H2SO4 + I2 + MnO2 = H2O + MnSO4 + HIO4

Input interpretation

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H_2SO_4 sulfuric acid + I_2 iodine + MnO_2 manganese dioxide ⟶ H_2O water + MnSO_4 manganese(II) sulfate + HIO4

Balanced equation

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Balance the chemical equation algebraically: H_2SO_4 + I_2 + MnO_2 ⟶ H_2O + MnSO_4 + HIO4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 I_2 + c_3 MnO_2 ⟶ c_4 H_2O + c_5 MnSO_4 + c_6 HIO4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, I and Mn: H: | 2 c_1 = 2 c_4 + c_6 O: | 4 c_1 + 2 c_3 = c_4 + 4 c_5 + 4 c_6 S: | c_1 = c_5 I: | 2 c_2 = c_6 Mn: | c_3 = 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 = 7 c_2 = 1 c_3 = 7 c_4 = 6 c_5 = 7 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 7 H_2SO_4 + I_2 + 7 MnO_2 ⟶ 6 H_2O + 7 MnSO_4 + 2 HIO4

+ + ⟶ + + HIO4

Names

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sulfuric acid + iodine + manganese dioxide ⟶ water + manganese(II) sulfate + HIO4

Equilibrium constant

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Construct the equilibrium constant, K, expression for: H_2SO_4 + I_2 + MnO_2 ⟶ H_2O + MnSO_4 + HIO4 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 + I_2 + 7 MnO_2 ⟶ 6 H_2O + 7 MnSO_4 + 2 HIO4 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 I_2 | 1 | -1 MnO_2 | 7 | -7 H_2O | 6 | 6 MnSO_4 | 7 | 7 HIO4 | 2 | 2 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) I_2 | 1 | -1 | ([I2])^(-1) MnO_2 | 7 | -7 | ([MnO2])^(-7) H_2O | 6 | 6 | ([H2O])^6 MnSO_4 | 7 | 7 | ([MnSO4])^7 HIO4 | 2 | 2 | ([HIO4])^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])^(-7) ([I2])^(-1) ([MnO2])^(-7) ([H2O])^6 ([MnSO4])^7 ([HIO4])^2 = (([H2O])^6 ([MnSO4])^7 ([HIO4])^2)/(([H2SO4])^7 [I2] ([MnO2])^7)

Rate of reaction

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Construct the rate of reaction expression for: H_2SO_4 + I_2 + MnO_2 ⟶ H_2O + MnSO_4 + HIO4 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 + I_2 + 7 MnO_2 ⟶ 6 H_2O + 7 MnSO_4 + 2 HIO4 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 I_2 | 1 | -1 MnO_2 | 7 | -7 H_2O | 6 | 6 MnSO_4 | 7 | 7 HIO4 | 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_2SO_4 | 7 | -7 | -1/7 (Δ[H2SO4])/(Δt) I_2 | 1 | -1 | -(Δ[I2])/(Δt) MnO_2 | 7 | -7 | -1/7 (Δ[MnO2])/(Δt) H_2O | 6 | 6 | 1/6 (Δ[H2O])/(Δt) MnSO_4 | 7 | 7 | 1/7 (Δ[MnSO4])/(Δt) HIO4 | 2 | 2 | 1/2 (Δ[HIO4])/(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) = -(Δ[I2])/(Δt) = -1/7 (Δ[MnO2])/(Δt) = 1/6 (Δ[H2O])/(Δt) = 1/7 (Δ[MnSO4])/(Δt) = 1/2 (Δ[HIO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)