H2O + NaOH + P = H2 + Na2HPO3

H_2O water + NaOH sodium hydroxide + P red phosphorus ⟶ H_2 hydrogen + Na2HPO3

Balance the chemical equation algebraically: H_2O + NaOH + P ⟶ H_2 + Na2HPO3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 NaOH + c_3 P ⟶ c_4 H_2 + c_5 Na2HPO3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Na and P: H: | 2 c_1 + c_2 = 2 c_4 + c_5 O: | c_1 + c_2 = 3 c_5 Na: | c_2 = 2 c_5 P: | 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 2 c_3 = 1 c_4 = 3/2 c_5 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 2 c_2 = 4 c_3 = 2 c_4 = 3 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2O + 4 NaOH + 2 P ⟶ 3 H_2 + 2 Na2HPO3

+ + ⟶ + Na2HPO3

water + sodium hydroxide + red phosphorus ⟶ hydrogen + Na2HPO3

Construct the equilibrium constant, K, expression for: H_2O + NaOH + P ⟶ H_2 + Na2HPO3 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 H_2O + 4 NaOH + 2 P ⟶ 3 H_2 + 2 Na2HPO3 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 H_2O | 2 | -2 NaOH | 4 | -4 P | 2 | -2 H_2 | 3 | 3 Na2HPO3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 2 | -2 | ([H2O])^(-2) NaOH | 4 | -4 | ([NaOH])^(-4) P | 2 | -2 | ([P])^(-2) H_2 | 3 | 3 | ([H2])^3 Na2HPO3 | 2 | 2 | ([Na2HPO3])^2 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 = ([H2O])^(-2) ([NaOH])^(-4) ([P])^(-2) ([H2])^3 ([Na2HPO3])^2 = (([H2])^3 ([Na2HPO3])^2)/(([H2O])^2 ([NaOH])^4 ([P])^2)

Construct the rate of reaction expression for: H_2O + NaOH + P ⟶ H_2 + Na2HPO3 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 H_2O + 4 NaOH + 2 P ⟶ 3 H_2 + 2 Na2HPO3 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 H_2O | 2 | -2 NaOH | 4 | -4 P | 2 | -2 H_2 | 3 | 3 Na2HPO3 | 2 | 2 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 H_2O | 2 | -2 | -1/2 (Δ[H2O])/(Δt) NaOH | 4 | -4 | -1/4 (Δ[NaOH])/(Δt) P | 2 | -2 | -1/2 (Δ[P])/(Δt) H_2 | 3 | 3 | 1/3 (Δ[H2])/(Δt) Na2HPO3 | 2 | 2 | 1/2 (Δ[Na2HPO3])/(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[H2O])/(Δt) = -1/4 (Δ[NaOH])/(Δt) = -1/2 (Δ[P])/(Δt) = 1/3 (Δ[H2])/(Δt) = 1/2 (Δ[Na2HPO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | sodium hydroxide | red phosphorus | hydrogen | Na2HPO3 formula | H_2O | NaOH | P | H_2 | Na2HPO3 Hill formula | H_2O | HNaO | P | H_2 | HNa2O3P name | water | sodium hydroxide | red phosphorus | hydrogen | IUPAC name | water | sodium hydroxide | phosphorus | molecular hydrogen |

| water | sodium hydroxide | red phosphorus | hydrogen | Na2HPO3 molar mass | 18.015 g/mol | 39.997 g/mol | 30.973761998 g/mol | 2.016 g/mol | 125.96 g/mol phase | liquid (at STP) | solid (at STP) | solid (at STP) | gas (at STP) | melting point | 0 °C | 323 °C | 579.2 °C | -259.2 °C | boiling point | 99.9839 °C | 1390 °C | | -252.8 °C | density | 1 g/cm^3 | 2.13 g/cm^3 | 2.16 g/cm^3 | 8.99×10^-5 g/cm^3 (at 0 °C) | solubility in water | | soluble | insoluble | | surface tension | 0.0728 N/m | 0.07435 N/m | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | 0.004 Pa s (at 350 °C) | 7.6×10^-4 Pa s (at 20.2 °C) | 8.9×10^-6 Pa s (at 25 °C) | odor | odorless | | | odorless |