SiO2 + K2O = K2SiO3

SiO_2 silicon dioxide + K_2O potassium oxide ⟶ K2SiO3

Balance the chemical equation algebraically: SiO_2 + K_2O ⟶ K2SiO3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 SiO_2 + c_2 K_2O ⟶ c_3 K2SiO3 Set the number of atoms in the reactants equal to the number of atoms in the products for O, Si and K: O: | 2 c_1 + c_2 = 3 c_3 Si: | c_1 = c_3 K: | 2 c_2 = 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: | | SiO_2 + K_2O ⟶ K2SiO3

+ ⟶ K2SiO3

silicon dioxide + potassium oxide ⟶ K2SiO3

Construct the equilibrium constant, K, expression for: SiO_2 + K_2O ⟶ K2SiO3 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: SiO_2 + K_2O ⟶ K2SiO3 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 SiO_2 | 1 | -1 K_2O | 1 | -1 K2SiO3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression SiO_2 | 1 | -1 | ([SiO2])^(-1) K_2O | 1 | -1 | ([K2O])^(-1) K2SiO3 | 1 | 1 | [K2SiO3] 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 = ([SiO2])^(-1) ([K2O])^(-1) [K2SiO3] = ([K2SiO3])/([SiO2] [K2O])

Construct the rate of reaction expression for: SiO_2 + K_2O ⟶ K2SiO3 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: SiO_2 + K_2O ⟶ K2SiO3 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 SiO_2 | 1 | -1 K_2O | 1 | -1 K2SiO3 | 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 SiO_2 | 1 | -1 | -(Δ[SiO2])/(Δt) K_2O | 1 | -1 | -(Δ[K2O])/(Δt) K2SiO3 | 1 | 1 | (Δ[K2SiO3])/(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[SiO2])/(Δt) = -(Δ[K2O])/(Δt) = (Δ[K2SiO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| silicon dioxide | potassium oxide | K2SiO3 formula | SiO_2 | K_2O | K2SiO3 Hill formula | O_2Si | K_2O | K2O3Si name | silicon dioxide | potassium oxide | IUPAC name | dioxosilane | dipotassium oxygen(2-) |

| silicon dioxide | potassium oxide | K2SiO3 molar mass | 60.083 g/mol | 94.196 g/mol | 154.28 g/mol phase | solid (at STP) | | melting point | 1713 °C | | boiling point | 2950 °C | | density | 2.196 g/cm^3 | | solubility in water | insoluble | | odor | odorless | |