H2S + Pb3(CO3)2(OH)2 = H2O + CO2 + PbS

H_2S hydrogen sulfide + Pb3(CO3)2(OH)2 ⟶ H_2O water + CO_2 carbon dioxide + PbS lead sulfide

Balance the chemical equation algebraically: H_2S + Pb3(CO3)2(OH)2 ⟶ H_2O + CO_2 + PbS Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2S + c_2 Pb3(CO3)2(OH)2 ⟶ c_3 H_2O + c_4 CO_2 + c_5 PbS Set the number of atoms in the reactants equal to the number of atoms in the products for H, S, Pb, C and O: H: | 2 c_1 + 2 c_2 = 2 c_3 S: | c_1 = c_5 Pb: | 3 c_2 = c_5 C: | 2 c_2 = c_4 O: | 8 c_2 = c_3 + 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 c_2 = 1 c_3 = 4 c_4 = 2 c_5 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2S + Pb3(CO3)2(OH)2 ⟶ 4 H_2O + 2 CO_2 + 3 PbS

+ Pb3(CO3)2(OH)2 ⟶ + +

hydrogen sulfide + Pb3(CO3)2(OH)2 ⟶ water + carbon dioxide + lead sulfide

Construct the equilibrium constant, K, expression for: H_2S + Pb3(CO3)2(OH)2 ⟶ H_2O + CO_2 + PbS 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 H_2S + Pb3(CO3)2(OH)2 ⟶ 4 H_2O + 2 CO_2 + 3 PbS 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 H_2S | 3 | -3 Pb3(CO3)2(OH)2 | 1 | -1 H_2O | 4 | 4 CO_2 | 2 | 2 PbS | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2S | 3 | -3 | ([H2S])^(-3) Pb3(CO3)2(OH)2 | 1 | -1 | ([Pb3(CO3)2(OH)2])^(-1) H_2O | 4 | 4 | ([H2O])^4 CO_2 | 2 | 2 | ([CO2])^2 PbS | 3 | 3 | ([PbS])^3 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 = ([H2S])^(-3) ([Pb3(CO3)2(OH)2])^(-1) ([H2O])^4 ([CO2])^2 ([PbS])^3 = (([H2O])^4 ([CO2])^2 ([PbS])^3)/(([H2S])^3 [Pb3(CO3)2(OH)2])

Construct the rate of reaction expression for: H_2S + Pb3(CO3)2(OH)2 ⟶ H_2O + CO_2 + PbS 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 H_2S + Pb3(CO3)2(OH)2 ⟶ 4 H_2O + 2 CO_2 + 3 PbS 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 H_2S | 3 | -3 Pb3(CO3)2(OH)2 | 1 | -1 H_2O | 4 | 4 CO_2 | 2 | 2 PbS | 3 | 3 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 H_2S | 3 | -3 | -1/3 (Δ[H2S])/(Δt) Pb3(CO3)2(OH)2 | 1 | -1 | -(Δ[Pb3(CO3)2(OH)2])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) CO_2 | 2 | 2 | 1/2 (Δ[CO2])/(Δt) PbS | 3 | 3 | 1/3 (Δ[PbS])/(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[H2S])/(Δt) = -(Δ[Pb3(CO3)2(OH)2])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/2 (Δ[CO2])/(Δt) = 1/3 (Δ[PbS])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen sulfide | Pb3(CO3)2(OH)2 | water | carbon dioxide | lead sulfide formula | H_2S | Pb3(CO3)2(OH)2 | H_2O | CO_2 | PbS Hill formula | H_2S | C2H2O8Pb3 | H_2O | CO_2 | PbS name | hydrogen sulfide | | water | carbon dioxide | lead sulfide

| hydrogen sulfide | Pb3(CO3)2(OH)2 | water | carbon dioxide | lead sulfide molar mass | 34.08 g/mol | 775.6 g/mol | 18.015 g/mol | 44.009 g/mol | 239.3 g/mol phase | gas (at STP) | | liquid (at STP) | gas (at STP) | solid (at STP) melting point | -85 °C | | 0 °C | -56.56 °C (at triple point) | 1114 °C boiling point | -60 °C | | 99.9839 °C | -78.5 °C (at sublimation point) | 1344 °C density | 0.001393 g/cm^3 (at 25 °C) | | 1 g/cm^3 | 0.00184212 g/cm^3 (at 20 °C) | 7.5 g/cm^3 solubility in water | | | | | insoluble surface tension | | | 0.0728 N/m | | dynamic viscosity | 1.239×10^-5 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | 1.491×10^-5 Pa s (at 25 °C) | odor | | | odorless | odorless |