HCl + H3PO4 = H2O + PCl5

HCl hydrogen chloride + H_3PO_4 phosphoric acid ⟶ H_2O water + PCl_5 phosphorus pentachloride

Balance the chemical equation algebraically: HCl + H_3PO_4 ⟶ H_2O + PCl_5 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 H_3PO_4 ⟶ c_3 H_2O + c_4 PCl_5 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, O and P: Cl: | c_1 = 5 c_4 H: | c_1 + 3 c_2 = 2 c_3 O: | 4 c_2 = c_3 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 = 5 c_2 = 1 c_3 = 4 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 5 HCl + H_3PO_4 ⟶ 4 H_2O + PCl_5

+ ⟶ +

hydrogen chloride + phosphoric acid ⟶ water + phosphorus pentachloride

Construct the equilibrium constant, K, expression for: HCl + H_3PO_4 ⟶ H_2O + PCl_5 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: 5 HCl + H_3PO_4 ⟶ 4 H_2O + PCl_5 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 HCl | 5 | -5 H_3PO_4 | 1 | -1 H_2O | 4 | 4 PCl_5 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 5 | -5 | ([HCl])^(-5) H_3PO_4 | 1 | -1 | ([H3PO4])^(-1) H_2O | 4 | 4 | ([H2O])^4 PCl_5 | 1 | 1 | [PCl5] 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 = ([HCl])^(-5) ([H3PO4])^(-1) ([H2O])^4 [PCl5] = (([H2O])^4 [PCl5])/(([HCl])^5 [H3PO4])

Construct the rate of reaction expression for: HCl + H_3PO_4 ⟶ H_2O + PCl_5 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: 5 HCl + H_3PO_4 ⟶ 4 H_2O + PCl_5 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 HCl | 5 | -5 H_3PO_4 | 1 | -1 H_2O | 4 | 4 PCl_5 | 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 HCl | 5 | -5 | -1/5 (Δ[HCl])/(Δt) H_3PO_4 | 1 | -1 | -(Δ[H3PO4])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) PCl_5 | 1 | 1 | (Δ[PCl5])/(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 = -1/5 (Δ[HCl])/(Δt) = -(Δ[H3PO4])/(Δt) = 1/4 (Δ[H2O])/(Δt) = (Δ[PCl5])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | phosphoric acid | water | phosphorus pentachloride formula | HCl | H_3PO_4 | H_2O | PCl_5 Hill formula | ClH | H_3O_4P | H_2O | Cl_5P name | hydrogen chloride | phosphoric acid | water | phosphorus pentachloride IUPAC name | hydrogen chloride | phosphoric acid | water | pentachlorophosphorane

| hydrogen chloride | phosphoric acid | water | phosphorus pentachloride molar mass | 36.46 g/mol | 97.994 g/mol | 18.015 g/mol | 208.2 g/mol phase | gas (at STP) | liquid (at STP) | liquid (at STP) | solid (at STP) melting point | -114.17 °C | 42.4 °C | 0 °C | 148 °C boiling point | -85 °C | 158 °C | 99.9839 °C | density | 0.00149 g/cm^3 (at 25 °C) | 1.685 g/cm^3 | 1 g/cm^3 | 3.6 g/cm^3 solubility in water | miscible | very soluble | | reacts surface tension | | | 0.0728 N/m | dynamic viscosity | | | 8.9×10^-4 Pa s (at 25 °C) | odor | | odorless | odorless |