CH4 = H2 + C

CH_4 (methane) ⟶ H_2 (hydrogen) + C (activated charcoal)

Balance the chemical equation algebraically: CH_4 ⟶ H_2 + C Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CH_4 ⟶ c_2 H_2 + c_3 C Set the number of atoms in the reactants equal to the number of atoms in the products for C and H: C: | c_1 = c_3 H: | 4 c_1 = 2 c_2 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 = 2 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | CH_4 ⟶ 2 H_2 + C

⟶ +

methane ⟶ hydrogen + activated charcoal

Construct the equilibrium constant, K, expression for: CH_4 ⟶ H_2 + C 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: CH_4 ⟶ 2 H_2 + C 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 CH_4 | 1 | -1 H_2 | 2 | 2 C | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression CH_4 | 1 | -1 | ([CH4])^(-1) H_2 | 2 | 2 | ([H2])^2 C | 1 | 1 | [C] 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 = ([CH4])^(-1) ([H2])^2 [C] = (([H2])^2 [C])/([CH4])

Construct the rate of reaction expression for: CH_4 ⟶ H_2 + C 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: CH_4 ⟶ 2 H_2 + C 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 CH_4 | 1 | -1 H_2 | 2 | 2 C | 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 CH_4 | 1 | -1 | -(Δ[CH4])/(Δt) H_2 | 2 | 2 | 1/2 (Δ[H2])/(Δt) C | 1 | 1 | (Δ[C])/(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[CH4])/(Δt) = 1/2 (Δ[H2])/(Δt) = (Δ[C])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| methane | hydrogen | activated charcoal formula | CH_4 | H_2 | C name | methane | hydrogen | activated charcoal IUPAC name | methane | molecular hydrogen | carbon

| methane | hydrogen | activated charcoal molar mass | 16.04 g/mol | 2.016 g/mol | 12.011 g/mol phase | gas (at STP) | gas (at STP) | solid (at STP) melting point | -182.47 °C | -259.2 °C | 3550 °C boiling point | -161.48 °C | -252.8 °C | 4027 °C density | 6.67151×10^-4 g/cm^3 (at 20 °C) | 8.99×10^-5 g/cm^3 (at 0 °C) | 2.26 g/cm^3 solubility in water | soluble | | insoluble surface tension | 0.0137 N/m | | dynamic viscosity | 1.114×10^-5 Pa s (at 25 °C) | 8.9×10^-6 Pa s (at 25 °C) | odor | odorless | odorless |