H3PO4 + Na3PO4 = NaH2PO4

H_3PO_4 phosphoric acid + Na_3PO_4 trisodium phosphate ⟶ NaH_2PO_4 sodium dihydrogen phosphate

Balance the chemical equation algebraically: H_3PO_4 + Na_3PO_4 ⟶ NaH_2PO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_3PO_4 + c_2 Na_3PO_4 ⟶ c_3 NaH_2PO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, P and Na: H: | 3 c_1 = 2 c_3 O: | 4 c_1 + 4 c_2 = 4 c_3 P: | c_1 + c_2 = c_3 Na: | 3 c_2 = c_3 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 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_3PO_4 + Na_3PO_4 ⟶ 3 NaH_2PO_4

+ ⟶

phosphoric acid + trisodium phosphate ⟶ sodium dihydrogen phosphate

Construct the equilibrium constant, K, expression for: H_3PO_4 + Na_3PO_4 ⟶ 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: 2 H_3PO_4 + Na_3PO_4 ⟶ 3 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 H_3PO_4 | 2 | -2 Na_3PO_4 | 1 | -1 NaH_2PO_4 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_3PO_4 | 2 | -2 | ([H3PO4])^(-2) Na_3PO_4 | 1 | -1 | ([Na3PO4])^(-1) NaH_2PO_4 | 3 | 3 | ([NaH2PO4])^3 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 = ([H3PO4])^(-2) ([Na3PO4])^(-1) ([NaH2PO4])^3 = ([NaH2PO4])^3/(([H3PO4])^2 [Na3PO4])

Construct the rate of reaction expression for: H_3PO_4 + Na_3PO_4 ⟶ 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: 2 H_3PO_4 + Na_3PO_4 ⟶ 3 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 H_3PO_4 | 2 | -2 Na_3PO_4 | 1 | -1 NaH_2PO_4 | 3 | 3 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 H_3PO_4 | 2 | -2 | -1/2 (Δ[H3PO4])/(Δt) Na_3PO_4 | 1 | -1 | -(Δ[Na3PO4])/(Δt) NaH_2PO_4 | 3 | 3 | 1/3 (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 = -1/2 (Δ[H3PO4])/(Δt) = -(Δ[Na3PO4])/(Δt) = 1/3 (Δ[NaH2PO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| phosphoric acid | trisodium phosphate | sodium dihydrogen phosphate formula | H_3PO_4 | Na_3PO_4 | NaH_2PO_4 Hill formula | H_3O_4P | Na_3O_4P | H_2NaO_4P name | phosphoric acid | trisodium phosphate | sodium dihydrogen phosphate

| phosphoric acid | trisodium phosphate | sodium dihydrogen phosphate molar mass | 97.994 g/mol | 163.94 g/mol | 119.98 g/mol phase | liquid (at STP) | solid (at STP) | melting point | 42.4 °C | 75 °C | boiling point | 158 °C | | density | 1.685 g/cm^3 | 2.536 g/cm^3 | 0.9996 g/cm^3 solubility in water | very soluble | soluble | odor | odorless | odorless | odorless