C + H2O5 = H2O + CO

C activated charcoal + H2O5 ⟶ H_2O water + CO carbon monoxide

Balance the chemical equation algebraically: C + H2O5 ⟶ H_2O + CO Add stoichiometric coefficients, c_i, to the reactants and products: c_1 C + c_2 H2O5 ⟶ c_3 H_2O + c_4 CO Set the number of atoms in the reactants equal to the number of atoms in the products for C, H and O: C: | c_1 = c_4 H: | 2 c_2 = 2 c_3 O: | 5 c_2 = c_3 + c_4 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 = 4 c_2 = 1 c_3 = 1 c_4 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 C + H2O5 ⟶ H_2O + 4 CO

+ H2O5 ⟶ +

activated charcoal + H2O5 ⟶ water + carbon monoxide

Construct the equilibrium constant, K, expression for: C + H2O5 ⟶ H_2O + 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: 4 C + H2O5 ⟶ H_2O + 4 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 | 4 | -4 H2O5 | 1 | -1 H_2O | 1 | 1 CO | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression C | 4 | -4 | ([C])^(-4) H2O5 | 1 | -1 | ([H2O5])^(-1) H_2O | 1 | 1 | [H2O] CO | 4 | 4 | ([CO])^4 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])^(-4) ([H2O5])^(-1) [H2O] ([CO])^4 = ([H2O] ([CO])^4)/(([C])^4 [H2O5])

Construct the rate of reaction expression for: C + H2O5 ⟶ H_2O + 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: 4 C + H2O5 ⟶ H_2O + 4 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 | 4 | -4 H2O5 | 1 | -1 H_2O | 1 | 1 CO | 4 | 4 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 | 4 | -4 | -1/4 (Δ[C])/(Δt) H2O5 | 1 | -1 | -(Δ[H2O5])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) CO | 4 | 4 | 1/4 (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 = -1/4 (Δ[C])/(Δt) = -(Δ[H2O5])/(Δt) = (Δ[H2O])/(Δt) = 1/4 (Δ[CO])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| activated charcoal | H2O5 | water | carbon monoxide formula | C | H2O5 | H_2O | CO name | activated charcoal | | water | carbon monoxide IUPAC name | carbon | | water | carbon monoxide

| activated charcoal | H2O5 | water | carbon monoxide molar mass | 12.011 g/mol | 82.01 g/mol | 18.015 g/mol | 28.01 g/mol phase | solid (at STP) | | liquid (at STP) | gas (at STP) melting point | 3550 °C | | 0 °C | -205 °C boiling point | 4027 °C | | 99.9839 °C | -191.5 °C density | 2.26 g/cm^3 | | 1 g/cm^3 | 0.001145 g/cm^3 (at 25 °C) solubility in water | insoluble | | | surface tension | | | 0.0728 N/m | dynamic viscosity | | | 8.9×10^-4 Pa s (at 25 °C) | 1.772×10^-5 Pa s (at 25 °C) odor | | | odorless | odorless