Na3PO4 + CaBr2 = NaBr + Ca3(PO4)2

Na_3PO_4 trisodium phosphate + CaBr_2 calcium bromide ⟶ NaBr sodium bromide + Ca_3(PO_4)_2 tricalcium diphosphate

Balance the chemical equation algebraically: Na_3PO_4 + CaBr_2 ⟶ NaBr + Ca_3(PO_4)_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Na_3PO_4 + c_2 CaBr_2 ⟶ c_3 NaBr + 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 Na, O, P, Br and Ca: Na: | 3 c_1 = c_3 O: | 4 c_1 = 8 c_4 P: | c_1 = 2 c_4 Br: | 2 c_2 = c_3 Ca: | c_2 = 3 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 = 2 c_2 = 3 c_3 = 6 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 Na_3PO_4 + 3 CaBr_2 ⟶ 6 NaBr + Ca_3(PO_4)_2

+ ⟶ +

trisodium phosphate + calcium bromide ⟶ sodium bromide + tricalcium diphosphate

Construct the equilibrium constant, K, expression for: Na_3PO_4 + CaBr_2 ⟶ NaBr + 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 Na_3PO_4 + 3 CaBr_2 ⟶ 6 NaBr + 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 Na_3PO_4 | 2 | -2 CaBr_2 | 3 | -3 NaBr | 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 Na_3PO_4 | 2 | -2 | ([Na3PO4])^(-2) CaBr_2 | 3 | -3 | ([CaBr2])^(-3) NaBr | 6 | 6 | ([NaBr])^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 = ([Na3PO4])^(-2) ([CaBr2])^(-3) ([NaBr])^6 [Ca3(PO4)2] = (([NaBr])^6 [Ca3(PO4)2])/(([Na3PO4])^2 ([CaBr2])^3)

Construct the rate of reaction expression for: Na_3PO_4 + CaBr_2 ⟶ NaBr + 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 Na_3PO_4 + 3 CaBr_2 ⟶ 6 NaBr + 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 Na_3PO_4 | 2 | -2 CaBr_2 | 3 | -3 NaBr | 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 Na_3PO_4 | 2 | -2 | -1/2 (Δ[Na3PO4])/(Δt) CaBr_2 | 3 | -3 | -1/3 (Δ[CaBr2])/(Δt) NaBr | 6 | 6 | 1/6 (Δ[NaBr])/(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[Na3PO4])/(Δt) = -1/3 (Δ[CaBr2])/(Δt) = 1/6 (Δ[NaBr])/(Δt) = (Δ[Ca3(PO4)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| trisodium phosphate | calcium bromide | sodium bromide | tricalcium diphosphate formula | Na_3PO_4 | CaBr_2 | NaBr | Ca_3(PO_4)_2 Hill formula | Na_3O_4P | Br_2Ca | BrNa | Ca_3O_8P_2 name | trisodium phosphate | calcium bromide | sodium bromide | tricalcium diphosphate IUPAC name | trisodium phosphate | calcium dibromide | sodium bromide | tricalcium diphosphate