H2O + Cr2(SO4)3 + PbO2 = PbSO4 + H2CrO4

Input interpretation

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H_2O water + Cr_2(SO_4)_3 chromium sulfate + PbO_2 lead dioxide ⟶ PbSO_4 lead(II) sulfate + H_2CrO_4 chromic acid

Balanced equation

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Balance the chemical equation algebraically: H_2O + Cr_2(SO_4)_3 + PbO_2 ⟶ PbSO_4 + H_2CrO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 Cr_2(SO_4)_3 + c_3 PbO_2 ⟶ c_4 PbSO_4 + c_5 H_2CrO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Cr, S and Pb: H: | 2 c_1 = 2 c_5 O: | c_1 + 12 c_2 + 2 c_3 = 4 c_4 + 4 c_5 Cr: | 2 c_2 = c_5 S: | 3 c_2 = c_4 Pb: | c_3 = 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 = 3 c_4 = 3 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2O + Cr_2(SO_4)_3 + 3 PbO_2 ⟶ 3 PbSO_4 + 2 H_2CrO_4

+ + ⟶ +

Names

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water + chromium sulfate + lead dioxide ⟶ lead(II) sulfate + chromic acid

Equilibrium constant

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Construct the equilibrium constant, K, expression for: H_2O + Cr_2(SO_4)_3 + PbO_2 ⟶ PbSO_4 + H_2CrO_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_2O + Cr_2(SO_4)_3 + 3 PbO_2 ⟶ 3 PbSO_4 + 2 H_2CrO_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_2O | 2 | -2 Cr_2(SO_4)_3 | 1 | -1 PbO_2 | 3 | -3 PbSO_4 | 3 | 3 H_2CrO_4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 2 | -2 | ([H2O])^(-2) Cr_2(SO_4)_3 | 1 | -1 | ([Cr2(SO4)3])^(-1) PbO_2 | 3 | -3 | ([PbO2])^(-3) PbSO_4 | 3 | 3 | ([PbSO4])^3 H_2CrO_4 | 2 | 2 | ([H2CrO4])^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 = ([H2O])^(-2) ([Cr2(SO4)3])^(-1) ([PbO2])^(-3) ([PbSO4])^3 ([H2CrO4])^2 = (([PbSO4])^3 ([H2CrO4])^2)/(([H2O])^2 [Cr2(SO4)3] ([PbO2])^3)

Rate of reaction

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Construct the rate of reaction expression for: H_2O + Cr_2(SO_4)_3 + PbO_2 ⟶ PbSO_4 + H_2CrO_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_2O + Cr_2(SO_4)_3 + 3 PbO_2 ⟶ 3 PbSO_4 + 2 H_2CrO_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_2O | 2 | -2 Cr_2(SO_4)_3 | 1 | -1 PbO_2 | 3 | -3 PbSO_4 | 3 | 3 H_2CrO_4 | 2 | 2 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_2O | 2 | -2 | -1/2 (Δ[H2O])/(Δt) Cr_2(SO_4)_3 | 1 | -1 | -(Δ[Cr2(SO4)3])/(Δt) PbO_2 | 3 | -3 | -1/3 (Δ[PbO2])/(Δt) PbSO_4 | 3 | 3 | 1/3 (Δ[PbSO4])/(Δt) H_2CrO_4 | 2 | 2 | 1/2 (Δ[H2CrO4])/(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[H2O])/(Δt) = -(Δ[Cr2(SO4)3])/(Δt) = -1/3 (Δ[PbO2])/(Δt) = 1/3 (Δ[PbSO4])/(Δt) = 1/2 (Δ[H2CrO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)