Al4C3 = Al + C

Al4C3 ⟶ Al aluminum + C activated charcoal

Balance the chemical equation algebraically: Al4C3 ⟶ Al + C Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Al4C3 ⟶ c_2 Al + c_3 C Set the number of atoms in the reactants equal to the number of atoms in the products for Al and C: Al: | 4 c_1 = c_2 C: | 3 c_1 = c_3 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 = 4 c_3 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Al4C3 ⟶ 4 Al + 3 C

Al4C3 ⟶ +

Al4C3 ⟶ aluminum + activated charcoal

Construct the equilibrium constant, K, expression for: Al4C3 ⟶ Al + C 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: Al4C3 ⟶ 4 Al + 3 C 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 Al4C3 | 1 | -1 Al | 4 | 4 C | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Al4C3 | 1 | -1 | ([Al4C3])^(-1) Al | 4 | 4 | ([Al])^4 C | 3 | 3 | ([C])^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 = ([Al4C3])^(-1) ([Al])^4 ([C])^3 = (([Al])^4 ([C])^3)/([Al4C3])

Construct the rate of reaction expression for: Al4C3 ⟶ Al + C 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: Al4C3 ⟶ 4 Al + 3 C 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 Al4C3 | 1 | -1 Al | 4 | 4 C | 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 Al4C3 | 1 | -1 | -(Δ[Al4C3])/(Δt) Al | 4 | 4 | 1/4 (Δ[Al])/(Δt) C | 3 | 3 | 1/3 (Δ[C])/(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[Al4C3])/(Δt) = 1/4 (Δ[Al])/(Δt) = 1/3 (Δ[C])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| Al4C3 | aluminum | activated charcoal formula | Al4C3 | Al | C Hill formula | C3Al4 | Al | C name | | aluminum | activated charcoal IUPAC name | | aluminum | carbon

| Al4C3 | aluminum | activated charcoal molar mass | 143.959 g/mol | 26.9815385 g/mol | 12.011 g/mol phase | | solid (at STP) | solid (at STP) melting point | | 660.4 °C | 3550 °C boiling point | | 2460 °C | 4027 °C density | | 2.7 g/cm^3 | 2.26 g/cm^3 solubility in water | | insoluble | insoluble surface tension | | 0.817 N/m | dynamic viscosity | | 1.5×10^-4 Pa s (at 760 °C) | odor | | odorless |