Al2O3 + CaO = Ca(AlO2)2

Al_2O_3 aluminum oxide + CaO lime ⟶ O_4Al_2Ca_1 calcium aluminate

Balance the chemical equation algebraically: Al_2O_3 + CaO ⟶ O_4Al_2Ca_1 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Al_2O_3 + c_2 CaO ⟶ c_3 O_4Al_2Ca_1 Set the number of atoms in the reactants equal to the number of atoms in the products for Al, O and Ca: Al: | 2 c_1 = 2 c_3 O: | 3 c_1 + c_2 = 4 c_3 Ca: | c_2 = 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 = 1 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Al_2O_3 + CaO ⟶ O_4Al_2Ca_1

+ ⟶

aluminum oxide + lime ⟶ calcium aluminate

Construct the equilibrium constant, K, expression for: Al_2O_3 + CaO ⟶ O_4Al_2Ca_1 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: Al_2O_3 + CaO ⟶ O_4Al_2Ca_1 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_2O_3 | 1 | -1 CaO | 1 | -1 O_4Al_2Ca_1 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Al_2O_3 | 1 | -1 | ([Al2O3])^(-1) CaO | 1 | -1 | ([CaO])^(-1) O_4Al_2Ca_1 | 1 | 1 | [O4Al2Ca1] 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 = ([Al2O3])^(-1) ([CaO])^(-1) [O4Al2Ca1] = ([O4Al2Ca1])/([Al2O3] [CaO])

Construct the rate of reaction expression for: Al_2O_3 + CaO ⟶ O_4Al_2Ca_1 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: Al_2O_3 + CaO ⟶ O_4Al_2Ca_1 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_2O_3 | 1 | -1 CaO | 1 | -1 O_4Al_2Ca_1 | 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_2O_3 | 1 | -1 | -(Δ[Al2O3])/(Δt) CaO | 1 | -1 | -(Δ[CaO])/(Δt) O_4Al_2Ca_1 | 1 | 1 | (Δ[O4Al2Ca1])/(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[Al2O3])/(Δt) = -(Δ[CaO])/(Δt) = (Δ[O4Al2Ca1])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| aluminum oxide | lime | calcium aluminate formula | Al_2O_3 | CaO | O_4Al_2Ca_1 Hill formula | Al_2O_3 | CaO | Al_2CaO_4 name | aluminum oxide | lime | calcium aluminate IUPAC name | dialuminum;oxygen(2-) | | calcium oxido(oxo)alumane

| aluminum oxide | lime | calcium aluminate molar mass | 101.96 g/mol | 56.077 g/mol | 158.04 g/mol phase | solid (at STP) | solid (at STP) | melting point | 2040 °C | 2580 °C | boiling point | | 2850 °C | density | | 3.3 g/cm^3 | solubility in water | | reacts | odor | odorless | |