H2SO4 + PbCO3 = H2O + CO2 + PbSO4

H_2SO_4 sulfuric acid + PbCO_3 cerussete ⟶ H_2O water + CO_2 carbon dioxide + PbSO_4 lead(II) sulfate

Balance the chemical equation algebraically: H_2SO_4 + PbCO_3 ⟶ H_2O + CO_2 + PbSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 PbCO_3 ⟶ c_3 H_2O + c_4 CO_2 + c_5 PbSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, C and Pb: H: | 2 c_1 = 2 c_3 O: | 4 c_1 + 3 c_2 = c_3 + 2 c_4 + 4 c_5 S: | c_1 = c_5 C: | c_2 = c_4 Pb: | c_2 = c_5 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 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2SO_4 + PbCO_3 ⟶ H_2O + CO_2 + PbSO_4

+ ⟶ + +

sulfuric acid + cerussete ⟶ water + carbon dioxide + lead(II) sulfate

Construct the equilibrium constant, K, expression for: H_2SO_4 + PbCO_3 ⟶ H_2O + CO_2 + PbSO_4 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: H_2SO_4 + PbCO_3 ⟶ H_2O + CO_2 + PbSO_4 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_2SO_4 | 1 | -1 PbCO_3 | 1 | -1 H_2O | 1 | 1 CO_2 | 1 | 1 PbSO_4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 1 | -1 | ([H2SO4])^(-1) PbCO_3 | 1 | -1 | ([PbCO3])^(-1) H_2O | 1 | 1 | [H2O] CO_2 | 1 | 1 | [CO2] PbSO_4 | 1 | 1 | [PbSO4] 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 = ([H2SO4])^(-1) ([PbCO3])^(-1) [H2O] [CO2] [PbSO4] = ([H2O] [CO2] [PbSO4])/([H2SO4] [PbCO3])

Construct the rate of reaction expression for: H_2SO_4 + PbCO_3 ⟶ H_2O + CO_2 + PbSO_4 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: H_2SO_4 + PbCO_3 ⟶ H_2O + CO_2 + PbSO_4 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_2SO_4 | 1 | -1 PbCO_3 | 1 | -1 H_2O | 1 | 1 CO_2 | 1 | 1 PbSO_4 | 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 H_2SO_4 | 1 | -1 | -(Δ[H2SO4])/(Δt) PbCO_3 | 1 | -1 | -(Δ[PbCO3])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) CO_2 | 1 | 1 | (Δ[CO2])/(Δt) PbSO_4 | 1 | 1 | (Δ[PbSO4])/(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[H2SO4])/(Δt) = -(Δ[PbCO3])/(Δt) = (Δ[H2O])/(Δt) = (Δ[CO2])/(Δt) = (Δ[PbSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | cerussete | water | carbon dioxide | lead(II) sulfate formula | H_2SO_4 | PbCO_3 | H_2O | CO_2 | PbSO_4 Hill formula | H_2O_4S | CO_3Pb | H_2O | CO_2 | O_4PbS name | sulfuric acid | cerussete | water | carbon dioxide | lead(II) sulfate IUPAC name | sulfuric acid | lead(+2) cation carbonate | water | carbon dioxide |