KOH + KClO3 + PH3 = H2O + KCl + K3PO4

KOH potassium hydroxide + KClO_3 potassium chlorate + PH_3 phosphine ⟶ H_2O water + KCl potassium chloride + K3PO4

Balance the chemical equation algebraically: KOH + KClO_3 + PH_3 ⟶ H_2O + KCl + K3PO4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 KClO_3 + c_3 PH_3 ⟶ c_4 H_2O + c_5 KCl + c_6 K3PO4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, K, O, Cl and P: H: | c_1 + 3 c_3 = 2 c_4 K: | c_1 + c_2 = c_5 + 3 c_6 O: | c_1 + 3 c_2 = c_4 + 4 c_6 Cl: | c_2 = c_5 P: | c_3 = c_6 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 4/3 c_3 = 1 c_4 = 3 c_5 = 4/3 c_6 = 1 Multiply by the least common denominator, 3, to eliminate fractional coefficients: c_1 = 9 c_2 = 4 c_3 = 3 c_4 = 9 c_5 = 4 c_6 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 9 KOH + 4 KClO_3 + 3 PH_3 ⟶ 9 H_2O + 4 KCl + 3 K3PO4

+ + ⟶ + + K3PO4

potassium hydroxide + potassium chlorate + phosphine ⟶ water + potassium chloride + K3PO4

Construct the equilibrium constant, K, expression for: KOH + KClO_3 + PH_3 ⟶ H_2O + KCl + K3PO4 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: 9 KOH + 4 KClO_3 + 3 PH_3 ⟶ 9 H_2O + 4 KCl + 3 K3PO4 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 KOH | 9 | -9 KClO_3 | 4 | -4 PH_3 | 3 | -3 H_2O | 9 | 9 KCl | 4 | 4 K3PO4 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 9 | -9 | ([KOH])^(-9) KClO_3 | 4 | -4 | ([KClO3])^(-4) PH_3 | 3 | -3 | ([PH3])^(-3) H_2O | 9 | 9 | ([H2O])^9 KCl | 4 | 4 | ([KCl])^4 K3PO4 | 3 | 3 | ([K3PO4])^3 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 = ([KOH])^(-9) ([KClO3])^(-4) ([PH3])^(-3) ([H2O])^9 ([KCl])^4 ([K3PO4])^3 = (([H2O])^9 ([KCl])^4 ([K3PO4])^3)/(([KOH])^9 ([KClO3])^4 ([PH3])^3)

Construct the rate of reaction expression for: KOH + KClO_3 + PH_3 ⟶ H_2O + KCl + K3PO4 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: 9 KOH + 4 KClO_3 + 3 PH_3 ⟶ 9 H_2O + 4 KCl + 3 K3PO4 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 KOH | 9 | -9 KClO_3 | 4 | -4 PH_3 | 3 | -3 H_2O | 9 | 9 KCl | 4 | 4 K3PO4 | 3 | 3 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 KOH | 9 | -9 | -1/9 (Δ[KOH])/(Δt) KClO_3 | 4 | -4 | -1/4 (Δ[KClO3])/(Δt) PH_3 | 3 | -3 | -1/3 (Δ[PH3])/(Δt) H_2O | 9 | 9 | 1/9 (Δ[H2O])/(Δt) KCl | 4 | 4 | 1/4 (Δ[KCl])/(Δt) K3PO4 | 3 | 3 | 1/3 (Δ[K3PO4])/(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 = -1/9 (Δ[KOH])/(Δt) = -1/4 (Δ[KClO3])/(Δt) = -1/3 (Δ[PH3])/(Δt) = 1/9 (Δ[H2O])/(Δt) = 1/4 (Δ[KCl])/(Δt) = 1/3 (Δ[K3PO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium hydroxide | potassium chlorate | phosphine | water | potassium chloride | K3PO4 formula | KOH | KClO_3 | PH_3 | H_2O | KCl | K3PO4 Hill formula | HKO | ClKO_3 | H_3P | H_2O | ClK | K3O4P name | potassium hydroxide | potassium chlorate | phosphine | water | potassium chloride |