H2O + Al4C3 = Al(OH)3 + CH4

H_2O (water) + Al4C3 ⟶ Al(OH)_3 (aluminum hydroxide) + CH_4 (methane)

Balance the chemical equation algebraically: H_2O + Al4C3 ⟶ Al(OH)_3 + CH_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 Al4C3 ⟶ c_3 Al(OH)_3 + c_4 CH_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Al and C: H: | 2 c_1 = 3 c_3 + 4 c_4 O: | c_1 = 3 c_3 Al: | 4 c_2 = c_3 C: | 3 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 = 12 c_2 = 1 c_3 = 4 c_4 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 12 H_2O + Al4C3 ⟶ 4 Al(OH)_3 + 3 CH_4

+ Al4C3 ⟶ +

water + Al4C3 ⟶ aluminum hydroxide + methane

Construct the equilibrium constant, K, expression for: H_2O + Al4C3 ⟶ Al(OH)_3 + CH_4 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: 12 H_2O + Al4C3 ⟶ 4 Al(OH)_3 + 3 CH_4 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 H_2O | 12 | -12 Al4C3 | 1 | -1 Al(OH)_3 | 4 | 4 CH_4 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 12 | -12 | ([H2O])^(-12) Al4C3 | 1 | -1 | ([Al4C3])^(-1) Al(OH)_3 | 4 | 4 | ([Al(OH)3])^4 CH_4 | 3 | 3 | ([CH4])^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 = ([H2O])^(-12) ([Al4C3])^(-1) ([Al(OH)3])^4 ([CH4])^3 = (([Al(OH)3])^4 ([CH4])^3)/(([H2O])^12 [Al4C3])

Construct the rate of reaction expression for: H_2O + Al4C3 ⟶ Al(OH)_3 + CH_4 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: 12 H_2O + Al4C3 ⟶ 4 Al(OH)_3 + 3 CH_4 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 H_2O | 12 | -12 Al4C3 | 1 | -1 Al(OH)_3 | 4 | 4 CH_4 | 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 H_2O | 12 | -12 | -1/12 (Δ[H2O])/(Δt) Al4C3 | 1 | -1 | -(Δ[Al4C3])/(Δt) Al(OH)_3 | 4 | 4 | 1/4 (Δ[Al(OH)3])/(Δt) CH_4 | 3 | 3 | 1/3 (Δ[CH4])/(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 = -1/12 (Δ[H2O])/(Δt) = -(Δ[Al4C3])/(Δt) = 1/4 (Δ[Al(OH)3])/(Δt) = 1/3 (Δ[CH4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | Al4C3 | aluminum hydroxide | methane formula | H_2O | Al4C3 | Al(OH)_3 | CH_4 Hill formula | H_2O | C3Al4 | AlH_3O_3 | CH_4 name | water | | aluminum hydroxide | methane

| water | Al4C3 | aluminum hydroxide | methane molar mass | 18.015 g/mol | 143.959 g/mol | 78.003 g/mol | 16.04 g/mol phase | liquid (at STP) | | | gas (at STP) melting point | 0 °C | | | -182.47 °C boiling point | 99.9839 °C | | | -161.48 °C density | 1 g/cm^3 | | | 6.67151×10^-4 g/cm^3 (at 20 °C) solubility in water | | | | soluble surface tension | 0.0728 N/m | | | 0.0137 N/m dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | | 1.114×10^-5 Pa s (at 25 °C) odor | odorless | | | odorless