C + BiO3 = CO + Bi

C activated charcoal + BiO3 ⟶ CO carbon monoxide + Bi bismuth

Balance the chemical equation algebraically: C + BiO3 ⟶ CO + Bi Add stoichiometric coefficients, c_i, to the reactants and products: c_1 C + c_2 BiO3 ⟶ c_3 CO + c_4 Bi Set the number of atoms in the reactants equal to the number of atoms in the products for C, Bi and O: C: | c_1 = c_3 Bi: | c_2 = c_4 O: | 3 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 1 c_3 = 3 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 C + BiO3 ⟶ 3 CO + Bi

+ BiO3 ⟶ +

activated charcoal + BiO3 ⟶ carbon monoxide + bismuth

Construct the equilibrium constant, K, expression for: C + BiO3 ⟶ CO + Bi 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: 3 C + BiO3 ⟶ 3 CO + Bi 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 | 3 | -3 BiO3 | 1 | -1 CO | 3 | 3 Bi | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression C | 3 | -3 | ([C])^(-3) BiO3 | 1 | -1 | ([BiO3])^(-1) CO | 3 | 3 | ([CO])^3 Bi | 1 | 1 | [Bi] 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])^(-3) ([BiO3])^(-1) ([CO])^3 [Bi] = (([CO])^3 [Bi])/(([C])^3 [BiO3])

Construct the rate of reaction expression for: C + BiO3 ⟶ CO + Bi 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: 3 C + BiO3 ⟶ 3 CO + Bi 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 | 3 | -3 BiO3 | 1 | -1 CO | 3 | 3 Bi | 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 | 3 | -3 | -1/3 (Δ[C])/(Δt) BiO3 | 1 | -1 | -(Δ[BiO3])/(Δt) CO | 3 | 3 | 1/3 (Δ[CO])/(Δt) Bi | 1 | 1 | (Δ[Bi])/(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 = -1/3 (Δ[C])/(Δt) = -(Δ[BiO3])/(Δt) = 1/3 (Δ[CO])/(Δt) = (Δ[Bi])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| activated charcoal | BiO3 | carbon monoxide | bismuth formula | C | BiO3 | CO | Bi name | activated charcoal | | carbon monoxide | bismuth IUPAC name | carbon | | carbon monoxide | bismuth

| activated charcoal | BiO3 | carbon monoxide | bismuth molar mass | 12.011 g/mol | 256.977 g/mol | 28.01 g/mol | 208.9804 g/mol phase | solid (at STP) | | gas (at STP) | solid (at STP) melting point | 3550 °C | | -205 °C | 271 °C boiling point | 4027 °C | | -191.5 °C | 1560 °C density | 2.26 g/cm^3 | | 0.001145 g/cm^3 (at 25 °C) | 9.8 g/cm^3 solubility in water | insoluble | | | insoluble dynamic viscosity | | | 1.772×10^-5 Pa s (at 25 °C) | 1.19×10^-4 Pa s (at 500 °C) odor | | | odorless |