H2SO4 + Pb(OH)4 = H2O + Pb(SO4)2

H_2SO_4 sulfuric acid + Pb(OH)4 ⟶ H_2O water + Pb(SO4)2

Balance the chemical equation algebraically: H_2SO_4 + Pb(OH)4 ⟶ H_2O + Pb(SO4)2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 Pb(OH)4 ⟶ c_3 H_2O + c_4 Pb(SO4)2 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 + 4 c_2 = 2 c_3 O: | 4 c_1 + 4 c_2 = c_3 + 8 c_4 S: | c_1 = 2 c_4 Pb: | 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 = 2 c_2 = 1 c_3 = 4 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2SO_4 + Pb(OH)4 ⟶ 4 H_2O + Pb(SO4)2

+ Pb(OH)4 ⟶ + Pb(SO4)2

sulfuric acid + Pb(OH)4 ⟶ water + Pb(SO4)2

Construct the equilibrium constant, K, expression for: H_2SO_4 + Pb(OH)4 ⟶ H_2O + Pb(SO4)2 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(OH)4 ⟶ 4 H_2O + Pb(SO4)2 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(OH)4 | 1 | -1 H_2O | 4 | 4 Pb(SO4)2 | 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(OH)4 | 1 | -1 | ([Pb(OH)4])^(-1) H_2O | 4 | 4 | ([H2O])^4 Pb(SO4)2 | 1 | 1 | [Pb(SO4)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 = ([H2SO4])^(-2) ([Pb(OH)4])^(-1) ([H2O])^4 [Pb(SO4)2] = (([H2O])^4 [Pb(SO4)2])/(([H2SO4])^2 [Pb(OH)4])

Construct the rate of reaction expression for: H_2SO_4 + Pb(OH)4 ⟶ H_2O + Pb(SO4)2 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(OH)4 ⟶ 4 H_2O + Pb(SO4)2 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(OH)4 | 1 | -1 H_2O | 4 | 4 Pb(SO4)2 | 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(OH)4 | 1 | -1 | -(Δ[Pb(OH)4])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) Pb(SO4)2 | 1 | 1 | (Δ[Pb(SO4)2])/(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(OH)4])/(Δt) = 1/4 (Δ[H2O])/(Δt) = (Δ[Pb(SO4)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | Pb(OH)4 | water | Pb(SO4)2 formula | H_2SO_4 | Pb(OH)4 | H_2O | Pb(SO4)2 Hill formula | H_2O_4S | H4O4Pb | H_2O | O8PbS2 name | sulfuric acid | | water |

| sulfuric acid | Pb(OH)4 | water | Pb(SO4)2 molar mass | 98.07 g/mol | 275.2 g/mol | 18.015 g/mol | 399.3 g/mol phase | liquid (at STP) | | liquid (at STP) | melting point | 10.371 °C | | 0 °C | boiling point | 279.6 °C | | 99.9839 °C | density | 1.8305 g/cm^3 | | 1 g/cm^3 | solubility in water | very soluble | | | surface tension | 0.0735 N/m | | 0.0728 N/m | dynamic viscosity | 0.021 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | odor | odorless | | odorless |