Ca(OH)2 + Na3PO4 = NaOH + Ca3(PO4)2

Ca(OH)_2 calcium hydroxide + Na_3PO_4 trisodium phosphate ⟶ NaOH sodium hydroxide + Ca_3(PO_4)_2 tricalcium diphosphate

Balance the chemical equation algebraically: Ca(OH)_2 + Na_3PO_4 ⟶ NaOH + Ca_3(PO_4)_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Ca(OH)_2 + c_2 Na_3PO_4 ⟶ c_3 NaOH + c_4 Ca_3(PO_4)_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Ca, H, O, Na and P: Ca: | c_1 = 3 c_4 H: | 2 c_1 = c_3 O: | 2 c_1 + 4 c_2 = c_3 + 8 c_4 Na: | 3 c_2 = c_3 P: | c_2 = 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 6 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 Ca(OH)_2 + 2 Na_3PO_4 ⟶ 6 NaOH + Ca_3(PO_4)_2

+ ⟶ +

calcium hydroxide + trisodium phosphate ⟶ sodium hydroxide + tricalcium diphosphate

Construct the equilibrium constant, K, expression for: Ca(OH)_2 + Na_3PO_4 ⟶ NaOH + Ca_3(PO_4)_2 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: 3 Ca(OH)_2 + 2 Na_3PO_4 ⟶ 6 NaOH + Ca_3(PO_4)_2 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 Ca(OH)_2 | 3 | -3 Na_3PO_4 | 2 | -2 NaOH | 6 | 6 Ca_3(PO_4)_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Ca(OH)_2 | 3 | -3 | ([Ca(OH)2])^(-3) Na_3PO_4 | 2 | -2 | ([Na3PO4])^(-2) NaOH | 6 | 6 | ([NaOH])^6 Ca_3(PO_4)_2 | 1 | 1 | [Ca3(PO4)2] 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 = ([Ca(OH)2])^(-3) ([Na3PO4])^(-2) ([NaOH])^6 [Ca3(PO4)2] = (([NaOH])^6 [Ca3(PO4)2])/(([Ca(OH)2])^3 ([Na3PO4])^2)

Construct the rate of reaction expression for: Ca(OH)_2 + Na_3PO_4 ⟶ NaOH + Ca_3(PO_4)_2 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: 3 Ca(OH)_2 + 2 Na_3PO_4 ⟶ 6 NaOH + Ca_3(PO_4)_2 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 Ca(OH)_2 | 3 | -3 Na_3PO_4 | 2 | -2 NaOH | 6 | 6 Ca_3(PO_4)_2 | 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 Ca(OH)_2 | 3 | -3 | -1/3 (Δ[Ca(OH)2])/(Δt) Na_3PO_4 | 2 | -2 | -1/2 (Δ[Na3PO4])/(Δt) NaOH | 6 | 6 | 1/6 (Δ[NaOH])/(Δt) Ca_3(PO_4)_2 | 1 | 1 | (Δ[Ca3(PO4)2])/(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 = -1/3 (Δ[Ca(OH)2])/(Δt) = -1/2 (Δ[Na3PO4])/(Δt) = 1/6 (Δ[NaOH])/(Δt) = (Δ[Ca3(PO4)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| calcium hydroxide | trisodium phosphate | sodium hydroxide | tricalcium diphosphate formula | Ca(OH)_2 | Na_3PO_4 | NaOH | Ca_3(PO_4)_2 Hill formula | CaH_2O_2 | Na_3O_4P | HNaO | Ca_3O_8P_2 name | calcium hydroxide | trisodium phosphate | sodium hydroxide | tricalcium diphosphate IUPAC name | calcium dihydroxide | trisodium phosphate | sodium hydroxide | tricalcium diphosphate

| calcium hydroxide | trisodium phosphate | sodium hydroxide | tricalcium diphosphate molar mass | 74.092 g/mol | 163.94 g/mol | 39.997 g/mol | 310.17 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | melting point | 550 °C | 75 °C | 323 °C | boiling point | | | 1390 °C | density | 2.24 g/cm^3 | 2.536 g/cm^3 | 2.13 g/cm^3 | 3.14 g/cm^3 solubility in water | slightly soluble | soluble | soluble | surface tension | | | 0.07435 N/m | dynamic viscosity | | | 0.004 Pa s (at 350 °C) | odor | odorless | odorless | |

