H2CO3 + Sc2(SO4)3 = H2SO4 + Sc2(CO3)3

Input interpretation

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H_2CO_3 carbonic acid + Sc2(SO4)3 ⟶ H_2SO_4 sulfuric acid + Sc2(CO3)3

Balanced equation

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Balance the chemical equation algebraically: H_2CO_3 + Sc2(SO4)3 ⟶ H_2SO_4 + Sc2(CO3)3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2CO_3 + c_2 Sc2(SO4)3 ⟶ c_3 H_2SO_4 + c_4 Sc2(CO3)3 Set the number of atoms in the reactants equal to the number of atoms in the products for C, H, O, Sc and S: C: | c_1 = 3 c_4 H: | 2 c_1 = 2 c_3 O: | 3 c_1 + 12 c_2 = 4 c_3 + 9 c_4 Sc: | 2 c_2 = 2 c_4 S: | 3 c_2 = c_3 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 = 3 c_2 = 1 c_3 = 3 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2CO_3 + Sc2(SO4)3 ⟶ 3 H_2SO_4 + Sc2(CO3)3

+ Sc2(SO4)3 ⟶ + Sc2(CO3)3

Names

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carbonic acid + Sc2(SO4)3 ⟶ sulfuric acid + Sc2(CO3)3

Equilibrium constant

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Construct the equilibrium constant, K, expression for: H_2CO_3 + Sc2(SO4)3 ⟶ H_2SO_4 + Sc2(CO3)3 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: 3 H_2CO_3 + Sc2(SO4)3 ⟶ 3 H_2SO_4 + Sc2(CO3)3 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_2CO_3 | 3 | -3 Sc2(SO4)3 | 1 | -1 H_2SO_4 | 3 | 3 Sc2(CO3)3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2CO_3 | 3 | -3 | ([H2CO3])^(-3) Sc2(SO4)3 | 1 | -1 | ([Sc2(SO4)3])^(-1) H_2SO_4 | 3 | 3 | ([H2SO4])^3 Sc2(CO3)3 | 1 | 1 | [Sc2(CO3)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 = ([H2CO3])^(-3) ([Sc2(SO4)3])^(-1) ([H2SO4])^3 [Sc2(CO3)3] = (([H2SO4])^3 [Sc2(CO3)3])/(([H2CO3])^3 [Sc2(SO4)3])

Rate of reaction

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Construct the rate of reaction expression for: H_2CO_3 + Sc2(SO4)3 ⟶ H_2SO_4 + Sc2(CO3)3 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: 3 H_2CO_3 + Sc2(SO4)3 ⟶ 3 H_2SO_4 + Sc2(CO3)3 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_2CO_3 | 3 | -3 Sc2(SO4)3 | 1 | -1 H_2SO_4 | 3 | 3 Sc2(CO3)3 | 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_2CO_3 | 3 | -3 | -1/3 (Δ[H2CO3])/(Δt) Sc2(SO4)3 | 1 | -1 | -(Δ[Sc2(SO4)3])/(Δt) H_2SO_4 | 3 | 3 | 1/3 (Δ[H2SO4])/(Δt) Sc2(CO3)3 | 1 | 1 | (Δ[Sc2(CO3)3])/(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 = -1/3 (Δ[H2CO3])/(Δt) = -(Δ[Sc2(SO4)3])/(Δt) = 1/3 (Δ[H2SO4])/(Δt) = (Δ[Sc2(CO3)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)