HCl + K2SiO3 = KCl + H2SiO3

HCl hydrogen chloride + K2SiO3 ⟶ KCl potassium chloride + H_2O_3Si metasilicic acid

Balance the chemical equation algebraically: HCl + K2SiO3 ⟶ KCl + H_2O_3Si Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 K2SiO3 ⟶ c_3 KCl + c_4 H_2O_3Si Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, K, Si and O: Cl: | c_1 = c_3 H: | c_1 = 2 c_4 K: | 2 c_2 = c_3 Si: | c_2 = c_4 O: | 3 c_2 = 3 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 = 2 c_2 = 1 c_3 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 HCl + K2SiO3 ⟶ 2 KCl + H_2O_3Si

+ K2SiO3 ⟶ +

hydrogen chloride + K2SiO3 ⟶ potassium chloride + metasilicic acid

Construct the equilibrium constant, K, expression for: HCl + K2SiO3 ⟶ KCl + H_2O_3Si 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: 2 HCl + K2SiO3 ⟶ 2 KCl + H_2O_3Si 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 HCl | 2 | -2 K2SiO3 | 1 | -1 KCl | 2 | 2 H_2O_3Si | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 2 | -2 | ([HCl])^(-2) K2SiO3 | 1 | -1 | ([K2SiO3])^(-1) KCl | 2 | 2 | ([KCl])^2 H_2O_3Si | 1 | 1 | [H2O3Si] 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 = ([HCl])^(-2) ([K2SiO3])^(-1) ([KCl])^2 [H2O3Si] = (([KCl])^2 [H2O3Si])/(([HCl])^2 [K2SiO3])

Construct the rate of reaction expression for: HCl + K2SiO3 ⟶ KCl + H_2O_3Si 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: 2 HCl + K2SiO3 ⟶ 2 KCl + H_2O_3Si 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 HCl | 2 | -2 K2SiO3 | 1 | -1 KCl | 2 | 2 H_2O_3Si | 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 HCl | 2 | -2 | -1/2 (Δ[HCl])/(Δt) K2SiO3 | 1 | -1 | -(Δ[K2SiO3])/(Δt) KCl | 2 | 2 | 1/2 (Δ[KCl])/(Δt) H_2O_3Si | 1 | 1 | (Δ[H2O3Si])/(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 = -1/2 (Δ[HCl])/(Δt) = -(Δ[K2SiO3])/(Δt) = 1/2 (Δ[KCl])/(Δt) = (Δ[H2O3Si])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | K2SiO3 | potassium chloride | metasilicic acid formula | HCl | K2SiO3 | KCl | H_2O_3Si Hill formula | ClH | K2O3Si | ClK | H_2O_3Si name | hydrogen chloride | | potassium chloride | metasilicic acid IUPAC name | hydrogen chloride | | potassium chloride | dihydroxy-oxo-silane

| hydrogen chloride | K2SiO3 | potassium chloride | metasilicic acid molar mass | 36.46 g/mol | 154.28 g/mol | 74.55 g/mol | 78.098 g/mol phase | gas (at STP) | | solid (at STP) | solid (at STP) melting point | -114.17 °C | | 770 °C | 1704 °C boiling point | -85 °C | | 1420 °C | density | 0.00149 g/cm^3 (at 25 °C) | | 1.98 g/cm^3 | 1 g/cm^3 solubility in water | miscible | | soluble | odor | | | odorless |