H2O + P4 + Ca(ClO)2 = HCl + Ca2P2O6

H_2O water + P_4 white phosphorus + Ca(ClO)2 ⟶ HCl hydrogen chloride + Ca2P2O6

Balance the chemical equation algebraically: H_2O + P_4 + Ca(ClO)2 ⟶ HCl + Ca2P2O6 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 P_4 + c_3 Ca(ClO)2 ⟶ c_4 HCl + c_5 Ca2P2O6 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, P, Ca and Cl: H: | 2 c_1 = c_4 O: | c_1 + 2 c_3 = 6 c_5 P: | 4 c_2 = 2 c_5 Ca: | c_3 = 2 c_5 Cl: | 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 = 4 c_2 = 1 c_3 = 4 c_4 = 8 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 H_2O + P_4 + 4 Ca(ClO)2 ⟶ 8 HCl + 2 Ca2P2O6

+ + Ca(ClO)2 ⟶ + Ca2P2O6

water + white phosphorus + Ca(ClO)2 ⟶ hydrogen chloride + Ca2P2O6

Construct the equilibrium constant, K, expression for: H_2O + P_4 + Ca(ClO)2 ⟶ HCl + Ca2P2O6 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: 4 H_2O + P_4 + 4 Ca(ClO)2 ⟶ 8 HCl + 2 Ca2P2O6 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 | 4 | -4 P_4 | 1 | -1 Ca(ClO)2 | 4 | -4 HCl | 8 | 8 Ca2P2O6 | 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 | 4 | -4 | ([H2O])^(-4) P_4 | 1 | -1 | ([P4])^(-1) Ca(ClO)2 | 4 | -4 | ([Ca(ClO)2])^(-4) HCl | 8 | 8 | ([HCl])^8 Ca2P2O6 | 2 | 2 | ([Ca2P2O6])^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])^(-4) ([P4])^(-1) ([Ca(ClO)2])^(-4) ([HCl])^8 ([Ca2P2O6])^2 = (([HCl])^8 ([Ca2P2O6])^2)/(([H2O])^4 [P4] ([Ca(ClO)2])^4)

Construct the rate of reaction expression for: H_2O + P_4 + Ca(ClO)2 ⟶ HCl + Ca2P2O6 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: 4 H_2O + P_4 + 4 Ca(ClO)2 ⟶ 8 HCl + 2 Ca2P2O6 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 | 4 | -4 P_4 | 1 | -1 Ca(ClO)2 | 4 | -4 HCl | 8 | 8 Ca2P2O6 | 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 | 4 | -4 | -1/4 (Δ[H2O])/(Δt) P_4 | 1 | -1 | -(Δ[P4])/(Δt) Ca(ClO)2 | 4 | -4 | -1/4 (Δ[Ca(ClO)2])/(Δt) HCl | 8 | 8 | 1/8 (Δ[HCl])/(Δt) Ca2P2O6 | 2 | 2 | 1/2 (Δ[Ca2P2O6])/(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 = -1/4 (Δ[H2O])/(Δt) = -(Δ[P4])/(Δt) = -1/4 (Δ[Ca(ClO)2])/(Δt) = 1/8 (Δ[HCl])/(Δt) = 1/2 (Δ[Ca2P2O6])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | white phosphorus | Ca(ClO)2 | hydrogen chloride | Ca2P2O6 formula | H_2O | P_4 | Ca(ClO)2 | HCl | Ca2P2O6 Hill formula | H_2O | P_4 | CaCl2O2 | ClH | Ca2O6P2 name | water | white phosphorus | | hydrogen chloride | IUPAC name | water | tetraphosphorus | | hydrogen chloride |