H2O + P4 + Ba(OH)2 = PH3 + Ba(H2PO2)2

water + white phosphorus + barium hydroxide ⟶ phosphine + Ba(H2PO2)2

Balance the chemical equation algebraically: + + ⟶ + Ba(H2PO2)2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 + c_2 + c_3 ⟶ c_4 + c_5 Ba(H2PO2)2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, P and Ba: H: | 2 c_1 + 2 c_3 = 3 c_4 + 4 c_5 O: | c_1 + 2 c_3 = 4 c_5 P: | 4 c_2 = c_4 + 2 c_5 Ba: | c_3 = 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 = 3/2 c_4 = 1 c_5 = 3/2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 6 c_2 = 2 c_3 = 3 c_4 = 2 c_5 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 + 2 + 3 ⟶ 2 + 3 Ba(H2PO2)2

+ + ⟶ + Ba(H2PO2)2

water + white phosphorus + barium hydroxide ⟶ phosphine + Ba(H2PO2)2

K_c = ([PH3]^2 [Ba(H2PO2)2]^3)/([H2O]^6 [P4]^2 [Ba(OH)2]^3)

rate = -1/6 (Δ[H2O])/(Δt) = -1/2 (Δ[P4])/(Δt) = -1/3 (Δ[Ba(OH)2])/(Δt) = 1/2 (Δ[PH3])/(Δt) = 1/3 (Δ[Ba(H2PO2)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | white phosphorus | barium hydroxide | phosphine | Ba(H2PO2)2 formula | | | | | Ba(H2PO2)2 Hill formula | H_2O | P_4 | BaH_2O_2 | H_3P | H4BaO4P2 name | water | white phosphorus | barium hydroxide | phosphine | IUPAC name | water | tetraphosphorus | barium(+2) cation dihydroxide | phosphine |

| water | white phosphorus | barium hydroxide | phosphine | Ba(H2PO2)2 molar mass | 18.015 g/mol | 123.89504799 g/mol | 171.34 g/mol | 33.998 g/mol | 267.3 g/mol phase | liquid (at STP) | solid (at STP) | solid (at STP) | gas (at STP) | melting point | 0 °C | 44.15 °C | 300 °C | -132.8 °C | boiling point | 99.9839 °C | 280.5 °C | | -87.5 °C | density | 1 g/cm^3 | 1.823 g/cm^3 | 2.2 g/cm^3 | 0.00139 g/cm^3 (at 25 °C) | solubility in water | | insoluble | | slightly soluble | surface tension | 0.0728 N/m | | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | 0.00169 Pa s (at 50 °C) | | 1.1×10^-5 Pa s (at 0 °C) | odor | odorless | odorless | | |