C + ZnO = Zn + CO

C (activated charcoal) + ZnO (zinc oxide) ⟶ Zn (zinc) + CO (carbon monoxide)

Balance the chemical equation algebraically: C + ZnO ⟶ Zn + CO Add stoichiometric coefficients, c_i, to the reactants and products: c_1 C + c_2 ZnO ⟶ c_3 Zn + c_4 CO Set the number of atoms in the reactants equal to the number of atoms in the products for C, O and Zn: C: | c_1 = c_4 O: | c_2 = c_4 Zn: | c_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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | C + ZnO ⟶ Zn + CO

+ ⟶ +

activated charcoal + zinc oxide ⟶ zinc + carbon monoxide

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

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

| activated charcoal | zinc oxide | zinc | carbon monoxide formula | C | ZnO | Zn | CO Hill formula | C | OZn | Zn | CO name | activated charcoal | zinc oxide | zinc | carbon monoxide IUPAC name | carbon | oxozinc | zinc | carbon monoxide

| activated charcoal | zinc oxide | zinc | carbon monoxide molar mass | 12.011 g/mol | 81.38 g/mol | 65.38 g/mol | 28.01 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | gas (at STP) melting point | 3550 °C | 1975 °C | 420 °C | -205 °C boiling point | 4027 °C | 2360 °C | 907 °C | -191.5 °C density | 2.26 g/cm^3 | 5.6 g/cm^3 | 7.14 g/cm^3 | 0.001145 g/cm^3 (at 25 °C) solubility in water | insoluble | | insoluble | dynamic viscosity | | | | 1.772×10^-5 Pa s (at 25 °C) odor | | odorless | odorless | odorless