H2O + HBrO3 + P2O3 = H3PO4 + HBr

H_2O water + HO_3Br bromic acid + P_2O_3 phosphorus trioxide ⟶ H_3PO_4 phosphoric acid + HBr hydrogen bromide

Balance the chemical equation algebraically: H_2O + HO_3Br + P_2O_3 ⟶ H_3PO_4 + HBr Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 HO_3Br + c_3 P_2O_3 ⟶ c_4 H_3PO_4 + c_5 HBr Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Br and P: H: | 2 c_1 + c_2 = 3 c_4 + c_5 O: | c_1 + 3 c_2 + 3 c_3 = 4 c_4 Br: | c_2 = c_5 P: | 2 c_3 = 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 = 9/2 c_2 = 1 c_3 = 3/2 c_4 = 3 c_5 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 9 c_2 = 2 c_3 = 3 c_4 = 6 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 9 H_2O + 2 HO_3Br + 3 P_2O_3 ⟶ 6 H_3PO_4 + 2 HBr

+ + ⟶ +

water + bromic acid + phosphorus trioxide ⟶ phosphoric acid + hydrogen bromide

K_c = ([H3PO4]^6 [HBr]^2)/([H2O]^9 [H1O3Br1]^2 [P2O3]^3)

rate = -1/9 (Δ[H2O])/(Δt) = -1/2 (Δ[H1O3Br1])/(Δt) = -1/3 (Δ[P2O3])/(Δt) = 1/6 (Δ[H3PO4])/(Δt) = 1/2 (Δ[HBr])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | bromic acid | phosphorus trioxide | phosphoric acid | hydrogen bromide formula | H_2O | HO_3Br | P_2O_3 | H_3PO_4 | HBr Hill formula | H_2O | BrHO_3 | O_3P_2 | H_3O_4P | BrH name | water | bromic acid | phosphorus trioxide | phosphoric acid | hydrogen bromide

| water | bromic acid | phosphorus trioxide | phosphoric acid | hydrogen bromide molar mass | 18.015 g/mol | 128.91 g/mol | 109.94 g/mol | 97.994 g/mol | 80.912 g/mol phase | liquid (at STP) | | solid (at STP) | liquid (at STP) | gas (at STP) melting point | 0 °C | | 23.8 °C | 42.4 °C | -86.8 °C boiling point | 99.9839 °C | | 173.1 °C | 158 °C | -66.38 °C density | 1 g/cm^3 | | 2.135 g/cm^3 | 1.685 g/cm^3 | 0.003307 g/cm^3 (at 25 °C) solubility in water | | | decomposes | very soluble | miscible surface tension | 0.0728 N/m | | | | 0.0271 N/m dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | | | 8.4×10^-4 Pa s (at -75 °C) odor | odorless | | | odorless |