H2 + C2H2 = C6H12

H_2 hydrogen + C_2H_2 acetylene ⟶ C_6H_12 cyclohexane

Balance the chemical equation algebraically: H_2 + C_2H_2 ⟶ C_6H_12 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2 + c_2 C_2H_2 ⟶ c_3 C_6H_12 Set the number of atoms in the reactants equal to the number of atoms in the products for H and C: H: | 2 c_1 + 2 c_2 = 12 c_3 C: | 2 c_2 = 6 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 3 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2 + 3 C_2H_2 ⟶ C_6H_12

+ ⟶

hydrogen + acetylene ⟶ cyclohexane

Construct the equilibrium constant, K, expression for: H_2 + C_2H_2 ⟶ C_6H_12 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: 3 H_2 + 3 C_2H_2 ⟶ C_6H_12 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_2 | 3 | -3 C_2H_2 | 3 | -3 C_6H_12 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2 | 3 | -3 | ([H2])^(-3) C_2H_2 | 3 | -3 | ([C2H2])^(-3) C_6H_12 | 1 | 1 | [C6H12] 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 = ([H2])^(-3) ([C2H2])^(-3) [C6H12] = ([C6H12])/(([H2])^3 ([C2H2])^3)

Construct the rate of reaction expression for: H_2 + C_2H_2 ⟶ C_6H_12 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: 3 H_2 + 3 C_2H_2 ⟶ C_6H_12 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_2 | 3 | -3 C_2H_2 | 3 | -3 C_6H_12 | 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 H_2 | 3 | -3 | -1/3 (Δ[H2])/(Δt) C_2H_2 | 3 | -3 | -1/3 (Δ[C2H2])/(Δt) C_6H_12 | 1 | 1 | (Δ[C6H12])/(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 = -1/3 (Δ[H2])/(Δt) = -1/3 (Δ[C2H2])/(Δt) = (Δ[C6H12])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen | acetylene | cyclohexane formula | H_2 | C_2H_2 | C_6H_12 name | hydrogen | acetylene | cyclohexane IUPAC name | molecular hydrogen | acetylene | cyclohexane

| hydrogen | acetylene | cyclohexane molar mass | 2.016 g/mol | 26.038 g/mol | 84.16 g/mol phase | gas (at STP) | gas (at STP) | liquid (at STP) melting point | -259.2 °C | -81 °C | 5.5 °C boiling point | -252.8 °C | -75 °C | 80.7 °C density | 8.99×10^-5 g/cm^3 (at 0 °C) | 0.618 g/cm^3 (at -55 °C) | 0.779 g/cm^3 solubility in water | | | insoluble surface tension | | 0.01431 N/m | 0.02499 N/m dynamic viscosity | 8.9×10^-6 Pa s (at 25 °C) | | 8.94×10^-4 Pa s (at 25 °C) odor | odorless | |