C7H14 = H2 + C7H8

C_6H_11CH_3 methylcyclohexane ⟶ H_2 hydrogen + C_6H_5CH_3 toluene

Balance the chemical equation algebraically: C_6H_11CH_3 ⟶ H_2 + C_6H_5CH_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 C_6H_11CH_3 ⟶ c_2 H_2 + c_3 C_6H_5CH_3 Set the number of atoms in the reactants equal to the number of atoms in the products for C and H: C: | 7 c_1 = 7 c_3 H: | 14 c_1 = 2 c_2 + 8 c_3 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 = 3 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | C_6H_11CH_3 ⟶ 3 H_2 + C_6H_5CH_3

⟶ +

methylcyclohexane ⟶ hydrogen + toluene

Construct the equilibrium constant, K, expression for: C_6H_11CH_3 ⟶ H_2 + C_6H_5CH_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: C_6H_11CH_3 ⟶ 3 H_2 + C_6H_5CH_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 C_6H_11CH_3 | 1 | -1 H_2 | 3 | 3 C_6H_5CH_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression C_6H_11CH_3 | 1 | -1 | ([C6H11CH3])^(-1) H_2 | 3 | 3 | ([H2])^3 C_6H_5CH_3 | 1 | 1 | [C6H5CH3] 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 = ([C6H11CH3])^(-1) ([H2])^3 [C6H5CH3] = (([H2])^3 [C6H5CH3])/([C6H11CH3])

Construct the rate of reaction expression for: C_6H_11CH_3 ⟶ H_2 + C_6H_5CH_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: C_6H_11CH_3 ⟶ 3 H_2 + C_6H_5CH_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 C_6H_11CH_3 | 1 | -1 H_2 | 3 | 3 C_6H_5CH_3 | 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 C_6H_11CH_3 | 1 | -1 | -(Δ[C6H11CH3])/(Δt) H_2 | 3 | 3 | 1/3 (Δ[H2])/(Δt) C_6H_5CH_3 | 1 | 1 | (Δ[C6H5CH3])/(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 = -(Δ[C6H11CH3])/(Δt) = 1/3 (Δ[H2])/(Δt) = (Δ[C6H5CH3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| methylcyclohexane | hydrogen | toluene formula | C_6H_11CH_3 | H_2 | C_6H_5CH_3 Hill formula | C_7H_14 | H_2 | C_7H_8 name | methylcyclohexane | hydrogen | toluene IUPAC name | methylcyclohexane | molecular hydrogen | methylbenzene

| methylcyclohexane | hydrogen | toluene molar mass | 98.19 g/mol | 2.016 g/mol | 92.14 g/mol phase | liquid (at STP) | gas (at STP) | liquid (at STP) melting point | -126 °C | -259.2 °C | -93 °C boiling point | 101 °C | -252.8 °C | 110.5 °C density | 0.77 g/cm^3 | 8.99×10^-5 g/cm^3 (at 0 °C) | 0.865 g/cm^3 solubility in water | insoluble | | surface tension | 0.02382 N/m | | 0.02971 N/m dynamic viscosity | 6.79×10^-4 Pa s (at 25 °C) | 8.9×10^-6 Pa s (at 25 °C) | 5.6×10^-4 Pa s (at 25 °C) odor | | odorless | sweet | benzene