H2SO4 + Pb = H2O + SO2 + PbSO4

H_2SO_4 sulfuric acid + Pb lead ⟶ H_2O water + SO_2 sulfur dioxide + PbSO_4 lead(II) sulfate

Balance the chemical equation algebraically: H_2SO_4 + Pb ⟶ H_2O + SO_2 + PbSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 Pb ⟶ c_3 H_2O + c_4 SO_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 and Pb: H: | 2 c_1 = 2 c_3 O: | 4 c_1 = c_3 + 2 c_4 + 4 c_5 S: | c_1 = c_4 + c_5 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 2 c_4 = 1 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2SO_4 + Pb ⟶ 2 H_2O + SO_2 + PbSO_4

+ ⟶ + +

sulfuric acid + lead ⟶ water + sulfur dioxide + lead(II) sulfate

| sulfuric acid | lead | water | sulfur dioxide | lead(II) sulfate molecular enthalpy | -814 kJ/mol | 0 kJ/mol | -285.8 kJ/mol | -296.8 kJ/mol | -920 kJ/mol total enthalpy | -1628 kJ/mol | 0 kJ/mol | -571.7 kJ/mol | -296.8 kJ/mol | -920 kJ/mol | H_initial = -1628 kJ/mol | | H_final = -1788 kJ/mol | | ΔH_rxn^0 | -1788 kJ/mol - -1628 kJ/mol = -160.5 kJ/mol (exothermic) | | | |

| sulfuric acid | lead | water | sulfur dioxide | lead(II) sulfate molecular entropy | 157 J/(mol K) | 65 J/(mol K) | 69.91 J/(mol K) | 248 J/(mol K) | 149 J/(mol K) total entropy | 314 J/(mol K) | 65 J/(mol K) | 139.8 J/(mol K) | 248 J/(mol K) | 149 J/(mol K) | S_initial = 379 J/(mol K) | | S_final = 536.8 J/(mol K) | | ΔS_rxn^0 | 536.8 J/(mol K) - 379 J/(mol K) = 157.8 J/(mol K) (endoentropic) | | | |

Construct the equilibrium constant, K, expression for: H_2SO_4 + Pb ⟶ H_2O + SO_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: 2 H_2SO_4 + Pb ⟶ 2 H_2O + SO_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 | 2 | -2 Pb | 1 | -1 H_2O | 2 | 2 SO_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 | 2 | -2 | ([H2SO4])^(-2) Pb | 1 | -1 | ([Pb])^(-1) H_2O | 2 | 2 | ([H2O])^2 SO_2 | 1 | 1 | [SO2] 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])^(-2) ([Pb])^(-1) ([H2O])^2 [SO2] [PbSO4] = (([H2O])^2 [SO2] [PbSO4])/(([H2SO4])^2 [Pb])

Construct the rate of reaction expression for: H_2SO_4 + Pb ⟶ H_2O + SO_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: 2 H_2SO_4 + Pb ⟶ 2 H_2O + SO_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 | 2 | -2 Pb | 1 | -1 H_2O | 2 | 2 SO_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 | 2 | -2 | -1/2 (Δ[H2SO4])/(Δt) Pb | 1 | -1 | -(Δ[Pb])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) SO_2 | 1 | 1 | (Δ[SO2])/(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 = -1/2 (Δ[H2SO4])/(Δt) = -(Δ[Pb])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[SO2])/(Δt) = (Δ[PbSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | lead | water | sulfur dioxide | lead(II) sulfate formula | H_2SO_4 | Pb | H_2O | SO_2 | PbSO_4 Hill formula | H_2O_4S | Pb | H_2O | O_2S | O_4PbS name | sulfuric acid | lead | water | sulfur dioxide | lead(II) sulfate