Ca(OH)_2 calcium hydroxide + Na3Po4 ⟶ NaOH sodium hydroxide + Ca3(Po4)2

Balance the chemical equation algebraically: Ca(OH)_2 + Na3Po4 ⟶ NaOH + Ca3(Po4)2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Ca(OH)_2 + c_2 Na3Po4 ⟶ c_3 NaOH + c_4 Ca3(Po4)2 Set the number of atoms in the reactants equal to the number of atoms in the products for Ca, H, O, Na and Po: Ca: | c_1 = 3 c_4 H: | 2 c_1 = c_3 O: | 2 c_1 = c_3 Na: | 3 c_2 = c_3 Po: | 4 c_2 = 8 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 6 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 Ca(OH)_2 + 2 Na3Po4 ⟶ 6 NaOH + Ca3(Po4)2

+ Na3Po4 ⟶ + Ca3(Po4)2

calcium hydroxide + Na3Po4 ⟶ sodium hydroxide + Ca3(Po4)2

Construct the equilibrium constant, K, expression for: Ca(OH)_2 + Na3Po4 ⟶ NaOH + Ca3(Po4)2 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: 3 Ca(OH)_2 + 2 Na3Po4 ⟶ 6 NaOH + Ca3(Po4)2 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 Ca(OH)_2 | 3 | -3 Na3Po4 | 2 | -2 NaOH | 6 | 6 Ca3(Po4)2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Ca(OH)_2 | 3 | -3 | ([Ca(OH)2])^(-3) Na3Po4 | 2 | -2 | ([Na3Po4])^(-2) NaOH | 6 | 6 | ([NaOH])^6 Ca3(Po4)2 | 1 | 1 | [Ca3(Po4)2] 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 = ([Ca(OH)2])^(-3) ([Na3Po4])^(-2) ([NaOH])^6 [Ca3(Po4)2] = (([NaOH])^6 [Ca3(Po4)2])/(([Ca(OH)2])^3 ([Na3Po4])^2)

Construct the rate of reaction expression for: Ca(OH)_2 + Na3Po4 ⟶ NaOH + Ca3(Po4)2 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: 3 Ca(OH)_2 + 2 Na3Po4 ⟶ 6 NaOH + Ca3(Po4)2 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 Ca(OH)_2 | 3 | -3 Na3Po4 | 2 | -2 NaOH | 6 | 6 Ca3(Po4)2 | 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 Ca(OH)_2 | 3 | -3 | -1/3 (Δ[Ca(OH)2])/(Δt) Na3Po4 | 2 | -2 | -1/2 (Δ[Na3Po4])/(Δt) NaOH | 6 | 6 | 1/6 (Δ[NaOH])/(Δt) Ca3(Po4)2 | 1 | 1 | (Δ[Ca3(Po4)2])/(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 = -1/3 (Δ[Ca(OH)2])/(Δt) = -1/2 (Δ[Na3Po4])/(Δt) = 1/6 (Δ[NaOH])/(Δt) = (Δ[Ca3(Po4)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| calcium hydroxide | Na3Po4 | sodium hydroxide | Ca3(Po4)2 formula | Ca(OH)_2 | Na3Po4 | NaOH | Ca3(Po4)2 Hill formula | CaH_2O_2 | Na3Po4 | HNaO | Ca3Po8 name | calcium hydroxide | | sodium hydroxide | IUPAC name | calcium dihydroxide | | sodium hydroxide |

| calcium hydroxide | Na3Po4 | sodium hydroxide | Ca3(Po4)2 molar mass | 74.092 g/mol | 905 g/mol | 39.997 g/mol | 1790 g/mol phase | solid (at STP) | | solid (at STP) | melting point | 550 °C | | 323 °C | boiling point | | | 1390 °C | density | 2.24 g/cm^3 | | 2.13 g/cm^3 | solubility in water | slightly soluble | | soluble | surface tension | | | 0.07435 N/m | dynamic viscosity | | | 0.004 Pa s (at 350 °C) | odor | odorless | | |

