H3PO4 + Na2SiO3 = Na3PO4 + H2SiO3

H_3PO_4 phosphoric acid + Na_2SiO_3 sodium metasilicate ⟶ Na_3PO_4 trisodium phosphate + H_2O_3Si metasilicic acid

Balance the chemical equation algebraically: H_3PO_4 + Na_2SiO_3 ⟶ Na_3PO_4 + H_2O_3Si Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_3PO_4 + c_2 Na_2SiO_3 ⟶ c_3 Na_3PO_4 + c_4 H_2O_3Si Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, P, Na and Si: H: | 3 c_1 = 2 c_4 O: | 4 c_1 + 3 c_2 = 4 c_3 + 3 c_4 P: | c_1 = c_3 Na: | 2 c_2 = 3 c_3 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 = 3/2 c_3 = 1 c_4 = 3/2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 2 c_2 = 3 c_3 = 2 c_4 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_3PO_4 + 3 Na_2SiO_3 ⟶ 2 Na_3PO_4 + 3 H_2O_3Si

+ ⟶ +

phosphoric acid + sodium metasilicate ⟶ trisodium phosphate + metasilicic acid

Construct the equilibrium constant, K, expression for: H_3PO_4 + Na_2SiO_3 ⟶ Na_3PO_4 + 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 H_3PO_4 + 3 Na_2SiO_3 ⟶ 2 Na_3PO_4 + 3 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 H_3PO_4 | 2 | -2 Na_2SiO_3 | 3 | -3 Na_3PO_4 | 2 | 2 H_2O_3Si | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_3PO_4 | 2 | -2 | ([H3PO4])^(-2) Na_2SiO_3 | 3 | -3 | ([Na2SiO3])^(-3) Na_3PO_4 | 2 | 2 | ([Na3PO4])^2 H_2O_3Si | 3 | 3 | ([H2O3Si])^3 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 = ([H3PO4])^(-2) ([Na2SiO3])^(-3) ([Na3PO4])^2 ([H2O3Si])^3 = (([Na3PO4])^2 ([H2O3Si])^3)/(([H3PO4])^2 ([Na2SiO3])^3)

Construct the rate of reaction expression for: H_3PO_4 + Na_2SiO_3 ⟶ Na_3PO_4 + 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 H_3PO_4 + 3 Na_2SiO_3 ⟶ 2 Na_3PO_4 + 3 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 H_3PO_4 | 2 | -2 Na_2SiO_3 | 3 | -3 Na_3PO_4 | 2 | 2 H_2O_3Si | 3 | 3 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_3PO_4 | 2 | -2 | -1/2 (Δ[H3PO4])/(Δt) Na_2SiO_3 | 3 | -3 | -1/3 (Δ[Na2SiO3])/(Δt) Na_3PO_4 | 2 | 2 | 1/2 (Δ[Na3PO4])/(Δt) H_2O_3Si | 3 | 3 | 1/3 (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[H3PO4])/(Δt) = -1/3 (Δ[Na2SiO3])/(Δt) = 1/2 (Δ[Na3PO4])/(Δt) = 1/3 (Δ[H2O3Si])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| phosphoric acid | sodium metasilicate | trisodium phosphate | metasilicic acid formula | H_3PO_4 | Na_2SiO_3 | Na_3PO_4 | H_2O_3Si Hill formula | H_3O_4P | Na_2O_3Si | Na_3O_4P | H_2O_3Si name | phosphoric acid | sodium metasilicate | trisodium phosphate | metasilicic acid IUPAC name | phosphoric acid | disodium dioxido-oxosilane | trisodium phosphate | dihydroxy-oxo-silane

| phosphoric acid | sodium metasilicate | trisodium phosphate | metasilicic acid molar mass | 97.994 g/mol | 122.06 g/mol | 163.94 g/mol | 78.098 g/mol phase | liquid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 42.4 °C | 72.2 °C | 75 °C | 1704 °C boiling point | 158 °C | | | density | 1.685 g/cm^3 | 1.749 g/cm^3 | 2.536 g/cm^3 | 1 g/cm^3 solubility in water | very soluble | soluble | soluble | dynamic viscosity | | 1 Pa s (at 1088 °C) | | odor | odorless | | odorless |