H2O + NH4Cl + Na2SiO3 = NaCl + NH4OH + H2SiO3

H_2O water + NH_4Cl ammonium chloride + Na_2SiO_3 sodium metasilicate ⟶ NaCl sodium chloride + NH_4OH ammonium hydroxide + H_2O_3Si metasilicic acid

Balance the chemical equation algebraically: H_2O + NH_4Cl + Na_2SiO_3 ⟶ NaCl + NH_4OH + H_2O_3Si Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 NH_4Cl + c_3 Na_2SiO_3 ⟶ c_4 NaCl + c_5 NH_4OH + c_6 H_2O_3Si Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Cl, N, Na and Si: H: | 2 c_1 + 4 c_2 = 5 c_5 + 2 c_6 O: | c_1 + 3 c_3 = c_5 + 3 c_6 Cl: | c_2 = c_4 N: | c_2 = c_5 Na: | 2 c_3 = c_4 Si: | c_3 = c_6 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 2 c_3 = 1 c_4 = 2 c_5 = 2 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2O + 2 NH_4Cl + Na_2SiO_3 ⟶ 2 NaCl + 2 NH_4OH + H_2O_3Si

+ + ⟶ + +

water + ammonium chloride + sodium metasilicate ⟶ sodium chloride + ammonium hydroxide + metasilicic acid

Construct the equilibrium constant, K, expression for: H_2O + NH_4Cl + Na_2SiO_3 ⟶ NaCl + NH_4OH + 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_2O + 2 NH_4Cl + Na_2SiO_3 ⟶ 2 NaCl + 2 NH_4OH + 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_2O | 2 | -2 NH_4Cl | 2 | -2 Na_2SiO_3 | 1 | -1 NaCl | 2 | 2 NH_4OH | 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 H_2O | 2 | -2 | ([H2O])^(-2) NH_4Cl | 2 | -2 | ([NH4Cl])^(-2) Na_2SiO_3 | 1 | -1 | ([Na2SiO3])^(-1) NaCl | 2 | 2 | ([NaCl])^2 NH_4OH | 2 | 2 | ([NH4OH])^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 = ([H2O])^(-2) ([NH4Cl])^(-2) ([Na2SiO3])^(-1) ([NaCl])^2 ([NH4OH])^2 [H2O3Si] = (([NaCl])^2 ([NH4OH])^2 [H2O3Si])/(([H2O])^2 ([NH4Cl])^2 [Na2SiO3])

Construct the rate of reaction expression for: H_2O + NH_4Cl + Na_2SiO_3 ⟶ NaCl + NH_4OH + 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_2O + 2 NH_4Cl + Na_2SiO_3 ⟶ 2 NaCl + 2 NH_4OH + 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_2O | 2 | -2 NH_4Cl | 2 | -2 Na_2SiO_3 | 1 | -1 NaCl | 2 | 2 NH_4OH | 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 H_2O | 2 | -2 | -1/2 (Δ[H2O])/(Δt) NH_4Cl | 2 | -2 | -1/2 (Δ[NH4Cl])/(Δt) Na_2SiO_3 | 1 | -1 | -(Δ[Na2SiO3])/(Δt) NaCl | 2 | 2 | 1/2 (Δ[NaCl])/(Δt) NH_4OH | 2 | 2 | 1/2 (Δ[NH4OH])/(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[H2O])/(Δt) = -1/2 (Δ[NH4Cl])/(Δt) = -(Δ[Na2SiO3])/(Δt) = 1/2 (Δ[NaCl])/(Δt) = 1/2 (Δ[NH4OH])/(Δt) = (Δ[H2O3Si])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | ammonium chloride | sodium metasilicate | sodium chloride | ammonium hydroxide | metasilicic acid formula | H_2O | NH_4Cl | Na_2SiO_3 | NaCl | NH_4OH | H_2O_3Si Hill formula | H_2O | ClH_4N | Na_2O_3Si | ClNa | H_5NO | H_2O_3Si name | water | ammonium chloride | sodium metasilicate | sodium chloride | ammonium hydroxide | metasilicic acid IUPAC name | water | ammonium chloride | disodium dioxido-oxosilane | sodium chloride | ammonium hydroxide | dihydroxy-oxo-silane

| water | ammonium chloride | sodium metasilicate | sodium chloride | ammonium hydroxide | metasilicic acid molar mass | 18.015 g/mol | 53.49 g/mol | 122.06 g/mol | 58.44 g/mol | 35.046 g/mol | 78.098 g/mol phase | liquid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) | aqueous (at STP) | solid (at STP) melting point | 0 °C | 340 °C | 72.2 °C | 801 °C | -57.5 °C | 1704 °C boiling point | 99.9839 °C | | | 1413 °C | 36 °C | density | 1 g/cm^3 | 1.5256 g/cm^3 | 1.749 g/cm^3 | 2.16 g/cm^3 | 0.9 g/cm^3 | 1 g/cm^3 solubility in water | | soluble | soluble | soluble | very soluble | surface tension | 0.0728 N/m | | | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | 1 Pa s (at 1088 °C) | | | odor | odorless | | | odorless | |