Ca(OH)_2 calcium hydroxide + Na3Po4 ⟶ NaOH sodium hydroxide + Ca3(Po4)2

Balance the chemical equation algebraically: Ca(OH)_2 + Na3Po4 ⟶ NaOH + Ca3(Po4)2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Ca(OH)_2 + c_2 Na3Po4 ⟶ c_3 NaOH + c_4 Ca3(Po4)2 Set the number of atoms in the reactants equal to the number of atoms in the products for Ca, H, O, Na and Po: Ca: | c_1 = 3 c_4 H: | 2 c_1 = c_3 O: | 2 c_1 = c_3 Na: | 3 c_2 = c_3 Po: | 4 c_2 = 8 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 6 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 Ca(OH)_2 + 2 Na3Po4 ⟶ 6 NaOH + Ca3(Po4)2

+ Na3Po4 ⟶ + Ca3(Po4)2

calcium hydroxide + Na3Po4 ⟶ sodium hydroxide + Ca3(Po4)2

Construct the equilibrium constant, K, expression for: Ca(OH)_2 + Na3Po4 ⟶ NaOH + Ca3(Po4)2 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: 3 Ca(OH)_2 + 2 Na3Po4 ⟶ 6 NaOH + Ca3(Po4)2 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 Ca(OH)_2 | 3 | -3 Na3Po4 | 2 | -2 NaOH | 6 | 6 Ca3(Po4)2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Ca(OH)_2 | 3 | -3 | ([Ca(OH)2])^(-3) Na3Po4 | 2 | -2 | ([Na3Po4])^(-2) NaOH | 6 | 6 | ([NaOH])^6 Ca3(Po4)2 | 1 | 1 | [Ca3(Po4)2] 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 = ([Ca(OH)2])^(-3) ([Na3Po4])^(-2) ([NaOH])^6 [Ca3(Po4)2] = (([NaOH])^6 [Ca3(Po4)2])/(([Ca(OH)2])^3 ([Na3Po4])^2)

Construct the rate of reaction expression for: Ca(OH)_2 + Na3Po4 ⟶ NaOH + Ca3(Po4)2 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: 3 Ca(OH)_2 + 2 Na3Po4 ⟶ 6 NaOH + Ca3(Po4)2 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 Ca(OH)_2 | 3 | -3 Na3Po4 | 2 | -2 NaOH | 6 | 6 Ca3(Po4)2 | 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 Ca(OH)_2 | 3 | -3 | -1/3 (Δ[Ca(OH)2])/(Δt) Na3Po4 | 2 | -2 | -1/2 (Δ[Na3Po4])/(Δt) NaOH | 6 | 6 | 1/6 (Δ[NaOH])/(Δt) Ca3(Po4)2 | 1 | 1 | (Δ[Ca3(Po4)2])/(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 = -1/3 (Δ[Ca(OH)2])/(Δt) = -1/2 (Δ[Na3Po4])/(Δt) = 1/6 (Δ[NaOH])/(Δt) = (Δ[Ca3(Po4)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| calcium hydroxide | Na3Po4 | sodium hydroxide | Ca3(Po4)2 formula | Ca(OH)_2 | Na3Po4 | NaOH | Ca3(Po4)2 Hill formula | CaH_2O_2 | Na3Po4 | HNaO | Ca3Po8 name | calcium hydroxide | | sodium hydroxide | IUPAC name | calcium dihydroxide | | sodium hydroxide |

| calcium hydroxide | Na3Po4 | sodium hydroxide | Ca3(Po4)2 molar mass | 74.092 g/mol | 905 g/mol | 39.997 g/mol | 1790 g/mol phase | solid (at STP) | | solid (at STP) | melting point | 550 °C | | 323 °C | boiling point | | | 1390 °C | density | 2.24 g/cm^3 | | 2.13 g/cm^3 | solubility in water | slightly soluble | | soluble | surface tension | | | 0.07435 N/m | dynamic viscosity | | | 0.004 Pa s (at 350 °C) | odor | odorless | | |