CaCl2 + NaPO4 = NaCl + Ca(PO4)2

CaCl_2 calcium chloride + NaPO4 ⟶ NaCl sodium chloride + Ca(PO4)2

Balance the chemical equation algebraically: CaCl_2 + NaPO4 ⟶ NaCl + Ca(PO4)2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CaCl_2 + c_2 NaPO4 ⟶ c_3 NaCl + c_4 Ca(PO4)2 Set the number of atoms in the reactants equal to the number of atoms in the products for Ca, Cl, Na, P and O: Ca: | c_1 = c_4 Cl: | 2 c_1 = c_3 Na: | c_2 = c_3 P: | c_2 = 2 c_4 O: | 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 2 c_3 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | CaCl_2 + 2 NaPO4 ⟶ 2 NaCl + Ca(PO4)2

+ NaPO4 ⟶ + Ca(PO4)2

calcium chloride + NaPO4 ⟶ sodium chloride + Ca(PO4)2

Construct the equilibrium constant, K, expression for: CaCl_2 + NaPO4 ⟶ NaCl + Ca(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: CaCl_2 + 2 NaPO4 ⟶ 2 NaCl + Ca(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 | 1 | -1 NaPO4 | 2 | -2 NaCl | 2 | 2 Ca(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 | 1 | -1 | ([CaCl2])^(-1) NaPO4 | 2 | -2 | ([NaPO4])^(-2) NaCl | 2 | 2 | ([NaCl])^2 Ca(PO4)2 | 1 | 1 | [Ca(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])^(-1) ([NaPO4])^(-2) ([NaCl])^2 [Ca(PO4)2] = (([NaCl])^2 [Ca(PO4)2])/([CaCl2] ([NaPO4])^2)

Construct the rate of reaction expression for: CaCl_2 + NaPO4 ⟶ NaCl + Ca(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: CaCl_2 + 2 NaPO4 ⟶ 2 NaCl + Ca(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 | 1 | -1 NaPO4 | 2 | -2 NaCl | 2 | 2 Ca(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 | 1 | -1 | -(Δ[CaCl2])/(Δt) NaPO4 | 2 | -2 | -1/2 (Δ[NaPO4])/(Δt) NaCl | 2 | 2 | 1/2 (Δ[NaCl])/(Δt) Ca(PO4)2 | 1 | 1 | (Δ[Ca(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 = -(Δ[CaCl2])/(Δt) = -1/2 (Δ[NaPO4])/(Δt) = 1/2 (Δ[NaCl])/(Δt) = (Δ[Ca(PO4)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| calcium chloride | NaPO4 | sodium chloride | Ca(PO4)2 formula | CaCl_2 | NaPO4 | NaCl | Ca(PO4)2 Hill formula | CaCl_2 | NaO4P | ClNa | CaO8P2 name | calcium chloride | | sodium chloride | IUPAC name | calcium dichloride | | sodium chloride |

| calcium chloride | NaPO4 | sodium chloride | Ca(PO4)2 molar mass | 111 g/mol | 117.96 g/mol | 58.44 g/mol | 230.02 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 |