_2 + Cr 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 CO + Cr_2O_3 ⟶ 3 CO_2 + 2 Cr 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 CO | 3 | -3 Cr_2O_3 | 1 | -1 CO_2 | 3 | 3 Cr | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression CO | 3 | -3 | ([CO])^(-3) Cr_2O_3 | 1 | -1 | ([Cr2O3])^(-1) CO_2 | 3 | 3 | ([CO2])^3 Cr | 2 | 2 | ([Cr])^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 = ([CO])^(-3) ([Cr2O3])^(-1) ([CO2])^3 ([Cr])^2 = (([CO2])^3 ([Cr])^2)/(([CO])^3 [Cr2O3])

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

| carbon monoxide | chromium(III) oxide | carbon dioxide | chromium formula | CO | Cr_2O_3 | CO_2 | Cr name | carbon monoxide | chromium(III) oxide | carbon dioxide | chromium

| carbon monoxide | chromium(III) oxide | carbon dioxide | chromium molar mass | 28.01 g/mol | 151.99 g/mol | 44.009 g/mol | 51.9961 g/mol phase | gas (at STP) | solid (at STP) | gas (at STP) | solid (at STP) melting point | -205 °C | 2435 °C | -56.56 °C (at triple point) | 1857 °C boiling point | -191.5 °C | 4000 °C | -78.5 °C (at sublimation point) | 2672 °C density | 0.001145 g/cm^3 (at 25 °C) | 4.8 g/cm^3 | 0.00184212 g/cm^3 (at 20 °C) | 7.14 g/cm^3 solubility in water | | insoluble | | insoluble dynamic viscosity | 1.772×10^-5 Pa s (at 25 °C) | | 1.491×10^-5 Pa s (at 25 °C) | odor | odorless | | odorless | odorless