Ca(OH)2 + Ca(H2PO4)2 = H2O + Ca3(PO4)2

Ca(OH)_2 calcium hydroxide + Ca(H_2PO_4)_2·H_2O calcium dihydrogen phosphate monohydrate ⟶ H_2O water + Ca_3(PO_4)_2 tricalcium diphosphate

Balance the chemical equation algebraically: Ca(OH)_2 + Ca(H_2PO_4)_2·H_2O ⟶ H_2O + Ca_3(PO_4)_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Ca(OH)_2 + c_2 Ca(H_2PO_4)_2·H_2O ⟶ c_3 H_2O + 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 and P: Ca: | c_1 + c_2 = 3 c_4 H: | 2 c_1 + 4 c_2 = 2 c_3 O: | 2 c_1 + 8 c_2 = c_3 + 8 c_4 P: | 2 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 4 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 Ca(OH)_2 + Ca(H_2PO_4)_2·H_2O ⟶ 4 H_2O + Ca_3(PO_4)_2

+ ⟶ +

calcium hydroxide + calcium dihydrogen phosphate monohydrate ⟶ water + tricalcium diphosphate

Construct the equilibrium constant, K, expression for: Ca(OH)_2 + Ca(H_2PO_4)_2·H_2O ⟶ H_2O + 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: 2 Ca(OH)_2 + Ca(H_2PO_4)_2·H_2O ⟶ 4 H_2O + 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 | 2 | -2 Ca(H_2PO_4)_2·H_2O | 1 | -1 H_2O | 4 | 4 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 | 2 | -2 | ([Ca(OH)2])^(-2) Ca(H_2PO_4)_2·H_2O | 1 | -1 | ([Ca(H2PO4)2·H2O])^(-1) H_2O | 4 | 4 | ([H2O])^4 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])^(-2) ([Ca(H2PO4)2·H2O])^(-1) ([H2O])^4 [Ca3(PO4)2] = (([H2O])^4 [Ca3(PO4)2])/(([Ca(OH)2])^2 [Ca(H2PO4)2·H2O])

Construct the rate of reaction expression for: Ca(OH)_2 + Ca(H_2PO_4)_2·H_2O ⟶ H_2O + 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: 2 Ca(OH)_2 + Ca(H_2PO_4)_2·H_2O ⟶ 4 H_2O + 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 | 2 | -2 Ca(H_2PO_4)_2·H_2O | 1 | -1 H_2O | 4 | 4 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 | 2 | -2 | -1/2 (Δ[Ca(OH)2])/(Δt) Ca(H_2PO_4)_2·H_2O | 1 | -1 | -(Δ[Ca(H2PO4)2·H2O])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(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 = -1/2 (Δ[Ca(OH)2])/(Δt) = -(Δ[Ca(H2PO4)2·H2O])/(Δt) = 1/4 (Δ[H2O])/(Δt) = (Δ[Ca3(PO4)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| calcium hydroxide | calcium dihydrogen phosphate monohydrate | water | tricalcium diphosphate formula | Ca(OH)_2 | Ca(H_2PO_4)_2·H_2O | H_2O | Ca_3(PO_4)_2 Hill formula | CaH_2O_2 | CaH_4O_8P_2 | H_2O | Ca_3O_8P_2 name | calcium hydroxide | calcium dihydrogen phosphate monohydrate | water | tricalcium diphosphate IUPAC name | calcium dihydroxide | calcium dihydrogen phosphate | water | tricalcium diphosphate

| calcium hydroxide | calcium dihydrogen phosphate monohydrate | water | tricalcium diphosphate molar mass | 74.092 g/mol | 234.05 g/mol | 18.015 g/mol | 310.17 g/mol phase | solid (at STP) | | liquid (at STP) | melting point | 550 °C | | 0 °C | boiling point | | | 99.9839 °C | density | 2.24 g/cm^3 | 2.22 g/cm^3 | 1 g/cm^3 | 3.14 g/cm^3 solubility in water | slightly soluble | soluble | | surface tension | | | 0.0728 N/m | dynamic viscosity | | | 8.9×10^-4 Pa s (at 25 °C) | odor | odorless | | odorless |