C + LiCoO2 = CoO2 + LiC6

C activated charcoal + CoLiO_2 lithium cobalt(III) oxide ⟶ CoO2 + LiC6

Balance the chemical equation algebraically: C + CoLiO_2 ⟶ CoO2 + LiC6 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 C + c_2 CoLiO_2 ⟶ c_3 CoO2 + c_4 LiC6 Set the number of atoms in the reactants equal to the number of atoms in the products for C, Co, Li and O: C: | c_1 = 6 c_4 Co: | c_2 = c_3 Li: | c_2 = c_4 O: | 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 = 6 c_2 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 C + CoLiO_2 ⟶ CoO2 + LiC6

+ ⟶ CoO2 + LiC6

activated charcoal + lithium cobalt(III) oxide ⟶ CoO2 + LiC6

Construct the equilibrium constant, K, expression for: C + CoLiO_2 ⟶ CoO2 + LiC6 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: 6 C + CoLiO_2 ⟶ CoO2 + LiC6 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 C | 6 | -6 CoLiO_2 | 1 | -1 CoO2 | 1 | 1 LiC6 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression C | 6 | -6 | ([C])^(-6) CoLiO_2 | 1 | -1 | ([CoLiO2])^(-1) CoO2 | 1 | 1 | [CoO2] LiC6 | 1 | 1 | [LiC6] 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 = ([C])^(-6) ([CoLiO2])^(-1) [CoO2] [LiC6] = ([CoO2] [LiC6])/(([C])^6 [CoLiO2])

Construct the rate of reaction expression for: C + CoLiO_2 ⟶ CoO2 + LiC6 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: 6 C + CoLiO_2 ⟶ CoO2 + LiC6 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 C | 6 | -6 CoLiO_2 | 1 | -1 CoO2 | 1 | 1 LiC6 | 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 C | 6 | -6 | -1/6 (Δ[C])/(Δt) CoLiO_2 | 1 | -1 | -(Δ[CoLiO2])/(Δt) CoO2 | 1 | 1 | (Δ[CoO2])/(Δt) LiC6 | 1 | 1 | (Δ[LiC6])/(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 = -1/6 (Δ[C])/(Δt) = -(Δ[CoLiO2])/(Δt) = (Δ[CoO2])/(Δt) = (Δ[LiC6])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| activated charcoal | lithium cobalt(III) oxide | CoO2 | LiC6 formula | C | CoLiO_2 | CoO2 | LiC6 Hill formula | C | CoLiO_2 | CoO2 | C6Li name | activated charcoal | lithium cobalt(III) oxide | | IUPAC name | carbon | lithium oxido-oxocobalt | |