H2 + C = C3H8

H_2 hydrogen + C activated charcoal ⟶ CH_3CH_2CH_3 propane

Balance the chemical equation algebraically: H_2 + C ⟶ CH_3CH_2CH_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2 + c_2 C ⟶ c_3 CH_3CH_2CH_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 = 8 c_3 C: | c_2 = 3 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 = 4 c_2 = 3 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 H_2 + 3 C ⟶ CH_3CH_2CH_3

+ ⟶

hydrogen + activated charcoal ⟶ propane

Construct the equilibrium constant, K, expression for: H_2 + C ⟶ CH_3CH_2CH_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: 4 H_2 + 3 C ⟶ CH_3CH_2CH_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 | 4 | -4 C | 3 | -3 CH_3CH_2CH_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 | 4 | -4 | ([H2])^(-4) C | 3 | -3 | ([C])^(-3) CH_3CH_2CH_3 | 1 | 1 | [CH3CH2CH3] 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])^(-4) ([C])^(-3) [CH3CH2CH3] = ([CH3CH2CH3])/(([H2])^4 ([C])^3)

Construct the rate of reaction expression for: H_2 + C ⟶ CH_3CH_2CH_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: 4 H_2 + 3 C ⟶ CH_3CH_2CH_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 | 4 | -4 C | 3 | -3 CH_3CH_2CH_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 | 4 | -4 | -1/4 (Δ[H2])/(Δt) C | 3 | -3 | -1/3 (Δ[C])/(Δt) CH_3CH_2CH_3 | 1 | 1 | (Δ[CH3CH2CH3])/(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 = -1/4 (Δ[H2])/(Δt) = -1/3 (Δ[C])/(Δt) = (Δ[CH3CH2CH3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen | activated charcoal | propane formula | H_2 | C | CH_3CH_2CH_3 Hill formula | H_2 | C | C_3H_8 name | hydrogen | activated charcoal | propane IUPAC name | molecular hydrogen | carbon | propane

| hydrogen | activated charcoal | propane molar mass | 2.016 g/mol | 12.011 g/mol | 44.1 g/mol phase | gas (at STP) | solid (at STP) | gas (at STP) melting point | -259.2 °C | 3550 °C | -187.63 °C boiling point | -252.8 °C | 4027 °C | -42.1 °C density | 8.99×10^-5 g/cm^3 (at 0 °C) | 2.26 g/cm^3 | 0.00187939 g/cm^3 (at 20 °C) solubility in water | | insoluble | surface tension | | | 0.01515 N/m dynamic viscosity | 8.9×10^-6 Pa s (at 25 °C) | | 8×10^-6 Pa s (at 25 °C) odor | odorless | |