NH3 + H3PO4 = NH4H2PO4

NH_3 ammonia + H_3PO_4 phosphoric acid ⟶ NH_4H_2PO_4 ammonium dihydrogen phosphate

Balance the chemical equation algebraically: NH_3 + H_3PO_4 ⟶ NH_4H_2PO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NH_3 + c_2 H_3PO_4 ⟶ c_3 NH_4H_2PO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O and P: H: | 3 c_1 + 3 c_2 = 6 c_3 N: | c_1 = c_3 O: | 4 c_2 = 4 c_3 P: | 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | NH_3 + H_3PO_4 ⟶ NH_4H_2PO_4

+ ⟶

ammonia + phosphoric acid ⟶ ammonium dihydrogen phosphate

Construct the equilibrium constant, K, expression for: NH_3 + H_3PO_4 ⟶ 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: NH_3 + H_3PO_4 ⟶ 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 NH_3 | 1 | -1 H_3PO_4 | 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 NH_3 | 1 | -1 | ([NH3])^(-1) H_3PO_4 | 1 | -1 | ([H3PO4])^(-1) 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 = ([NH3])^(-1) ([H3PO4])^(-1) [NH4H2PO4] = ([NH4H2PO4])/([NH3] [H3PO4])

Construct the rate of reaction expression for: NH_3 + H_3PO_4 ⟶ 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: NH_3 + H_3PO_4 ⟶ 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 NH_3 | 1 | -1 H_3PO_4 | 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 NH_3 | 1 | -1 | -(Δ[NH3])/(Δt) H_3PO_4 | 1 | -1 | -(Δ[H3PO4])/(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[NH3])/(Δt) = -(Δ[H3PO4])/(Δt) = (Δ[NH4H2PO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| ammonia | phosphoric acid | ammonium dihydrogen phosphate formula | NH_3 | H_3PO_4 | NH_4H_2PO_4 Hill formula | H_3N | H_3O_4P | H_6NO_4P name | ammonia | phosphoric acid | ammonium dihydrogen phosphate

| ammonia | phosphoric acid | ammonium dihydrogen phosphate molar mass | 17.031 g/mol | 97.994 g/mol | 115.02 g/mol phase | gas (at STP) | liquid (at STP) | solid (at STP) melting point | -77.73 °C | 42.4 °C | 190 °C boiling point | -33.33 °C | 158 °C | density | 6.96×10^-4 g/cm^3 (at 25 °C) | 1.685 g/cm^3 | 1.8 g/cm^3 solubility in water | | very soluble | surface tension | 0.0234 N/m | | dynamic viscosity | 1.009×10^-5 Pa s (at 25 °C) | | odor | | odorless |