H2 + C = CH2

H_2 hydrogen + C activated charcoal ⟶ CH2

Balance the chemical equation algebraically: H_2 + C ⟶ CH2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2 + c_2 C ⟶ c_3 CH2 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_3 C: | c_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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2 + C ⟶ CH2

+ ⟶ CH2

hydrogen + activated charcoal ⟶ CH2

Construct the equilibrium constant, K, expression for: H_2 + C ⟶ CH2 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: H_2 + C ⟶ CH2 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 | 1 | -1 C | 1 | -1 CH2 | 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 | 1 | -1 | ([H2])^(-1) C | 1 | -1 | ([C])^(-1) CH2 | 1 | 1 | [CH2] 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])^(-1) ([C])^(-1) [CH2] = ([CH2])/([H2] [C])

Construct the rate of reaction expression for: H_2 + C ⟶ CH2 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: H_2 + C ⟶ CH2 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 | 1 | -1 C | 1 | -1 CH2 | 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 | 1 | -1 | -(Δ[H2])/(Δt) C | 1 | -1 | -(Δ[C])/(Δt) CH2 | 1 | 1 | (Δ[CH2])/(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[H2])/(Δt) = -(Δ[C])/(Δt) = (Δ[CH2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen | activated charcoal | CH2 formula | H_2 | C | CH2 name | hydrogen | activated charcoal | IUPAC name | molecular hydrogen | carbon |

| hydrogen | activated charcoal | CH2 molar mass | 2.016 g/mol | 12.011 g/mol | 14.027 g/mol phase | gas (at STP) | solid (at STP) | melting point | -259.2 °C | 3550 °C | boiling point | -252.8 °C | 4027 °C | density | 8.99×10^-5 g/cm^3 (at 0 °C) | 2.26 g/cm^3 | solubility in water | | insoluble | dynamic viscosity | 8.9×10^-6 Pa s (at 25 °C) | | odor | odorless | |