H2O + KOH + P = PH3 + KH2PO4

water + potassium hydroxide + red phosphorus ⟶ phosphine + potassium dihydrogen phosphate

Balance the chemical equation algebraically: + + ⟶ + Add stoichiometric coefficients, c_i, to the reactants and products: c_1 + c_2 + c_3 ⟶ c_4 + c_5 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, K and P: H: | 2 c_1 + c_2 = 3 c_4 + 2 c_5 O: | c_1 + c_2 = 4 c_5 K: | c_2 = c_5 P: | c_3 = c_4 + c_5 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 = 3 c_2 = 1 c_3 = 8/3 c_4 = 5/3 c_5 = 1 Multiply by the least common denominator, 3, to eliminate fractional coefficients: c_1 = 9 c_2 = 3 c_3 = 8 c_4 = 5 c_5 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 9 + 3 + 8 ⟶ 5 + 3

+ + ⟶ +

water + potassium hydroxide + red phosphorus ⟶ phosphine + potassium dihydrogen phosphate

| water | potassium hydroxide | red phosphorus | phosphine | potassium dihydrogen phosphate molecular enthalpy | -285.8 kJ/mol | -424.6 kJ/mol | -17.6 kJ/mol | 5.4 kJ/mol | -1568 kJ/mol total enthalpy | -2572 kJ/mol | -1274 kJ/mol | -140.8 kJ/mol | 27 kJ/mol | -4705 kJ/mol | H_initial = -3987 kJ/mol | | | H_final = -4678 kJ/mol | ΔH_rxn^0 | -4678 kJ/mol - -3987 kJ/mol = -690.8 kJ/mol (exothermic) | | | |

K_c = ([PH3]^5 [KH2PO4]^3)/([H2O]^9 [KOH]^3 [P]^8)

rate = -1/9 (Δ[H2O])/(Δt) = -1/3 (Δ[KOH])/(Δt) = -1/8 (Δ[P])/(Δt) = 1/5 (Δ[PH3])/(Δt) = 1/3 (Δ[KH2PO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | potassium hydroxide | red phosphorus | phosphine | potassium dihydrogen phosphate Hill formula | H_2O | HKO | P | H_3P | H_2KO_4P name | water | potassium hydroxide | red phosphorus | phosphine | potassium dihydrogen phosphate IUPAC name | water | potassium hydroxide | phosphorus | phosphine | potassium dihydrogen phosphate