CaCl2 + Na3PO4 = NaCl + Ca3(PO4)2

calcium chloride + trisodium phosphate ⟶ sodium chloride + tricalcium diphosphate

Balance the chemical equation algebraically: + ⟶ + Add stoichiometric coefficients, c_i, to the reactants and products: c_1 + c_2 ⟶ c_3 + c_4 Set the number of atoms in the reactants equal to the number of atoms in the products for Ca, Cl, Na, O and P: Ca: | c_1 = 3 c_4 Cl: | 2 c_1 = c_3 Na: | 3 c_2 = c_3 O: | 4 c_2 = 8 c_4 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 + 2 ⟶ 6 +

+ ⟶ +

calcium chloride + trisodium phosphate ⟶ sodium chloride + tricalcium diphosphate

| calcium chloride | trisodium phosphate | sodium chloride | tricalcium diphosphate Hill formula | CaCl_2 | Na_3O_4P | ClNa | Ca_3O_8P_2 name | calcium chloride | trisodium phosphate | sodium chloride | tricalcium diphosphate IUPAC name | calcium dichloride | trisodium phosphate | sodium chloride | tricalcium diphosphate

| calcium chloride | trisodium phosphate | sodium chloride | tricalcium diphosphate molar mass | 111 g/mol | 163.94 g/mol | 58.44 g/mol | 310.17 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | melting point | 772 °C | 75 °C | 801 °C | boiling point | | | 1413 °C | density | 2.15 g/cm^3 | 2.536 g/cm^3 | 2.16 g/cm^3 | 3.14 g/cm^3 solubility in water | soluble | soluble | soluble | odor | | odorless | odorless |

CaCl_2 calcium chloride + Na3Po4 ⟶ NaCl sodium chloride + Ca3(Po4)2

Balance the chemical equation algebraically: CaCl_2 + Na3Po4 ⟶ NaCl + Ca3(Po4)2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CaCl_2 + c_2 Na3Po4 ⟶ c_3 NaCl + c_4 Ca3(Po4)2 Set the number of atoms in the reactants equal to the number of atoms in the products for Ca, Cl, Na and Po: Ca: | c_1 = 3 c_4 Cl: | 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 CaCl_2 + 2 Na3Po4 ⟶ 6 NaCl + Ca3(Po4)2

+ Na3Po4 ⟶ + Ca3(Po4)2

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

Construct the equilibrium constant, K, expression for: CaCl_2 + Na3Po4 ⟶ NaCl + 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 CaCl_2 + 2 Na3Po4 ⟶ 6 NaCl + 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 CaCl_2 | 3 | -3 Na3Po4 | 2 | -2 NaCl | 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 CaCl_2 | 3 | -3 | ([CaCl2])^(-3) Na3Po4 | 2 | -2 | ([Na3Po4])^(-2) NaCl | 6 | 6 | ([NaCl])^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 = ([CaCl2])^(-3) ([Na3Po4])^(-2) ([NaCl])^6 [Ca3(Po4)2] = (([NaCl])^6 [Ca3(Po4)2])/(([CaCl2])^3 ([Na3Po4])^2)

Construct the rate of reaction expression for: CaCl_2 + Na3Po4 ⟶ NaCl + 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 CaCl_2 + 2 Na3Po4 ⟶ 6 NaCl + 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 CaCl_2 | 3 | -3 Na3Po4 | 2 | -2 NaCl | 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 CaCl_2 | 3 | -3 | -1/3 (Δ[CaCl2])/(Δt) Na3Po4 | 2 | -2 | -1/2 (Δ[Na3Po4])/(Δt) NaCl | 6 | 6 | 1/6 (Δ[NaCl])/(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[CaCl2])/(Δt) = -1/2 (Δ[Na3Po4])/(Δt) = 1/6 (Δ[NaCl])/(Δt) = (Δ[Ca3(Po4)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| calcium chloride | Na3Po4 | sodium chloride | Ca3(Po4)2 formula | CaCl_2 | Na3Po4 | NaCl | Ca3(Po4)2 Hill formula | CaCl_2 | Na3Po4 | ClNa | Ca3Po8 name | calcium chloride | | sodium chloride | IUPAC name | calcium dichloride | | sodium chloride |

| calcium chloride | Na3Po4 | sodium chloride | Ca3(Po4)2 molar mass | 111 g/mol | 905 g/mol | 58.44 g/mol | 1790 g/mol phase | solid (at STP) | | solid (at STP) | melting point | 772 °C | | 801 °C | boiling point | | | 1413 °C | density | 2.15 g/cm^3 | | 2.16 g/cm^3 | solubility in water | soluble | | soluble | odor | | | odorless |

CaCl_2 calcium chloride + Na3Po4 ⟶ NaCl sodium chloride + Ca3(Po4)2

Balance the chemical equation algebraically: CaCl_2 + Na3Po4 ⟶ NaCl + Ca3(Po4)2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CaCl_2 + c_2 Na3Po4 ⟶ c_3 NaCl + c_4 Ca3(Po4)2 Set the number of atoms in the reactants equal to the number of atoms in the products for Ca, Cl, Na and Po: Ca: | c_1 = 3 c_4 Cl: | 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 CaCl_2 + 2 Na3Po4 ⟶ 6 NaCl + Ca3(Po4)2

+ Na3Po4 ⟶ + Ca3(Po4)2

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

Construct the equilibrium constant, K, expression for: CaCl_2 + Na3Po4 ⟶ NaCl + 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 CaCl_2 + 2 Na3Po4 ⟶ 6 NaCl + 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 CaCl_2 | 3 | -3 Na3Po4 | 2 | -2 NaCl | 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 CaCl_2 | 3 | -3 | ([CaCl2])^(-3) Na3Po4 | 2 | -2 | ([Na3Po4])^(-2) NaCl | 6 | 6 | ([NaCl])^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 = ([CaCl2])^(-3) ([Na3Po4])^(-2) ([NaCl])^6 [Ca3(Po4)2] = (([NaCl])^6 [Ca3(Po4)2])/(([CaCl2])^3 ([Na3Po4])^2)

Construct the rate of reaction expression for: CaCl_2 + Na3Po4 ⟶ NaCl + 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 CaCl_2 + 2 Na3Po4 ⟶ 6 NaCl + 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 CaCl_2 | 3 | -3 Na3Po4 | 2 | -2 NaCl | 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 CaCl_2 | 3 | -3 | -1/3 (Δ[CaCl2])/(Δt) Na3Po4 | 2 | -2 | -1/2 (Δ[Na3Po4])/(Δt) NaCl | 6 | 6 | 1/6 (Δ[NaCl])/(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[CaCl2])/(Δt) = -1/2 (Δ[Na3Po4])/(Δt) = 1/6 (Δ[NaCl])/(Δt) = (Δ[Ca3(Po4)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| calcium chloride | Na3Po4 | sodium chloride | Ca3(Po4)2 formula | CaCl_2 | Na3Po4 | NaCl | Ca3(Po4)2 Hill formula | CaCl_2 | Na3Po4 | ClNa | Ca3Po8 name | calcium chloride | | sodium chloride | IUPAC name | calcium dichloride | | sodium chloride |

| calcium chloride | Na3Po4 | sodium chloride | Ca3(Po4)2 molar mass | 111 g/mol | 905 g/mol | 58.44 g/mol | 1790 g/mol phase | solid (at STP) | | solid (at STP) | melting point | 772 °C | | 801 °C | boiling point | | | 1413 °C | density | 2.15 g/cm^3 | | 2.16 g/cm^3 | solubility in water | soluble | | soluble | odor | | | odorless |