CH3OH = H2 + CO

CH_3OH methanol ⟶ H_2 hydrogen + CO carbon monoxide

Balance the chemical equation algebraically: CH_3OH ⟶ H_2 + CO Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CH_3OH ⟶ c_2 H_2 + c_3 CO Set the number of atoms in the reactants equal to the number of atoms in the products for C, H and O: C: | c_1 = c_3 H: | 4 c_1 = 2 c_2 O: | c_1 = 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 = 2 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | CH_3OH ⟶ 2 H_2 + CO

⟶ +

methanol ⟶ hydrogen + carbon monoxide

| methanol | hydrogen | carbon monoxide molecular enthalpy | -238.7 kJ/mol | 0 kJ/mol | -110.5 kJ/mol total enthalpy | -238.7 kJ/mol | 0 kJ/mol | -110.5 kJ/mol | H_initial = -238.7 kJ/mol | H_final = -110.5 kJ/mol | ΔH_rxn^0 | -110.5 kJ/mol - -238.7 kJ/mol = 128.2 kJ/mol (endothermic) | |

| methanol | hydrogen | carbon monoxide molecular free energy | -166.3 kJ/mol | 0 kJ/mol | -137 kJ/mol total free energy | -166.3 kJ/mol | 0 kJ/mol | -137 kJ/mol | G_initial = -166.3 kJ/mol | G_final = -137 kJ/mol | ΔG_rxn^0 | -137 kJ/mol - -166.3 kJ/mol = 29.27 kJ/mol (endergonic) | |

| methanol | hydrogen | carbon monoxide molecular entropy | 126.8 J/(mol K) | 115 J/(mol K) | 198 J/(mol K) total entropy | 126.8 J/(mol K) | 230 J/(mol K) | 198 J/(mol K) | S_initial = 126.8 J/(mol K) | S_final = 428 J/(mol K) | ΔS_rxn^0 | 428 J/(mol K) - 126.8 J/(mol K) = 301.2 J/(mol K) (endoentropic) | |

Construct the equilibrium constant, K, expression for: CH_3OH ⟶ H_2 + CO 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_3OH ⟶ 2 H_2 + CO 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_3OH | 1 | -1 H_2 | 2 | 2 CO | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression CH_3OH | 1 | -1 | ([CH3OH])^(-1) H_2 | 2 | 2 | ([H2])^2 CO | 1 | 1 | [CO] 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 = ([CH3OH])^(-1) ([H2])^2 [CO] = (([H2])^2 [CO])/([CH3OH])

Construct the rate of reaction expression for: CH_3OH ⟶ H_2 + CO 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_3OH ⟶ 2 H_2 + CO 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_3OH | 1 | -1 H_2 | 2 | 2 CO | 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_3OH | 1 | -1 | -(Δ[CH3OH])/(Δt) H_2 | 2 | 2 | 1/2 (Δ[H2])/(Δt) CO | 1 | 1 | (Δ[CO])/(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[CH3OH])/(Δt) = 1/2 (Δ[H2])/(Δt) = (Δ[CO])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| methanol | hydrogen | carbon monoxide formula | CH_3OH | H_2 | CO Hill formula | CH_4O | H_2 | CO name | methanol | hydrogen | carbon monoxide IUPAC name | methanol | molecular hydrogen | carbon monoxide

| methanol | hydrogen | carbon monoxide molar mass | 32.042 g/mol | 2.016 g/mol | 28.01 g/mol phase | liquid (at STP) | gas (at STP) | gas (at STP) melting point | -98 °C | -259.2 °C | -205 °C boiling point | 64.7 °C | -252.8 °C | -191.5 °C density | 0.791 g/cm^3 | 8.99×10^-5 g/cm^3 (at 0 °C) | 0.001145 g/cm^3 (at 25 °C) solubility in water | miscible | | dynamic viscosity | 5.44×10^-4 Pa s (at 25 °C) | 8.9×10^-6 Pa s (at 25 °C) | 1.772×10^-5 Pa s (at 25 °C) odor | pungent | odorless | odorless