CaO + SiO2 = CaSiO3

CaO (lime) + SiO_2 (silicon dioxide) ⟶ CaSiO_3 (calcium silicate)

Balance the chemical equation algebraically: CaO + SiO_2 ⟶ CaSiO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CaO + c_2 SiO_2 ⟶ c_3 CaSiO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Ca, O and Si: Ca: | c_1 = c_3 O: | c_1 + 2 c_2 = 3 c_3 Si: | 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: | | CaO + SiO_2 ⟶ CaSiO_3

+ ⟶

lime + silicon dioxide ⟶ calcium silicate

Construct the equilibrium constant, K, expression for: CaO + SiO_2 ⟶ CaSiO_3 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: CaO + SiO_2 ⟶ CaSiO_3 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 CaO | 1 | -1 SiO_2 | 1 | -1 CaSiO_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression CaO | 1 | -1 | ([CaO])^(-1) SiO_2 | 1 | -1 | ([SiO2])^(-1) CaSiO_3 | 1 | 1 | [CaSiO3] 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 = ([CaO])^(-1) ([SiO2])^(-1) [CaSiO3] = ([CaSiO3])/([CaO] [SiO2])

Construct the rate of reaction expression for: CaO + SiO_2 ⟶ CaSiO_3 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: CaO + SiO_2 ⟶ CaSiO_3 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 CaO | 1 | -1 SiO_2 | 1 | -1 CaSiO_3 | 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 CaO | 1 | -1 | -(Δ[CaO])/(Δt) SiO_2 | 1 | -1 | -(Δ[SiO2])/(Δt) CaSiO_3 | 1 | 1 | (Δ[CaSiO3])/(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[CaO])/(Δt) = -(Δ[SiO2])/(Δt) = (Δ[CaSiO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| lime | silicon dioxide | calcium silicate formula | CaO | SiO_2 | CaSiO_3 Hill formula | CaO | O_2Si | CaO_3Si name | lime | silicon dioxide | calcium silicate IUPAC name | | dioxosilane | calcium dioxido-oxosilane

| lime | silicon dioxide | calcium silicate molar mass | 56.077 g/mol | 60.083 g/mol | 116.16 g/mol phase | solid (at STP) | solid (at STP) | melting point | 2580 °C | 1713 °C | boiling point | 2850 °C | 2950 °C | density | 3.3 g/cm^3 | 2.196 g/cm^3 | solubility in water | reacts | insoluble | odor | | odorless |