P + NaClO = NaCl + P2O5

P red phosphorus + NaOCl sodium hypochlorite ⟶ NaCl sodium chloride + P2O5

Balance the chemical equation algebraically: P + NaOCl ⟶ NaCl + P2O5 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 P + c_2 NaOCl ⟶ c_3 NaCl + c_4 P2O5 Set the number of atoms in the reactants equal to the number of atoms in the products for P, Cl, Na and O: P: | c_1 = 2 c_4 Cl: | c_2 = c_3 Na: | c_2 = c_3 O: | c_2 = 5 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 5 c_3 = 5 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 P + 5 NaOCl ⟶ 5 NaCl + P2O5

+ ⟶ + P2O5

red phosphorus + sodium hypochlorite ⟶ sodium chloride + P2O5

Construct the equilibrium constant, K, expression for: P + NaOCl ⟶ NaCl + P2O5 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 P + 5 NaOCl ⟶ 5 NaCl + P2O5 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 P | 2 | -2 NaOCl | 5 | -5 NaCl | 5 | 5 P2O5 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression P | 2 | -2 | ([P])^(-2) NaOCl | 5 | -5 | ([NaOCl])^(-5) NaCl | 5 | 5 | ([NaCl])^5 P2O5 | 1 | 1 | [P2O5] 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 = ([P])^(-2) ([NaOCl])^(-5) ([NaCl])^5 [P2O5] = (([NaCl])^5 [P2O5])/(([P])^2 ([NaOCl])^5)

Construct the rate of reaction expression for: P + NaOCl ⟶ NaCl + P2O5 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 P + 5 NaOCl ⟶ 5 NaCl + P2O5 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 P | 2 | -2 NaOCl | 5 | -5 NaCl | 5 | 5 P2O5 | 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 P | 2 | -2 | -1/2 (Δ[P])/(Δt) NaOCl | 5 | -5 | -1/5 (Δ[NaOCl])/(Δt) NaCl | 5 | 5 | 1/5 (Δ[NaCl])/(Δt) P2O5 | 1 | 1 | (Δ[P2O5])/(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[P])/(Δt) = -1/5 (Δ[NaOCl])/(Δt) = 1/5 (Δ[NaCl])/(Δt) = (Δ[P2O5])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| red phosphorus | sodium hypochlorite | sodium chloride | P2O5 formula | P | NaOCl | NaCl | P2O5 Hill formula | P | ClNaO | ClNa | O5P2 name | red phosphorus | sodium hypochlorite | sodium chloride | IUPAC name | phosphorus | sodium hypochlorite | sodium chloride |

| red phosphorus | sodium hypochlorite | sodium chloride | P2O5 molar mass | 30.973761998 g/mol | 74.44 g/mol | 58.44 g/mol | 141.94 g/mol phase | solid (at STP) | liquid (at STP) | solid (at STP) | melting point | 579.2 °C | -6 °C | 801 °C | boiling point | | | 1413 °C | density | 2.16 g/cm^3 | 1.11 g/cm^3 | 2.16 g/cm^3 | solubility in water | insoluble | miscible | soluble | dynamic viscosity | 7.6×10^-4 Pa s (at 20.2 °C) | | | odor | | | odorless |