H2SO4 + Co2O3 = H2O + O2 + CoSO4

H_2SO_4 sulfuric acid + O_3Co_2 cobalt(III) oxide ⟶ H_2O water + O_2 oxygen + CoSO_4 cobalt(II) sulfate

Balance the chemical equation algebraically: H_2SO_4 + O_3Co_2 ⟶ H_2O + O_2 + CoSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 O_3Co_2 ⟶ c_3 H_2O + c_4 O_2 + c_5 CoSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S and Co: H: | 2 c_1 = 2 c_3 O: | 4 c_1 + 3 c_2 = c_3 + 2 c_4 + 4 c_5 S: | c_1 = c_5 Co: | 2 c_2 = 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 4 c_2 = 2 c_3 = 4 c_4 = 1 c_5 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 H_2SO_4 + 2 O_3Co_2 ⟶ 4 H_2O + O_2 + 4 CoSO_4

+ ⟶ + +

sulfuric acid + cobalt(III) oxide ⟶ water + oxygen + cobalt(II) sulfate

Construct the equilibrium constant, K, expression for: H_2SO_4 + O_3Co_2 ⟶ H_2O + O_2 + CoSO_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: 4 H_2SO_4 + 2 O_3Co_2 ⟶ 4 H_2O + O_2 + 4 CoSO_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_2SO_4 | 4 | -4 O_3Co_2 | 2 | -2 H_2O | 4 | 4 O_2 | 1 | 1 CoSO_4 | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 4 | -4 | ([H2SO4])^(-4) O_3Co_2 | 2 | -2 | ([O3Co2])^(-2) H_2O | 4 | 4 | ([H2O])^4 O_2 | 1 | 1 | [O2] CoSO_4 | 4 | 4 | ([CoSO4])^4 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])^(-4) ([O3Co2])^(-2) ([H2O])^4 [O2] ([CoSO4])^4 = (([H2O])^4 [O2] ([CoSO4])^4)/(([H2SO4])^4 ([O3Co2])^2)

Construct the rate of reaction expression for: H_2SO_4 + O_3Co_2 ⟶ H_2O + O_2 + CoSO_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: 4 H_2SO_4 + 2 O_3Co_2 ⟶ 4 H_2O + O_2 + 4 CoSO_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_2SO_4 | 4 | -4 O_3Co_2 | 2 | -2 H_2O | 4 | 4 O_2 | 1 | 1 CoSO_4 | 4 | 4 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 | 4 | -4 | -1/4 (Δ[H2SO4])/(Δt) O_3Co_2 | 2 | -2 | -1/2 (Δ[O3Co2])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) O_2 | 1 | 1 | (Δ[O2])/(Δt) CoSO_4 | 4 | 4 | 1/4 (Δ[CoSO4])/(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 = -1/4 (Δ[H2SO4])/(Δt) = -1/2 (Δ[O3Co2])/(Δt) = 1/4 (Δ[H2O])/(Δt) = (Δ[O2])/(Δt) = 1/4 (Δ[CoSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | cobalt(III) oxide | water | oxygen | cobalt(II) sulfate formula | H_2SO_4 | O_3Co_2 | H_2O | O_2 | CoSO_4 Hill formula | H_2O_4S | Co_2O_3 | H_2O | O_2 | CoO_4S name | sulfuric acid | cobalt(III) oxide | water | oxygen | cobalt(II) sulfate IUPAC name | sulfuric acid | oxo(oxocobaltiooxy)cobalt | water | molecular oxygen | cobalt(+2) cation sulfate

| sulfuric acid | cobalt(III) oxide | water | oxygen | cobalt(II) sulfate molar mass | 98.07 g/mol | 165.863 g/mol | 18.015 g/mol | 31.998 g/mol | 154.99 g/mol phase | liquid (at STP) | | liquid (at STP) | gas (at STP) | melting point | 10.371 °C | | 0 °C | -218 °C | boiling point | 279.6 °C | | 99.9839 °C | -183 °C | density | 1.8305 g/cm^3 | | 1 g/cm^3 | 0.001429 g/cm^3 (at 0 °C) | 1.948 g/cm^3 solubility in water | very soluble | | | | surface tension | 0.0735 N/m | | 0.0728 N/m | 0.01347 N/m | dynamic viscosity | 0.021 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | 2.055×10^-5 Pa s (at 25 °C) | odor | odorless | | odorless | odorless |