H3PO4 + C5H10 = H2O + CO2 + P2O3

H_3PO_4 phosphoric acid + C_5H_10 cyclopentane ⟶ H_2O water + CO_2 carbon dioxide + P_2O_3 phosphorus trioxide

Balance the chemical equation algebraically: H_3PO_4 + C_5H_10 ⟶ H_2O + CO_2 + P_2O_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_3PO_4 + c_2 C_5H_10 ⟶ c_3 H_2O + c_4 CO_2 + c_5 P_2O_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, P and C: H: | 3 c_1 + 10 c_2 = 2 c_3 O: | 4 c_1 = c_3 + 2 c_4 + 3 c_5 P: | c_1 = 2 c_5 C: | 5 c_2 = 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 = 15 c_2 = 1 c_3 = 55/2 c_4 = 5 c_5 = 15/2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 30 c_2 = 2 c_3 = 55 c_4 = 10 c_5 = 15 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 30 H_3PO_4 + 2 C_5H_10 ⟶ 55 H_2O + 10 CO_2 + 15 P_2O_3

+ ⟶ + +

phosphoric acid + cyclopentane ⟶ water + carbon dioxide + phosphorus trioxide

Construct the equilibrium constant, K, expression for: H_3PO_4 + C_5H_10 ⟶ H_2O + CO_2 + P_2O_3 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: 30 H_3PO_4 + 2 C_5H_10 ⟶ 55 H_2O + 10 CO_2 + 15 P_2O_3 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_3PO_4 | 30 | -30 C_5H_10 | 2 | -2 H_2O | 55 | 55 CO_2 | 10 | 10 P_2O_3 | 15 | 15 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_3PO_4 | 30 | -30 | ([H3PO4])^(-30) C_5H_10 | 2 | -2 | ([C5H10])^(-2) H_2O | 55 | 55 | ([H2O])^55 CO_2 | 10 | 10 | ([CO2])^10 P_2O_3 | 15 | 15 | ([P2O3])^15 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 = ([H3PO4])^(-30) ([C5H10])^(-2) ([H2O])^55 ([CO2])^10 ([P2O3])^15 = (([H2O])^55 ([CO2])^10 ([P2O3])^15)/(([H3PO4])^30 ([C5H10])^2)

Construct the rate of reaction expression for: H_3PO_4 + C_5H_10 ⟶ H_2O + CO_2 + P_2O_3 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: 30 H_3PO_4 + 2 C_5H_10 ⟶ 55 H_2O + 10 CO_2 + 15 P_2O_3 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_3PO_4 | 30 | -30 C_5H_10 | 2 | -2 H_2O | 55 | 55 CO_2 | 10 | 10 P_2O_3 | 15 | 15 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_3PO_4 | 30 | -30 | -1/30 (Δ[H3PO4])/(Δt) C_5H_10 | 2 | -2 | -1/2 (Δ[C5H10])/(Δt) H_2O | 55 | 55 | 1/55 (Δ[H2O])/(Δt) CO_2 | 10 | 10 | 1/10 (Δ[CO2])/(Δt) P_2O_3 | 15 | 15 | 1/15 (Δ[P2O3])/(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 = -1/30 (Δ[H3PO4])/(Δt) = -1/2 (Δ[C5H10])/(Δt) = 1/55 (Δ[H2O])/(Δt) = 1/10 (Δ[CO2])/(Δt) = 1/15 (Δ[P2O3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| phosphoric acid | cyclopentane | water | carbon dioxide | phosphorus trioxide formula | H_3PO_4 | C_5H_10 | H_2O | CO_2 | P_2O_3 Hill formula | H_3O_4P | C_5H_10 | H_2O | CO_2 | O_3P_2 name | phosphoric acid | cyclopentane | water | carbon dioxide | phosphorus trioxide