Na + CH3OH = H2 + CH3ONa

Na sodium + CH_3OH methanol ⟶ H_2 hydrogen + NaOCH_3 sodium methoxide

Balance the chemical equation algebraically: Na + CH_3OH ⟶ H_2 + NaOCH_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Na + c_2 CH_3OH ⟶ c_3 H_2 + c_4 NaOCH_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Na, C, H and O: Na: | c_1 = c_4 C: | c_2 = c_4 H: | 4 c_2 = 2 c_3 + 3 c_4 O: | c_2 = c_4 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 = 2 c_2 = 2 c_3 = 1 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 Na + 2 CH_3OH ⟶ H_2 + 2 NaOCH_3

+ ⟶ +

sodium + methanol ⟶ hydrogen + sodium methoxide

Construct the equilibrium constant, K, expression for: Na + CH_3OH ⟶ H_2 + NaOCH_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 Na + 2 CH_3OH ⟶ H_2 + 2 NaOCH_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 Na | 2 | -2 CH_3OH | 2 | -2 H_2 | 1 | 1 NaOCH_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Na | 2 | -2 | ([Na])^(-2) CH_3OH | 2 | -2 | ([CH3OH])^(-2) H_2 | 1 | 1 | [H2] NaOCH_3 | 2 | 2 | ([NaOCH3])^2 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 = ([Na])^(-2) ([CH3OH])^(-2) [H2] ([NaOCH3])^2 = ([H2] ([NaOCH3])^2)/(([Na])^2 ([CH3OH])^2)

Construct the rate of reaction expression for: Na + CH_3OH ⟶ H_2 + NaOCH_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 Na + 2 CH_3OH ⟶ H_2 + 2 NaOCH_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 Na | 2 | -2 CH_3OH | 2 | -2 H_2 | 1 | 1 NaOCH_3 | 2 | 2 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 Na | 2 | -2 | -1/2 (Δ[Na])/(Δt) CH_3OH | 2 | -2 | -1/2 (Δ[CH3OH])/(Δt) H_2 | 1 | 1 | (Δ[H2])/(Δt) NaOCH_3 | 2 | 2 | 1/2 (Δ[NaOCH3])/(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[Na])/(Δt) = -1/2 (Δ[CH3OH])/(Δt) = (Δ[H2])/(Δt) = 1/2 (Δ[NaOCH3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium | methanol | hydrogen | sodium methoxide formula | Na | CH_3OH | H_2 | NaOCH_3 Hill formula | Na | CH_4O | H_2 | CH_3NaO name | sodium | methanol | hydrogen | sodium methoxide IUPAC name | sodium | methanol | molecular hydrogen | sodium methanolate

| sodium | methanol | hydrogen | sodium methoxide molar mass | 22.98976928 g/mol | 32.042 g/mol | 2.016 g/mol | 54.024 g/mol phase | solid (at STP) | liquid (at STP) | gas (at STP) | solid (at STP) melting point | 97.8 °C | -98 °C | -259.2 °C | 127 °C boiling point | 883 °C | 64.7 °C | -252.8 °C | density | 0.968 g/cm^3 | 0.791 g/cm^3 | 8.99×10^-5 g/cm^3 (at 0 °C) | 0.99 g/cm^3 solubility in water | decomposes | miscible | | decomposes dynamic viscosity | 1.413×10^-5 Pa s (at 527 °C) | 5.44×10^-4 Pa s (at 25 °C) | 8.9×10^-6 Pa s (at 25 °C) | odor | | pungent | odorless |