K + H2SiO3 = H2 + K2SiO3

K potassium + H_2O_3Si metasilicic acid ⟶ H_2 hydrogen + K2SiO3

Balance the chemical equation algebraically: K + H_2O_3Si ⟶ H_2 + K2SiO3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 K + c_2 H_2O_3Si ⟶ c_3 H_2 + c_4 K2SiO3 Set the number of atoms in the reactants equal to the number of atoms in the products for K, H, O and Si: K: | c_1 = 2 c_4 H: | 2 c_2 = 2 c_3 O: | 3 c_2 = 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 K + H_2O_3Si ⟶ H_2 + K2SiO3

+ ⟶ + K2SiO3

potassium + metasilicic acid ⟶ hydrogen + K2SiO3

Construct the equilibrium constant, K, expression for: K + H_2O_3Si ⟶ H_2 + 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: 2 K + H_2O_3Si ⟶ H_2 + 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 K | 2 | -2 H_2O_3Si | 1 | -1 H_2 | 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 K | 2 | -2 | ([K])^(-2) H_2O_3Si | 1 | -1 | ([H2O3Si])^(-1) H_2 | 1 | 1 | [H2] 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 = ([K])^(-2) ([H2O3Si])^(-1) [H2] [K2SiO3] = ([H2] [K2SiO3])/(([K])^2 [H2O3Si])

Construct the rate of reaction expression for: K + H_2O_3Si ⟶ H_2 + 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: 2 K + H_2O_3Si ⟶ H_2 + 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 K | 2 | -2 H_2O_3Si | 1 | -1 H_2 | 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 K | 2 | -2 | -1/2 (Δ[K])/(Δt) H_2O_3Si | 1 | -1 | -(Δ[H2O3Si])/(Δt) H_2 | 1 | 1 | (Δ[H2])/(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 = -1/2 (Δ[K])/(Δt) = -(Δ[H2O3Si])/(Δt) = (Δ[H2])/(Δt) = (Δ[K2SiO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium | metasilicic acid | hydrogen | K2SiO3 formula | K | H_2O_3Si | H_2 | K2SiO3 Hill formula | K | H_2O_3Si | H_2 | K2O3Si name | potassium | metasilicic acid | hydrogen | IUPAC name | potassium | dihydroxy-oxo-silane | molecular hydrogen |

| potassium | metasilicic acid | hydrogen | K2SiO3 molar mass | 39.0983 g/mol | 78.098 g/mol | 2.016 g/mol | 154.28 g/mol phase | solid (at STP) | solid (at STP) | gas (at STP) | melting point | 64 °C | 1704 °C | -259.2 °C | boiling point | 760 °C | | -252.8 °C | density | 0.86 g/cm^3 | 1 g/cm^3 | 8.99×10^-5 g/cm^3 (at 0 °C) | solubility in water | reacts | | | dynamic viscosity | | | 8.9×10^-6 Pa s (at 25 °C) | odor | | | odorless |