C + H2SO3 = CO2 + H2S

C activated charcoal + H_2SO_3 sulfurous acid ⟶ CO_2 carbon dioxide + H_2S hydrogen sulfide

Balance the chemical equation algebraically: C + H_2SO_3 ⟶ CO_2 + H_2S Add stoichiometric coefficients, c_i, to the reactants and products: c_1 C + c_2 H_2SO_3 ⟶ c_3 CO_2 + c_4 H_2S Set the number of atoms in the reactants equal to the number of atoms in the products for C, H, O and S: C: | c_1 = c_3 H: | 2 c_2 = 2 c_4 O: | 3 c_2 = 2 c_3 S: | c_2 = 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 = 3/2 c_2 = 1 c_3 = 3/2 c_4 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 3 c_2 = 2 c_3 = 3 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 C + 2 H_2SO_3 ⟶ 3 CO_2 + 2 H_2S

+ ⟶ +

activated charcoal + sulfurous acid ⟶ carbon dioxide + hydrogen sulfide

Construct the equilibrium constant, K, expression for: C + H_2SO_3 ⟶ CO_2 + H_2S 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 + 2 H_2SO_3 ⟶ 3 CO_2 + 2 H_2S 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 H_2SO_3 | 2 | -2 CO_2 | 3 | 3 H_2S | 2 | 2 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) H_2SO_3 | 2 | -2 | ([H2SO3])^(-2) CO_2 | 3 | 3 | ([CO2])^3 H_2S | 2 | 2 | ([H2S])^2 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) ([H2SO3])^(-2) ([CO2])^3 ([H2S])^2 = (([CO2])^3 ([H2S])^2)/(([C])^3 ([H2SO3])^2)

Construct the rate of reaction expression for: C + H_2SO_3 ⟶ CO_2 + H_2S 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 + 2 H_2SO_3 ⟶ 3 CO_2 + 2 H_2S 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 H_2SO_3 | 2 | -2 CO_2 | 3 | 3 H_2S | 2 | 2 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) H_2SO_3 | 2 | -2 | -1/2 (Δ[H2SO3])/(Δt) CO_2 | 3 | 3 | 1/3 (Δ[CO2])/(Δt) H_2S | 2 | 2 | 1/2 (Δ[H2S])/(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) = -1/2 (Δ[H2SO3])/(Δt) = 1/3 (Δ[CO2])/(Δt) = 1/2 (Δ[H2S])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| activated charcoal | sulfurous acid | carbon dioxide | hydrogen sulfide formula | C | H_2SO_3 | CO_2 | H_2S Hill formula | C | H_2O_3S | CO_2 | H_2S name | activated charcoal | sulfurous acid | carbon dioxide | hydrogen sulfide IUPAC name | carbon | sulfurous acid | carbon dioxide | hydrogen sulfide

| activated charcoal | sulfurous acid | carbon dioxide | hydrogen sulfide molar mass | 12.011 g/mol | 82.07 g/mol | 44.009 g/mol | 34.08 g/mol phase | solid (at STP) | | gas (at STP) | gas (at STP) melting point | 3550 °C | | -56.56 °C (at triple point) | -85 °C boiling point | 4027 °C | | -78.5 °C (at sublimation point) | -60 °C density | 2.26 g/cm^3 | 1.03 g/cm^3 | 0.00184212 g/cm^3 (at 20 °C) | 0.001393 g/cm^3 (at 25 °C) solubility in water | insoluble | very soluble | | dynamic viscosity | | | 1.491×10^-5 Pa s (at 25 °C) | 1.239×10^-5 Pa s (at 25 °C) odor | | | odorless |