H3PO4 + NH4OH = H2O + NH4H2PO4

H_3PO_4 phosphoric acid + NH_4OH ammonium hydroxide ⟶ H_2O water + NH_4H_2PO_4 ammonium dihydrogen phosphate

Balance the chemical equation algebraically: H_3PO_4 + NH_4OH ⟶ H_2O + NH_4H_2PO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_3PO_4 + c_2 NH_4OH ⟶ c_3 H_2O + c_4 NH_4H_2PO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, P and N: H: | 3 c_1 + 5 c_2 = 2 c_3 + 6 c_4 O: | 4 c_1 + c_2 = c_3 + 4 c_4 P: | c_1 = c_4 N: | c_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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_3PO_4 + NH_4OH ⟶ H_2O + NH_4H_2PO_4

+ ⟶ +

phosphoric acid + ammonium hydroxide ⟶ water + ammonium dihydrogen phosphate

Construct the equilibrium constant, K, expression for: H_3PO_4 + NH_4OH ⟶ H_2O + NH_4H_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: H_3PO_4 + NH_4OH ⟶ H_2O + NH_4H_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 | 1 | -1 NH_4OH | 1 | -1 H_2O | 1 | 1 NH_4H_2PO_4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_3PO_4 | 1 | -1 | ([H3PO4])^(-1) NH_4OH | 1 | -1 | ([NH4OH])^(-1) H_2O | 1 | 1 | [H2O] NH_4H_2PO_4 | 1 | 1 | [NH4H2PO4] 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])^(-1) ([NH4OH])^(-1) [H2O] [NH4H2PO4] = ([H2O] [NH4H2PO4])/([H3PO4] [NH4OH])

Construct the rate of reaction expression for: H_3PO_4 + NH_4OH ⟶ H_2O + NH_4H_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: H_3PO_4 + NH_4OH ⟶ H_2O + NH_4H_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 | 1 | -1 NH_4OH | 1 | -1 H_2O | 1 | 1 NH_4H_2PO_4 | 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 H_3PO_4 | 1 | -1 | -(Δ[H3PO4])/(Δt) NH_4OH | 1 | -1 | -(Δ[NH4OH])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) NH_4H_2PO_4 | 1 | 1 | (Δ[NH4H2PO4])/(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[H3PO4])/(Δt) = -(Δ[NH4OH])/(Δt) = (Δ[H2O])/(Δt) = (Δ[NH4H2PO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| phosphoric acid | ammonium hydroxide | water | ammonium dihydrogen phosphate formula | H_3PO_4 | NH_4OH | H_2O | NH_4H_2PO_4 Hill formula | H_3O_4P | H_5NO | H_2O | H_6NO_4P name | phosphoric acid | ammonium hydroxide | water | ammonium dihydrogen phosphate

| phosphoric acid | ammonium hydroxide | water | ammonium dihydrogen phosphate molar mass | 97.994 g/mol | 35.046 g/mol | 18.015 g/mol | 115.02 g/mol phase | liquid (at STP) | aqueous (at STP) | liquid (at STP) | solid (at STP) melting point | 42.4 °C | -57.5 °C | 0 °C | 190 °C boiling point | 158 °C | 36 °C | 99.9839 °C | density | 1.685 g/cm^3 | 0.9 g/cm^3 | 1 g/cm^3 | 1.8 g/cm^3 solubility in water | very soluble | very soluble | | surface tension | | | 0.0728 N/m | dynamic viscosity | | | 8.9×10^-4 Pa s (at 25 °C) | odor | odorless | | odorless |