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H2O2 + Ce(SO4)2 = H2SO4 + O2 + Ce2(SO4)3

Input interpretation

H_2O_2 hydrogen peroxide + Ce(SO_4)_2 ceric sulfate ⟶ H_2SO_4 sulfuric acid + O_2 oxygen + Ce_2(SO_4)_3 cerium(III) sulfate
H_2O_2 hydrogen peroxide + Ce(SO_4)_2 ceric sulfate ⟶ H_2SO_4 sulfuric acid + O_2 oxygen + Ce_2(SO_4)_3 cerium(III) sulfate

Balanced equation

Balance the chemical equation algebraically: H_2O_2 + Ce(SO_4)_2 ⟶ H_2SO_4 + O_2 + Ce_2(SO_4)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O_2 + c_2 Ce(SO_4)_2 ⟶ c_3 H_2SO_4 + c_4 O_2 + c_5 Ce_2(SO_4)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Ce and S: H: | 2 c_1 = 2 c_3 O: | 2 c_1 + 8 c_2 = 4 c_3 + 2 c_4 + 12 c_5 Ce: | c_2 = 2 c_5 S: | 2 c_2 = c_3 + 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 2 c_3 = 1 c_4 = 1 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2O_2 + 2 Ce(SO_4)_2 ⟶ H_2SO_4 + O_2 + Ce_2(SO_4)_3
Balance the chemical equation algebraically: H_2O_2 + Ce(SO_4)_2 ⟶ H_2SO_4 + O_2 + Ce_2(SO_4)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O_2 + c_2 Ce(SO_4)_2 ⟶ c_3 H_2SO_4 + c_4 O_2 + c_5 Ce_2(SO_4)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Ce and S: H: | 2 c_1 = 2 c_3 O: | 2 c_1 + 8 c_2 = 4 c_3 + 2 c_4 + 12 c_5 Ce: | c_2 = 2 c_5 S: | 2 c_2 = c_3 + 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 2 c_3 = 1 c_4 = 1 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2O_2 + 2 Ce(SO_4)_2 ⟶ H_2SO_4 + O_2 + Ce_2(SO_4)_3

Structures

+ ⟶ + +
+ ⟶ + +

Names

hydrogen peroxide + ceric sulfate ⟶ sulfuric acid + oxygen + cerium(III) sulfate
hydrogen peroxide + ceric sulfate ⟶ sulfuric acid + oxygen + cerium(III) sulfate

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2O_2 + Ce(SO_4)_2 ⟶ H_2SO_4 + O_2 + Ce_2(SO_4)_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: H_2O_2 + 2 Ce(SO_4)_2 ⟶ H_2SO_4 + O_2 + Ce_2(SO_4)_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_2O_2 | 1 | -1 Ce(SO_4)_2 | 2 | -2 H_2SO_4 | 1 | 1 O_2 | 1 | 1 Ce_2(SO_4)_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_2O_2 | 1 | -1 | ([H2O2])^(-1) Ce(SO_4)_2 | 2 | -2 | ([Ce(SO4)2])^(-2) H_2SO_4 | 1 | 1 | [H2SO4] O_2 | 1 | 1 | [O2] Ce_2(SO_4)_3 | 1 | 1 | [Ce2(SO4)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 = ([H2O2])^(-1) ([Ce(SO4)2])^(-2) [H2SO4] [O2] [Ce2(SO4)3] = ([H2SO4] [O2] [Ce2(SO4)3])/([H2O2] ([Ce(SO4)2])^2)
Construct the equilibrium constant, K, expression for: H_2O_2 + Ce(SO_4)_2 ⟶ H_2SO_4 + O_2 + Ce_2(SO_4)_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: H_2O_2 + 2 Ce(SO_4)_2 ⟶ H_2SO_4 + O_2 + Ce_2(SO_4)_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_2O_2 | 1 | -1 Ce(SO_4)_2 | 2 | -2 H_2SO_4 | 1 | 1 O_2 | 1 | 1 Ce_2(SO_4)_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_2O_2 | 1 | -1 | ([H2O2])^(-1) Ce(SO_4)_2 | 2 | -2 | ([Ce(SO4)2])^(-2) H_2SO_4 | 1 | 1 | [H2SO4] O_2 | 1 | 1 | [O2] Ce_2(SO_4)_3 | 1 | 1 | [Ce2(SO4)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 = ([H2O2])^(-1) ([Ce(SO4)2])^(-2) [H2SO4] [O2] [Ce2(SO4)3] = ([H2SO4] [O2] [Ce2(SO4)3])/([H2O2] ([Ce(SO4)2])^2)

