NaOH + H3PO4 = H2O + Na2HPO4

NaOH sodium hydroxide + H_3PO_4 phosphoric acid ⟶ H_2O water + Na_2HPO_4 disodium hydrogen phosphate

Balance the chemical equation algebraically: NaOH + H_3PO_4 ⟶ H_2O + Na_2HPO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 H_3PO_4 ⟶ c_3 H_2O + c_4 Na_2HPO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, Na, O and P: H: | c_1 + 3 c_2 = 2 c_3 + c_4 Na: | c_1 = 2 c_4 O: | c_1 + 4 c_2 = c_3 + 4 c_4 P: | 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 NaOH + H_3PO_4 ⟶ 2 H_2O + Na_2HPO_4

+ ⟶ +

sodium hydroxide + phosphoric acid ⟶ water + disodium hydrogen phosphate

| sodium hydroxide | phosphoric acid | water | disodium hydrogen phosphate molecular free energy | -379.7 kJ/mol | -1124 kJ/mol | -237.1 kJ/mol | -1608 kJ/mol total free energy | -759.4 kJ/mol | -1124 kJ/mol | -474.2 kJ/mol | -1608 kJ/mol | G_initial = -1883 kJ/mol | | G_final = -2082 kJ/mol | ΔG_rxn^0 | -2082 kJ/mol - -1883 kJ/mol = -199.4 kJ/mol (exergonic) | | |

Construct the equilibrium constant, K, expression for: NaOH + H_3PO_4 ⟶ H_2O + Na_2HPO_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 NaOH + H_3PO_4 ⟶ 2 H_2O + Na_2HPO_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 NaOH | 2 | -2 H_3PO_4 | 1 | -1 H_2O | 2 | 2 Na_2HPO_4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaOH | 2 | -2 | ([NaOH])^(-2) H_3PO_4 | 1 | -1 | ([H3PO4])^(-1) H_2O | 2 | 2 | ([H2O])^2 Na_2HPO_4 | 1 | 1 | [Na2HPO4] 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 = ([NaOH])^(-2) ([H3PO4])^(-1) ([H2O])^2 [Na2HPO4] = (([H2O])^2 [Na2HPO4])/(([NaOH])^2 [H3PO4])

Construct the rate of reaction expression for: NaOH + H_3PO_4 ⟶ H_2O + Na_2HPO_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 NaOH + H_3PO_4 ⟶ 2 H_2O + Na_2HPO_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 NaOH | 2 | -2 H_3PO_4 | 1 | -1 H_2O | 2 | 2 Na_2HPO_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 NaOH | 2 | -2 | -1/2 (Δ[NaOH])/(Δt) H_3PO_4 | 1 | -1 | -(Δ[H3PO4])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) Na_2HPO_4 | 1 | 1 | (Δ[Na2HPO4])/(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[NaOH])/(Δt) = -(Δ[H3PO4])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[Na2HPO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium hydroxide | phosphoric acid | water | disodium hydrogen phosphate formula | NaOH | H_3PO_4 | H_2O | Na_2HPO_4 Hill formula | HNaO | H_3O_4P | H_2O | HNa_2O_4P name | sodium hydroxide | phosphoric acid | water | disodium hydrogen phosphate

| sodium hydroxide | phosphoric acid | water | disodium hydrogen phosphate molar mass | 39.997 g/mol | 97.994 g/mol | 18.015 g/mol | 141.96 g/mol phase | solid (at STP) | liquid (at STP) | liquid (at STP) | solid (at STP) melting point | 323 °C | 42.4 °C | 0 °C | 250 °C boiling point | 1390 °C | 158 °C | 99.9839 °C | density | 2.13 g/cm^3 | 1.685 g/cm^3 | 1 g/cm^3 | 1.53 g/cm^3 solubility in water | soluble | very soluble | | soluble surface tension | 0.07435 N/m | | 0.0728 N/m | dynamic viscosity | 0.004 Pa s (at 350 °C) | | 8.9×10^-4 Pa s (at 25 °C) | odor | | odorless | odorless |