H2SO4 + BaCe2 = Ba(SO4) + H2Ce2

H_2SO_4 sulfuric acid + BaCe2 ⟶ BaSO_4 barium sulfate + H2Ce2

Balance the chemical equation algebraically: H_2SO_4 + BaCe2 ⟶ BaSO_4 + H2Ce2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 BaCe2 ⟶ c_3 BaSO_4 + c_4 H2Ce2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Ba and Ce: H: | 2 c_1 = 2 c_4 O: | 4 c_1 = 4 c_3 S: | c_1 = c_3 Ba: | c_2 = c_3 Ce: | 2 c_2 = 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2SO_4 + BaCe2 ⟶ BaSO_4 + H2Ce2

+ BaCe2 ⟶ + H2Ce2

sulfuric acid + BaCe2 ⟶ barium sulfate + H2Ce2

Construct the equilibrium constant, K, expression for: H_2SO_4 + BaCe2 ⟶ BaSO_4 + H2Ce2 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: H_2SO_4 + BaCe2 ⟶ BaSO_4 + H2Ce2 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 | 1 | -1 BaCe2 | 1 | -1 BaSO_4 | 1 | 1 H2Ce2 | 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 | 1 | -1 | ([H2SO4])^(-1) BaCe2 | 1 | -1 | ([BaCe2])^(-1) BaSO_4 | 1 | 1 | [BaSO4] H2Ce2 | 1 | 1 | [H2Ce2] 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])^(-1) ([BaCe2])^(-1) [BaSO4] [H2Ce2] = ([BaSO4] [H2Ce2])/([H2SO4] [BaCe2])

Construct the rate of reaction expression for: H_2SO_4 + BaCe2 ⟶ BaSO_4 + H2Ce2 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: H_2SO_4 + BaCe2 ⟶ BaSO_4 + H2Ce2 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 | 1 | -1 BaCe2 | 1 | -1 BaSO_4 | 1 | 1 H2Ce2 | 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 | 1 | -1 | -(Δ[H2SO4])/(Δt) BaCe2 | 1 | -1 | -(Δ[BaCe2])/(Δt) BaSO_4 | 1 | 1 | (Δ[BaSO4])/(Δt) H2Ce2 | 1 | 1 | (Δ[H2Ce2])/(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 = -(Δ[H2SO4])/(Δt) = -(Δ[BaCe2])/(Δt) = (Δ[BaSO4])/(Δt) = (Δ[H2Ce2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | BaCe2 | barium sulfate | H2Ce2 formula | H_2SO_4 | BaCe2 | BaSO_4 | H2Ce2 Hill formula | H_2O_4S | BaCe2 | BaO_4S | H2Ce2 name | sulfuric acid | | barium sulfate | IUPAC name | sulfuric acid | | barium(+2) cation sulfate |

| sulfuric acid | BaCe2 | barium sulfate | H2Ce2 molar mass | 98.07 g/mol | 417.559 g/mol | 233.38 g/mol | 282.248 g/mol phase | liquid (at STP) | | solid (at STP) | melting point | 10.371 °C | | 1345 °C | boiling point | 279.6 °C | | | density | 1.8305 g/cm^3 | | 4.5 g/cm^3 | solubility in water | very soluble | | insoluble | surface tension | 0.0735 N/m | | | dynamic viscosity | 0.021 Pa s (at 25 °C) | | | odor | odorless | | |