Rate of reaction

Construct the rate of reaction expression for: H_2O_2 + Ce(SO_4)_2 ⟶ H_2SO_4 + O_2 + Ce_2(SO_4)_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: H_2O_2 + 2 Ce(SO_4)_2 ⟶ H_2SO_4 + O_2 + Ce_2(SO_4)_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_2O_2 | 1 | -1 Ce(SO_4)_2 | 2 | -2 H_2SO_4 | 1 | 1 O_2 | 1 | 1 Ce_2(SO_4)_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_2O_2 | 1 | -1 | -(Δ[H2O2])/(Δt) Ce(SO_4)_2 | 2 | -2 | -1/2 (Δ[Ce(SO4)2])/(Δt) H_2SO_4 | 1 | 1 | (Δ[H2SO4])/(Δt) O_2 | 1 | 1 | (Δ[O2])/(Δt) Ce_2(SO_4)_3 | 1 | 1 | (Δ[Ce2(SO4)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 = -(Δ[H2O2])/(Δt) = -1/2 (Δ[Ce(SO4)2])/(Δt) = (Δ[H2SO4])/(Δt) = (Δ[O2])/(Δt) = (Δ[Ce2(SO4)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2O_2 + Ce(SO_4)_2 ⟶ H_2SO_4 + O_2 + Ce_2(SO_4)_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: H_2O_2 + 2 Ce(SO_4)_2 ⟶ H_2SO_4 + O_2 + Ce_2(SO_4)_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_2O_2 | 1 | -1 Ce(SO_4)_2 | 2 | -2 H_2SO_4 | 1 | 1 O_2 | 1 | 1 Ce_2(SO_4)_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_2O_2 | 1 | -1 | -(Δ[H2O2])/(Δt) Ce(SO_4)_2 | 2 | -2 | -1/2 (Δ[Ce(SO4)2])/(Δt) H_2SO_4 | 1 | 1 | (Δ[H2SO4])/(Δt) O_2 | 1 | 1 | (Δ[O2])/(Δt) Ce_2(SO_4)_3 | 1 | 1 | (Δ[Ce2(SO4)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 = -(Δ[H2O2])/(Δt) = -1/2 (Δ[Ce(SO4)2])/(Δt) = (Δ[H2SO4])/(Δt) = (Δ[O2])/(Δt) = (Δ[Ce2(SO4)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| hydrogen peroxide | ceric sulfate | sulfuric acid | oxygen | cerium(III) sulfate formula | H_2O_2 | Ce(SO_4)_2 | H_2SO_4 | O_2 | Ce_2(SO_4)_3 Hill formula | H_2O_2 | CeO_8S_2 | H_2O_4S | O_2 | Ce_2O_12S_3 name | hydrogen peroxide | ceric sulfate | sulfuric acid | oxygen | cerium(III) sulfate IUPAC name | hydrogen peroxide | cerium(+4) cation disulfate | sulfuric acid | molecular oxygen | cerium(+3) cation trisulfate
| hydrogen peroxide | ceric sulfate | sulfuric acid | oxygen | cerium(III) sulfate formula | H_2O_2 | Ce(SO_4)_2 | H_2SO_4 | O_2 | Ce_2(SO_4)_3 Hill formula | H_2O_2 | CeO_8S_2 | H_2O_4S | O_2 | Ce_2O_12S_3 name | hydrogen peroxide | ceric sulfate | sulfuric acid | oxygen | cerium(III) sulfate IUPAC name | hydrogen peroxide | cerium(+4) cation disulfate | sulfuric acid | molecular oxygen | cerium(+3) cation trisulfate

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