O2 + C10H8 = H2O + CO2

O_2 oxygen + C_10H_8 naphthalene ⟶ H_2O water + CO_2 carbon dioxide

Balance the chemical equation algebraically: O_2 + C_10H_8 ⟶ H_2O + CO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 O_2 + c_2 C_10H_8 ⟶ 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: | 10 c_2 = c_4 H: | 8 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 = 12 c_2 = 1 c_3 = 4 c_4 = 10 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 12 O_2 + C_10H_8 ⟶ 4 H_2O + 10 CO_2

+ ⟶ +

oxygen + naphthalene ⟶ water + carbon dioxide

| oxygen | naphthalene | water | carbon dioxide molecular enthalpy | 0 kJ/mol | 78.5 kJ/mol | -285.8 kJ/mol | -393.5 kJ/mol total enthalpy | 0 kJ/mol | 78.5 kJ/mol | -1143 kJ/mol | -3935 kJ/mol | H_initial = 78.5 kJ/mol | | H_final = -5078 kJ/mol | ΔH_rxn^0 | -5078 kJ/mol - 78.5 kJ/mol = -5157 kJ/mol (exothermic) | | |

| oxygen | naphthalene | water | carbon dioxide molecular free energy | 231.7 kJ/mol | 201.6 kJ/mol | -237.1 kJ/mol | -394.4 kJ/mol total free energy | 2780 kJ/mol | 201.6 kJ/mol | -948.4 kJ/mol | -3944 kJ/mol | G_initial = 2982 kJ/mol | | G_final = -4892 kJ/mol | ΔG_rxn^0 | -4892 kJ/mol - 2982 kJ/mol = -7874 kJ/mol (exergonic) | | |

Construct the equilibrium constant, K, expression for: O_2 + C_10H_8 ⟶ 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: 12 O_2 + C_10H_8 ⟶ 4 H_2O + 10 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 | 12 | -12 C_10H_8 | 1 | -1 H_2O | 4 | 4 CO_2 | 10 | 10 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression O_2 | 12 | -12 | ([O2])^(-12) C_10H_8 | 1 | -1 | ([C10H8])^(-1) H_2O | 4 | 4 | ([H2O])^4 CO_2 | 10 | 10 | ([CO2])^10 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])^(-12) ([C10H8])^(-1) ([H2O])^4 ([CO2])^10 = (([H2O])^4 ([CO2])^10)/(([O2])^12 [C10H8])

Construct the rate of reaction expression for: O_2 + C_10H_8 ⟶ 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: 12 O_2 + C_10H_8 ⟶ 4 H_2O + 10 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 | 12 | -12 C_10H_8 | 1 | -1 H_2O | 4 | 4 CO_2 | 10 | 10 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 | 12 | -12 | -1/12 (Δ[O2])/(Δt) C_10H_8 | 1 | -1 | -(Δ[C10H8])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) CO_2 | 10 | 10 | 1/10 (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 = -1/12 (Δ[O2])/(Δt) = -(Δ[C10H8])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/10 (Δ[CO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| oxygen | naphthalene | water | carbon dioxide formula | O_2 | C_10H_8 | H_2O | CO_2 name | oxygen | naphthalene | water | carbon dioxide IUPAC name | molecular oxygen | naphthalene | water | carbon dioxide

| oxygen | naphthalene | water | carbon dioxide molar mass | 31.998 g/mol | 128.17 g/mol | 18.015 g/mol | 44.009 g/mol phase | gas (at STP) | solid (at STP) | liquid (at STP) | gas (at STP) melting point | -218 °C | 81 °C | 0 °C | -56.56 °C (at triple point) boiling point | -183 °C | 218 °C | 99.9839 °C | -78.5 °C (at sublimation point) density | 0.001429 g/cm^3 (at 0 °C) | 0.979 g/cm^3 | 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