Al + C = Al4C3

Al (aluminum) + C (activated charcoal) ⟶ Al4C3

Balance the chemical equation algebraically: Al + C ⟶ Al4C3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Al + c_2 C ⟶ c_3 Al4C3 Set the number of atoms in the reactants equal to the number of atoms in the products for Al and C: Al: | c_1 = 4 c_3 C: | c_2 = 3 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 4 c_2 = 3 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 Al + 3 C ⟶ Al4C3

+ ⟶ Al4C3

aluminum + activated charcoal ⟶ Al4C3

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

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

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

| aluminum | activated charcoal | Al4C3 molar mass | 26.9815385 g/mol | 12.011 g/mol | 143.959 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 | |