CaCO3 + SiO2 = CO2 + CaSiO3

CaCO_3 calcium carbonate + SiO_2 silicon dioxide ⟶ CO_2 carbon dioxide + CaSiO_3 calcium silicate

Balance the chemical equation algebraically: CaCO_3 + SiO_2 ⟶ CO_2 + CaSiO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CaCO_3 + c_2 SiO_2 ⟶ c_3 CO_2 + c_4 CaSiO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for C, Ca, O and Si: C: | c_1 = c_3 Ca: | c_1 = c_4 O: | 3 c_1 + 2 c_2 = 2 c_3 + 3 c_4 Si: | 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | CaCO_3 + SiO_2 ⟶ CO_2 + CaSiO_3

+ ⟶ +

calcium carbonate + silicon dioxide ⟶ carbon dioxide + calcium silicate

Construct the equilibrium constant, K, expression for: CaCO_3 + SiO_2 ⟶ CO_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: CaCO_3 + SiO_2 ⟶ CO_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 CaCO_3 | 1 | -1 SiO_2 | 1 | -1 CO_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 CaCO_3 | 1 | -1 | ([CaCO3])^(-1) SiO_2 | 1 | -1 | ([SiO2])^(-1) CO_2 | 1 | 1 | [CO2] 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 = ([CaCO3])^(-1) ([SiO2])^(-1) [CO2] [CaSiO3] = ([CO2] [CaSiO3])/([CaCO3] [SiO2])

Construct the rate of reaction expression for: CaCO_3 + SiO_2 ⟶ CO_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: CaCO_3 + SiO_2 ⟶ CO_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 CaCO_3 | 1 | -1 SiO_2 | 1 | -1 CO_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 CaCO_3 | 1 | -1 | -(Δ[CaCO3])/(Δt) SiO_2 | 1 | -1 | -(Δ[SiO2])/(Δt) CO_2 | 1 | 1 | (Δ[CO2])/(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[CaCO3])/(Δt) = -(Δ[SiO2])/(Δt) = (Δ[CO2])/(Δt) = (Δ[CaSiO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| calcium carbonate | silicon dioxide | carbon dioxide | calcium silicate formula | CaCO_3 | SiO_2 | CO_2 | CaSiO_3 Hill formula | CCaO_3 | O_2Si | CO_2 | CaO_3Si name | calcium carbonate | silicon dioxide | carbon dioxide | calcium silicate IUPAC name | calcium carbonate | dioxosilane | carbon dioxide | calcium dioxido-oxosilane

| calcium carbonate | silicon dioxide | carbon dioxide | calcium silicate molar mass | 100.09 g/mol | 60.083 g/mol | 44.009 g/mol | 116.16 g/mol phase | solid (at STP) | solid (at STP) | gas (at STP) | melting point | 1340 °C | 1713 °C | -56.56 °C (at triple point) | boiling point | | 2950 °C | -78.5 °C (at sublimation point) | density | 2.71 g/cm^3 | 2.196 g/cm^3 | 0.00184212 g/cm^3 (at 20 °C) | solubility in water | insoluble | insoluble | | dynamic viscosity | | | 1.491×10^-5 Pa s (at 25 °C) | odor | | odorless | odorless |