H2SO4 + Pb = H2O + S + Pb(HSO4)2

Input interpretation

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H_2SO_4 sulfuric acid + Pb lead ⟶ H_2O water + S mixed sulfur + Pb(HSO4)2

Balanced equation

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Balance the chemical equation algebraically: H_2SO_4 + Pb ⟶ H_2O + S + Pb(HSO4)2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 Pb ⟶ c_3 H_2O + c_4 S + c_5 Pb(HSO4)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 = 2 c_3 + 2 c_5 O: | 4 c_1 = c_3 + 8 c_5 S: | c_1 = c_4 + 2 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 7 c_2 = 3 c_3 = 4 c_4 = 1 c_5 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 7 H_2SO_4 + 3 Pb ⟶ 4 H_2O + S + 3 Pb(HSO4)2

+ ⟶ + + Pb(HSO4)2

Names

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sulfuric acid + lead ⟶ water + mixed sulfur + Pb(HSO4)2

Equilibrium constant

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Construct the equilibrium constant, K, expression for: H_2SO_4 + Pb ⟶ H_2O + S + Pb(HSO4)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: 7 H_2SO_4 + 3 Pb ⟶ 4 H_2O + S + 3 Pb(HSO4)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 | 7 | -7 Pb | 3 | -3 H_2O | 4 | 4 S | 1 | 1 Pb(HSO4)2 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 7 | -7 | ([H2SO4])^(-7) Pb | 3 | -3 | ([Pb])^(-3) H_2O | 4 | 4 | ([H2O])^4 S | 1 | 1 | [S] Pb(HSO4)2 | 3 | 3 | ([Pb(HSO4)2])^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 = ([H2SO4])^(-7) ([Pb])^(-3) ([H2O])^4 [S] ([Pb(HSO4)2])^3 = (([H2O])^4 [S] ([Pb(HSO4)2])^3)/(([H2SO4])^7 ([Pb])^3)

Rate of reaction

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Construct the rate of reaction expression for: H_2SO_4 + Pb ⟶ H_2O + S + Pb(HSO4)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: 7 H_2SO_4 + 3 Pb ⟶ 4 H_2O + S + 3 Pb(HSO4)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 | 7 | -7 Pb | 3 | -3 H_2O | 4 | 4 S | 1 | 1 Pb(HSO4)2 | 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_2SO_4 | 7 | -7 | -1/7 (Δ[H2SO4])/(Δt) Pb | 3 | -3 | -1/3 (Δ[Pb])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) S | 1 | 1 | (Δ[S])/(Δt) Pb(HSO4)2 | 3 | 3 | 1/3 (Δ[Pb(HSO4)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 = -1/7 (Δ[H2SO4])/(Δt) = -1/3 (Δ[Pb])/(Δt) = 1/4 (Δ[H2O])/(Δt) = (Δ[S])/(Δt) = 1/3 (Δ[Pb(HSO4)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)