H2O + Na2SiO3 = NaOH + NaHSiO3

H_2O water + Na_2SiO_3 sodium metasilicate ⟶ NaOH sodium hydroxide + NaHSiO3

Balance the chemical equation algebraically: H_2O + Na_2SiO_3 ⟶ NaOH + NaHSiO3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 Na_2SiO_3 ⟶ c_3 NaOH + c_4 NaHSiO3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Na and Si: H: | 2 c_1 = c_3 + c_4 O: | c_1 + 3 c_2 = c_3 + 3 c_4 Na: | 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 + Na_2SiO_3 ⟶ NaOH + NaHSiO3

+ ⟶ + NaHSiO3

water + sodium metasilicate ⟶ sodium hydroxide + NaHSiO3

Construct the equilibrium constant, K, expression for: H_2O + Na_2SiO_3 ⟶ NaOH + NaHSiO3 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 + Na_2SiO_3 ⟶ NaOH + NaHSiO3 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 Na_2SiO_3 | 1 | -1 NaOH | 1 | 1 NaHSiO3 | 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) Na_2SiO_3 | 1 | -1 | ([Na2SiO3])^(-1) NaOH | 1 | 1 | [NaOH] NaHSiO3 | 1 | 1 | [NaHSiO3] 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) ([Na2SiO3])^(-1) [NaOH] [NaHSiO3] = ([NaOH] [NaHSiO3])/([H2O] [Na2SiO3])

Construct the rate of reaction expression for: H_2O + Na_2SiO_3 ⟶ NaOH + NaHSiO3 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 + Na_2SiO_3 ⟶ NaOH + NaHSiO3 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 Na_2SiO_3 | 1 | -1 NaOH | 1 | 1 NaHSiO3 | 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) Na_2SiO_3 | 1 | -1 | -(Δ[Na2SiO3])/(Δt) NaOH | 1 | 1 | (Δ[NaOH])/(Δt) NaHSiO3 | 1 | 1 | (Δ[NaHSiO3])/(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[Na2SiO3])/(Δt) = (Δ[NaOH])/(Δt) = (Δ[NaHSiO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | sodium metasilicate | sodium hydroxide | NaHSiO3 formula | H_2O | Na_2SiO_3 | NaOH | NaHSiO3 Hill formula | H_2O | Na_2O_3Si | HNaO | HNaO3Si name | water | sodium metasilicate | sodium hydroxide | IUPAC name | water | disodium dioxido-oxosilane | sodium hydroxide |

| water | sodium metasilicate | sodium hydroxide | NaHSiO3 molar mass | 18.015 g/mol | 122.06 g/mol | 39.997 g/mol | 100.08 g/mol phase | liquid (at STP) | solid (at STP) | solid (at STP) | melting point | 0 °C | 72.2 °C | 323 °C | boiling point | 99.9839 °C | | 1390 °C | density | 1 g/cm^3 | 1.749 g/cm^3 | 2.13 g/cm^3 | solubility in water | | soluble | soluble | surface tension | 0.0728 N/m | | 0.07435 N/m | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | 1 Pa s (at 1088 °C) | 0.004 Pa s (at 350 °C) | odor | odorless | | |