O2 + CH2 = H2O + CO2

O_2 oxygen + CH2 ⟶ H_2O water + CO_2 carbon dioxide

Balance the chemical equation algebraically: O_2 + CH2 ⟶ H_2O + CO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 O_2 + c_2 CH2 ⟶ c_3 H_2O + c_4 CO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for O, C and H: O: | 2 c_1 = c_3 + 2 c_4 C: | c_2 = c_4 H: | 2 c_2 = 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3/2 c_2 = 1 c_3 = 1 c_4 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 3 c_2 = 2 c_3 = 2 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 O_2 + 2 CH2 ⟶ 2 H_2O + 2 CO_2

+ CH2 ⟶ +

oxygen + CH2 ⟶ water + carbon dioxide

Construct the equilibrium constant, K, expression for: O_2 + CH2 ⟶ H_2O + CO_2 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: 3 O_2 + 2 CH2 ⟶ 2 H_2O + 2 CO_2 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 O_2 | 3 | -3 CH2 | 2 | -2 H_2O | 2 | 2 CO_2 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression O_2 | 3 | -3 | ([O2])^(-3) CH2 | 2 | -2 | ([CH2])^(-2) H_2O | 2 | 2 | ([H2O])^2 CO_2 | 2 | 2 | ([CO2])^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 = ([O2])^(-3) ([CH2])^(-2) ([H2O])^2 ([CO2])^2 = (([H2O])^2 ([CO2])^2)/(([O2])^3 ([CH2])^2)

Construct the rate of reaction expression for: O_2 + CH2 ⟶ H_2O + CO_2 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: 3 O_2 + 2 CH2 ⟶ 2 H_2O + 2 CO_2 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 O_2 | 3 | -3 CH2 | 2 | -2 H_2O | 2 | 2 CO_2 | 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 O_2 | 3 | -3 | -1/3 (Δ[O2])/(Δt) CH2 | 2 | -2 | -1/2 (Δ[CH2])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) CO_2 | 2 | 2 | 1/2 (Δ[CO2])/(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 = -1/3 (Δ[O2])/(Δt) = -1/2 (Δ[CH2])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/2 (Δ[CO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| oxygen | CH2 | water | carbon dioxide formula | O_2 | CH2 | H_2O | CO_2 name | oxygen | | water | carbon dioxide IUPAC name | molecular oxygen | | water | carbon dioxide

| oxygen | CH2 | water | carbon dioxide molar mass | 31.998 g/mol | 14.027 g/mol | 18.015 g/mol | 44.009 g/mol phase | gas (at STP) | | liquid (at STP) | gas (at STP) melting point | -218 °C | | 0 °C | -56.56 °C (at triple point) boiling point | -183 °C | | 99.9839 °C | -78.5 °C (at sublimation point) density | 0.001429 g/cm^3 (at 0 °C) | | 1 g/cm^3 | 0.00184212 g/cm^3 (at 20 °C) surface tension | 0.01347 N/m | | 0.0728 N/m | dynamic viscosity | 2.055×10^-5 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | 1.491×10^-5 Pa s (at 25 °C) odor | odorless | | odorless | odorless