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N2 + C + Al2O3 = CO + AlN

Input interpretation

N_2 nitrogen + C activated charcoal + Al_2O_3 aluminum oxide ⟶ CO carbon monoxide + AlN aluminum nitride
N_2 nitrogen + C activated charcoal + Al_2O_3 aluminum oxide ⟶ CO carbon monoxide + AlN aluminum nitride

Balanced equation

Balance the chemical equation algebraically: N_2 + C + Al_2O_3 ⟶ CO + AlN Add stoichiometric coefficients, c_i, to the reactants and products: c_1 N_2 + c_2 C + c_3 Al_2O_3 ⟶ c_4 CO + c_5 AlN Set the number of atoms in the reactants equal to the number of atoms in the products for N, C, Al and O: N: | 2 c_1 = c_5 C: | c_2 = c_4 Al: | 2 c_3 = c_5 O: | 3 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 3 c_3 = 1 c_4 = 3 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | N_2 + 3 C + Al_2O_3 ⟶ 3 CO + 2 AlN
Balance the chemical equation algebraically: N_2 + C + Al_2O_3 ⟶ CO + AlN Add stoichiometric coefficients, c_i, to the reactants and products: c_1 N_2 + c_2 C + c_3 Al_2O_3 ⟶ c_4 CO + c_5 AlN Set the number of atoms in the reactants equal to the number of atoms in the products for N, C, Al and O: N: | 2 c_1 = c_5 C: | c_2 = c_4 Al: | 2 c_3 = c_5 O: | 3 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 3 c_3 = 1 c_4 = 3 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | N_2 + 3 C + Al_2O_3 ⟶ 3 CO + 2 AlN

Structures

+ + ⟶ +
+ + ⟶ +

Names

nitrogen + activated charcoal + aluminum oxide ⟶ carbon monoxide + aluminum nitride
nitrogen + activated charcoal + aluminum oxide ⟶ carbon monoxide + aluminum nitride

Equilibrium constant

Construct the equilibrium constant, K, expression for: N_2 + C + Al_2O_3 ⟶ CO + AlN 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: N_2 + 3 C + Al_2O_3 ⟶ 3 CO + 2 AlN 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 N_2 | 1 | -1 C | 3 | -3 Al_2O_3 | 1 | -1 CO | 3 | 3 AlN | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression N_2 | 1 | -1 | ([N2])^(-1) C | 3 | -3 | ([C])^(-3) Al_2O_3 | 1 | -1 | ([Al2O3])^(-1) CO | 3 | 3 | ([CO])^3 AlN | 2 | 2 | ([AlN])^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 = ([N2])^(-1) ([C])^(-3) ([Al2O3])^(-1) ([CO])^3 ([AlN])^2 = (([CO])^3 ([AlN])^2)/([N2] ([C])^3 [Al2O3])
Construct the equilibrium constant, K, expression for: N_2 + C + Al_2O_3 ⟶ CO + AlN 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: N_2 + 3 C + Al_2O_3 ⟶ 3 CO + 2 AlN 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 N_2 | 1 | -1 C | 3 | -3 Al_2O_3 | 1 | -1 CO | 3 | 3 AlN | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression N_2 | 1 | -1 | ([N2])^(-1) C | 3 | -3 | ([C])^(-3) Al_2O_3 | 1 | -1 | ([Al2O3])^(-1) CO | 3 | 3 | ([CO])^3 AlN | 2 | 2 | ([AlN])^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 = ([N2])^(-1) ([C])^(-3) ([Al2O3])^(-1) ([CO])^3 ([AlN])^2 = (([CO])^3 ([AlN])^2)/([N2] ([C])^3 [Al2O3])

