H2 + C2H2 = C2H6

H_2 hydrogen + C_2H_2 acetylene ⟶ CH_3CH_3 ethane

Balance the chemical equation algebraically: H_2 + C_2H_2 ⟶ CH_3CH_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2 + c_2 C_2H_2 ⟶ c_3 CH_3CH_3 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 = 6 c_3 C: | 2 c_2 = 2 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2 + C_2H_2 ⟶ CH_3CH_3

+ ⟶

hydrogen + acetylene ⟶ ethane

| hydrogen | acetylene | ethane molecular enthalpy | 0 kJ/mol | 227.4 kJ/mol | -84 kJ/mol total enthalpy | 0 kJ/mol | 227.4 kJ/mol | -84 kJ/mol | H_initial = 227.4 kJ/mol | | H_final = -84 kJ/mol ΔH_rxn^0 | -84 kJ/mol - 227.4 kJ/mol = -311.4 kJ/mol (exothermic) | |

| hydrogen | acetylene | ethane molecular free energy | 0 kJ/mol | 209.9 kJ/mol | -32 kJ/mol total free energy | 0 kJ/mol | 209.9 kJ/mol | -32 kJ/mol | G_initial = 209.9 kJ/mol | | G_final = -32 kJ/mol ΔG_rxn^0 | -32 kJ/mol - 209.9 kJ/mol = -241.9 kJ/mol (exergonic) | |

| hydrogen | acetylene | ethane molecular entropy | 115 J/(mol K) | 201 J/(mol K) | 229.5 J/(mol K) total entropy | 230 J/(mol K) | 201 J/(mol K) | 229.5 J/(mol K) | S_initial = 431 J/(mol K) | | S_final = 229.5 J/(mol K) ΔS_rxn^0 | 229.5 J/(mol K) - 431 J/(mol K) = -201.5 J/(mol K) (exoentropic) | |

Construct the equilibrium constant, K, expression for: H_2 + C_2H_2 ⟶ CH_3CH_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: 2 H_2 + C_2H_2 ⟶ CH_3CH_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_2 | 2 | -2 C_2H_2 | 1 | -1 CH_3CH_3 | 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 | 2 | -2 | ([H2])^(-2) C_2H_2 | 1 | -1 | ([C2H2])^(-1) CH_3CH_3 | 1 | 1 | [CH3CH3] 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])^(-2) ([C2H2])^(-1) [CH3CH3] = ([CH3CH3])/(([H2])^2 [C2H2])

Construct the rate of reaction expression for: H_2 + C_2H_2 ⟶ CH_3CH_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: 2 H_2 + C_2H_2 ⟶ CH_3CH_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_2 | 2 | -2 C_2H_2 | 1 | -1 CH_3CH_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 H_2 | 2 | -2 | -1/2 (Δ[H2])/(Δt) C_2H_2 | 1 | -1 | -(Δ[C2H2])/(Δt) CH_3CH_3 | 1 | 1 | (Δ[CH3CH3])/(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 = -1/2 (Δ[H2])/(Δt) = -(Δ[C2H2])/(Δt) = (Δ[CH3CH3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen | acetylene | ethane formula | H_2 | C_2H_2 | CH_3CH_3 Hill formula | H_2 | C_2H_2 | C_2H_6 name | hydrogen | acetylene | ethane IUPAC name | molecular hydrogen | acetylene | ethane

| hydrogen | acetylene | ethane molar mass | 2.016 g/mol | 26.038 g/mol | 30.07 g/mol phase | gas (at STP) | gas (at STP) | gas (at STP) melting point | -259.2 °C | -81 °C | -182.79 °C boiling point | -252.8 °C | -75 °C | -88.6 °C density | 8.99×10^-5 g/cm^3 (at 0 °C) | 0.618 g/cm^3 (at -55 °C) | 0.00125324 g/cm^3 (at 20 °C) solubility in water | | | soluble surface tension | | 0.01431 N/m | dynamic viscosity | 8.9×10^-6 Pa s (at 25 °C) | | 9.446×10^-6 Pa s (at 25 °C) odor | odorless | | odorless