CaCl2 + Na2HPO4 = NaCl + Ca3(PO4)2 + NaH2PO4

CaCl_2 calcium chloride + Na_2HPO_4 disodium hydrogen phosphate ⟶ NaCl sodium chloride + Ca_3(PO_4)_2 tricalcium diphosphate + NaH_2PO_4 sodium dihydrogen phosphate

Balance the chemical equation algebraically: CaCl_2 + Na_2HPO_4 ⟶ NaCl + Ca_3(PO_4)_2 + NaH_2PO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CaCl_2 + c_2 Na_2HPO_4 ⟶ c_3 NaCl + c_4 Ca_3(PO_4)_2 + c_5 NaH_2PO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for Ca, Cl, H, Na, O and P: Ca: | c_1 = 3 c_4 Cl: | 2 c_1 = c_3 H: | c_2 = 2 c_5 Na: | 2 c_2 = c_3 + c_5 O: | 4 c_2 = 8 c_4 + 4 c_5 P: | c_2 = 2 c_4 + c_5 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 = 4 c_3 = 6 c_4 = 1 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 CaCl_2 + 4 Na_2HPO_4 ⟶ 6 NaCl + Ca_3(PO_4)_2 + 2 NaH_2PO_4

+ ⟶ + +

calcium chloride + disodium hydrogen phosphate ⟶ sodium chloride + tricalcium diphosphate + sodium dihydrogen phosphate

Construct the equilibrium constant, K, expression for: CaCl_2 + Na_2HPO_4 ⟶ NaCl + Ca_3(PO_4)_2 + NaH_2PO_4 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 + 4 Na_2HPO_4 ⟶ 6 NaCl + Ca_3(PO_4)_2 + 2 NaH_2PO_4 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 Na_2HPO_4 | 4 | -4 NaCl | 6 | 6 Ca_3(PO_4)_2 | 1 | 1 NaH_2PO_4 | 2 | 2 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) Na_2HPO_4 | 4 | -4 | ([Na2HPO4])^(-4) NaCl | 6 | 6 | ([NaCl])^6 Ca_3(PO_4)_2 | 1 | 1 | [Ca3(PO4)2] NaH_2PO_4 | 2 | 2 | ([NaH2PO4])^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) ([Na2HPO4])^(-4) ([NaCl])^6 [Ca3(PO4)2] ([NaH2PO4])^2 = (([NaCl])^6 [Ca3(PO4)2] ([NaH2PO4])^2)/(([CaCl2])^3 ([Na2HPO4])^4)

Construct the rate of reaction expression for: CaCl_2 + Na_2HPO_4 ⟶ NaCl + Ca_3(PO_4)_2 + NaH_2PO_4 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 + 4 Na_2HPO_4 ⟶ 6 NaCl + Ca_3(PO_4)_2 + 2 NaH_2PO_4 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 Na_2HPO_4 | 4 | -4 NaCl | 6 | 6 Ca_3(PO_4)_2 | 1 | 1 NaH_2PO_4 | 2 | 2 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) Na_2HPO_4 | 4 | -4 | -1/4 (Δ[Na2HPO4])/(Δt) NaCl | 6 | 6 | 1/6 (Δ[NaCl])/(Δt) Ca_3(PO_4)_2 | 1 | 1 | (Δ[Ca3(PO4)2])/(Δt) NaH_2PO_4 | 2 | 2 | 1/2 (Δ[NaH2PO4])/(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) = -1/4 (Δ[Na2HPO4])/(Δt) = 1/6 (Δ[NaCl])/(Δt) = (Δ[Ca3(PO4)2])/(Δt) = 1/2 (Δ[NaH2PO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| calcium chloride | disodium hydrogen phosphate | sodium chloride | tricalcium diphosphate | sodium dihydrogen phosphate formula | CaCl_2 | Na_2HPO_4 | NaCl | Ca_3(PO_4)_2 | NaH_2PO_4 Hill formula | CaCl_2 | HNa_2O_4P | ClNa | Ca_3O_8P_2 | H_2NaO_4P name | calcium chloride | disodium hydrogen phosphate | sodium chloride | tricalcium diphosphate | sodium dihydrogen phosphate IUPAC name | calcium dichloride | disodium hydrogen phosphate | sodium chloride | tricalcium diphosphate | sodium dihydrogen phosphate

| calcium chloride | disodium hydrogen phosphate | sodium chloride | tricalcium diphosphate | sodium dihydrogen phosphate molar mass | 111 g/mol | 141.96 g/mol | 58.44 g/mol | 310.17 g/mol | 119.98 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | | melting point | 772 °C | 250 °C | 801 °C | | boiling point | | | 1413 °C | | density | 2.15 g/cm^3 | 1.53 g/cm^3 | 2.16 g/cm^3 | 3.14 g/cm^3 | 0.9996 g/cm^3 solubility in water | soluble | soluble | soluble | | odor | | | odorless | | odorless