O2 + C2H6 = H2O + CO2 + C

O_2 oxygen + CH_3CH_3 ethane ⟶ H_2O water + CO_2 carbon dioxide + C activated charcoal

Balance the chemical equation algebraically: O_2 + CH_3CH_3 ⟶ H_2O + CO_2 + C Add stoichiometric coefficients, c_i, to the reactants and products: c_1 O_2 + c_2 CH_3CH_3 ⟶ c_3 H_2O + c_4 CO_2 + c_5 C 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: | 2 c_2 = c_4 + c_5 H: | 6 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_2 = 1 c_3 = 3 c_4 = c_1 - 3/2 c_5 = 7/2 - c_1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_2 = 2 c_3 = 6 c_4 = c_1 - 3 c_5 = 7 - c_1 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 5 and solve for the remaining coefficients: c_1 = 5 c_2 = 2 c_3 = 6 c_4 = 2 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 5 O_2 + 2 CH_3CH_3 ⟶ 6 H_2O + 2 CO_2 + 2 C

+ ⟶ + +

oxygen + ethane ⟶ water + carbon dioxide + activated charcoal

Construct the equilibrium constant, K, expression for: O_2 + CH_3CH_3 ⟶ H_2O + CO_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: 5 O_2 + 2 CH_3CH_3 ⟶ 6 H_2O + 2 CO_2 + 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 O_2 | 5 | -5 CH_3CH_3 | 2 | -2 H_2O | 6 | 6 CO_2 | 2 | 2 C | 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 | 5 | -5 | ([O2])^(-5) CH_3CH_3 | 2 | -2 | ([CH3CH3])^(-2) H_2O | 6 | 6 | ([H2O])^6 CO_2 | 2 | 2 | ([CO2])^2 C | 2 | 2 | ([C])^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])^(-5) ([CH3CH3])^(-2) ([H2O])^6 ([CO2])^2 ([C])^2 = (([H2O])^6 ([CO2])^2 ([C])^2)/(([O2])^5 ([CH3CH3])^2)

Construct the rate of reaction expression for: O_2 + CH_3CH_3 ⟶ H_2O + CO_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: 5 O_2 + 2 CH_3CH_3 ⟶ 6 H_2O + 2 CO_2 + 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 O_2 | 5 | -5 CH_3CH_3 | 2 | -2 H_2O | 6 | 6 CO_2 | 2 | 2 C | 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 | 5 | -5 | -1/5 (Δ[O2])/(Δt) CH_3CH_3 | 2 | -2 | -1/2 (Δ[CH3CH3])/(Δt) H_2O | 6 | 6 | 1/6 (Δ[H2O])/(Δt) CO_2 | 2 | 2 | 1/2 (Δ[CO2])/(Δt) C | 2 | 2 | 1/2 (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 = -1/5 (Δ[O2])/(Δt) = -1/2 (Δ[CH3CH3])/(Δt) = 1/6 (Δ[H2O])/(Δt) = 1/2 (Δ[CO2])/(Δt) = 1/2 (Δ[C])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| oxygen | ethane | water | carbon dioxide | activated charcoal formula | O_2 | CH_3CH_3 | H_2O | CO_2 | C Hill formula | O_2 | C_2H_6 | H_2O | CO_2 | C name | oxygen | ethane | water | carbon dioxide | activated charcoal IUPAC name | molecular oxygen | ethane | water | carbon dioxide | carbon

| oxygen | ethane | water | carbon dioxide | activated charcoal molar mass | 31.998 g/mol | 30.07 g/mol | 18.015 g/mol | 44.009 g/mol | 12.011 g/mol phase | gas (at STP) | gas (at STP) | liquid (at STP) | gas (at STP) | solid (at STP) melting point | -218 °C | -182.79 °C | 0 °C | -56.56 °C (at triple point) | 3550 °C boiling point | -183 °C | -88.6 °C | 99.9839 °C | -78.5 °C (at sublimation point) | 4027 °C density | 0.001429 g/cm^3 (at 0 °C) | 0.00125324 g/cm^3 (at 20 °C) | 1 g/cm^3 | 0.00184212 g/cm^3 (at 20 °C) | 2.26 g/cm^3 solubility in water | | soluble | | | insoluble surface tension | 0.01347 N/m | | 0.0728 N/m | | dynamic viscosity | 2.055×10^-5 Pa s (at 25 °C) | 9.446×10^-6 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 | odorless |