H2O + K2SiO3 = KOH + KHSiO3

H_2O water + K2SiO3 ⟶ KOH potassium hydroxide + KHSiO3

Balance the chemical equation algebraically: H_2O + K2SiO3 ⟶ KOH + KHSiO3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 K2SiO3 ⟶ c_3 KOH + c_4 KHSiO3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, K and Si: H: | 2 c_1 = c_3 + c_4 O: | c_1 + 3 c_2 = c_3 + 3 c_4 K: | 2 c_2 = c_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: | | H_2O + K2SiO3 ⟶ KOH + KHSiO3

+ K2SiO3 ⟶ + KHSiO3

water + K2SiO3 ⟶ potassium hydroxide + KHSiO3

Construct the equilibrium constant, K, expression for: H_2O + K2SiO3 ⟶ KOH + KHSiO3 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: H_2O + K2SiO3 ⟶ KOH + KHSiO3 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 H_2O | 1 | -1 K2SiO3 | 1 | -1 KOH | 1 | 1 KHSiO3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 1 | -1 | ([H2O])^(-1) K2SiO3 | 1 | -1 | ([K2SiO3])^(-1) KOH | 1 | 1 | [KOH] KHSiO3 | 1 | 1 | [KHSiO3] 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 = ([H2O])^(-1) ([K2SiO3])^(-1) [KOH] [KHSiO3] = ([KOH] [KHSiO3])/([H2O] [K2SiO3])

Construct the rate of reaction expression for: H_2O + K2SiO3 ⟶ KOH + KHSiO3 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: H_2O + K2SiO3 ⟶ KOH + KHSiO3 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 H_2O | 1 | -1 K2SiO3 | 1 | -1 KOH | 1 | 1 KHSiO3 | 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 H_2O | 1 | -1 | -(Δ[H2O])/(Δt) K2SiO3 | 1 | -1 | -(Δ[K2SiO3])/(Δt) KOH | 1 | 1 | (Δ[KOH])/(Δt) KHSiO3 | 1 | 1 | (Δ[KHSiO3])/(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[H2O])/(Δt) = -(Δ[K2SiO3])/(Δt) = (Δ[KOH])/(Δt) = (Δ[KHSiO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | K2SiO3 | potassium hydroxide | KHSiO3 formula | H_2O | K2SiO3 | KOH | KHSiO3 Hill formula | H_2O | K2O3Si | HKO | HKO3Si name | water | | potassium hydroxide |

| water | K2SiO3 | potassium hydroxide | KHSiO3 molar mass | 18.015 g/mol | 154.28 g/mol | 56.105 g/mol | 116.19 g/mol phase | liquid (at STP) | | solid (at STP) | melting point | 0 °C | | 406 °C | boiling point | 99.9839 °C | | 1327 °C | density | 1 g/cm^3 | | 2.044 g/cm^3 | solubility in water | | | soluble | surface tension | 0.0728 N/m | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | 0.001 Pa s (at 550 °C) | odor | odorless | | |