Rate of reaction

Construct the rate of reaction expression for: N_2 + C + Al_2O_3 ⟶ CO + AlN 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: N_2 + 3 C + Al_2O_3 ⟶ 3 CO + 2 AlN 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 N_2 | 1 | -1 C | 3 | -3 Al_2O_3 | 1 | -1 CO | 3 | 3 AlN | 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 N_2 | 1 | -1 | -(Δ[N2])/(Δt) C | 3 | -3 | -1/3 (Δ[C])/(Δt) Al_2O_3 | 1 | -1 | -(Δ[Al2O3])/(Δt) CO | 3 | 3 | 1/3 (Δ[CO])/(Δt) AlN | 2 | 2 | 1/2 (Δ[AlN])/(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 = -(Δ[N2])/(Δt) = -1/3 (Δ[C])/(Δt) = -(Δ[Al2O3])/(Δt) = 1/3 (Δ[CO])/(Δt) = 1/2 (Δ[AlN])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: N_2 + C + Al_2O_3 ⟶ CO + AlN 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: N_2 + 3 C + Al_2O_3 ⟶ 3 CO + 2 AlN 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 N_2 | 1 | -1 C | 3 | -3 Al_2O_3 | 1 | -1 CO | 3 | 3 AlN | 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 N_2 | 1 | -1 | -(Δ[N2])/(Δt) C | 3 | -3 | -1/3 (Δ[C])/(Δt) Al_2O_3 | 1 | -1 | -(Δ[Al2O3])/(Δt) CO | 3 | 3 | 1/3 (Δ[CO])/(Δt) AlN | 2 | 2 | 1/2 (Δ[AlN])/(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 = -(Δ[N2])/(Δt) = -1/3 (Δ[C])/(Δt) = -(Δ[Al2O3])/(Δt) = 1/3 (Δ[CO])/(Δt) = 1/2 (Δ[AlN])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| nitrogen | activated charcoal | aluminum oxide | carbon monoxide | aluminum nitride formula | N_2 | C | Al_2O_3 | CO | AlN name | nitrogen | activated charcoal | aluminum oxide | carbon monoxide | aluminum nitride IUPAC name | molecular nitrogen | carbon | dialuminum;oxygen(2-) | carbon monoxide | nitriloalumane
| nitrogen | activated charcoal | aluminum oxide | carbon monoxide | aluminum nitride formula | N_2 | C | Al_2O_3 | CO | AlN name | nitrogen | activated charcoal | aluminum oxide | carbon monoxide | aluminum nitride IUPAC name | molecular nitrogen | carbon | dialuminum;oxygen(2-) | carbon monoxide | nitriloalumane

Substance properties

| nitrogen | activated charcoal | aluminum oxide | carbon monoxide | aluminum nitride molar mass | 28.014 g/mol | 12.011 g/mol | 101.96 g/mol | 28.01 g/mol | 40.989 g/mol phase | gas (at STP) | solid (at STP) | solid (at STP) | gas (at STP) | solid (at STP) melting point | -210 °C | 3550 °C | 2040 °C | -205 °C | 2200 °C boiling point | -195.79 °C | 4027 °C | | -191.5 °C | 2517 °C density | 0.001251 g/cm^3 (at 0 °C) | 2.26 g/cm^3 | | 0.001145 g/cm^3 (at 25 °C) | 3.26 g/cm^3 solubility in water | insoluble | insoluble | | | decomposes surface tension | 0.0066 N/m | | | | dynamic viscosity | 1.78×10^-5 Pa s (at 25 °C) | | | 1.772×10^-5 Pa s (at 25 °C) | odor | odorless | | odorless | odorless |
| nitrogen | activated charcoal | aluminum oxide | carbon monoxide | aluminum nitride molar mass | 28.014 g/mol | 12.011 g/mol | 101.96 g/mol | 28.01 g/mol | 40.989 g/mol phase | gas (at STP) | solid (at STP) | solid (at STP) | gas (at STP) | solid (at STP) melting point | -210 °C | 3550 °C | 2040 °C | -205 °C | 2200 °C boiling point | -195.79 °C | 4027 °C | | -191.5 °C | 2517 °C density | 0.001251 g/cm^3 (at 0 °C) | 2.26 g/cm^3 | | 0.001145 g/cm^3 (at 25 °C) | 3.26 g/cm^3 solubility in water | insoluble | insoluble | | | decomposes surface tension | 0.0066 N/m | | | | dynamic viscosity | 1.78×10^-5 Pa s (at 25 °C) | | | 1.772×10^-5 Pa s (at 25 °C) | odor | odorless | | odorless | odorless |

Units

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