CO2 = O2 + C

CO_2 carbon dioxide ⟶ O_2 oxygen + C activated charcoal

Balance the chemical equation algebraically: CO_2 ⟶ O_2 + C Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CO_2 ⟶ c_2 O_2 + c_3 C Set the number of atoms in the reactants equal to the number of atoms in the products for C and O: C: | c_1 = c_3 O: | 2 c_1 = 2 c_2 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 = 1 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | CO_2 ⟶ O_2 + C

⟶ +

carbon dioxide ⟶ oxygen + activated charcoal

Construct the equilibrium constant, K, expression for: CO_2 ⟶ O_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: CO_2 ⟶ O_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 CO_2 | 1 | -1 O_2 | 1 | 1 C | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression CO_2 | 1 | -1 | ([CO2])^(-1) O_2 | 1 | 1 | [O2] C | 1 | 1 | [C] 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 = ([CO2])^(-1) [O2] [C] = ([O2] [C])/([CO2])

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

| carbon dioxide | oxygen | activated charcoal formula | CO_2 | O_2 | C name | carbon dioxide | oxygen | activated charcoal IUPAC name | carbon dioxide | molecular oxygen | carbon

| carbon dioxide | oxygen | activated charcoal molar mass | 44.009 g/mol | 31.998 g/mol | 12.011 g/mol phase | gas (at STP) | gas (at STP) | solid (at STP) melting point | -56.56 °C (at triple point) | -218 °C | 3550 °C boiling point | -78.5 °C (at sublimation point) | -183 °C | 4027 °C density | 0.00184212 g/cm^3 (at 20 °C) | 0.001429 g/cm^3 (at 0 °C) | 2.26 g/cm^3 solubility in water | | | insoluble surface tension | | 0.01347 N/m | dynamic viscosity | 1.491×10^-5 Pa s (at 25 °C) | 2.055×10^-5 Pa s (at 25 °C) | odor | odorless | odorless |