H2SO4 + Cr = H2O + H2S + Cr2(SO4)3

H_2SO_4 sulfuric acid + Cr chromium ⟶ H_2O water + H_2S hydrogen sulfide + Cr_2(SO_4)_3 chromium sulfate

Balance the chemical equation algebraically: H_2SO_4 + Cr ⟶ H_2O + H_2S + Cr_2(SO_4)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 Cr ⟶ c_3 H_2O + c_4 H_2S + c_5 Cr_2(SO_4)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S and Cr: H: | 2 c_1 = 2 c_3 + 2 c_4 O: | 4 c_1 = c_3 + 12 c_5 S: | c_1 = c_4 + 3 c_5 Cr: | c_2 = 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 = 5 c_2 = 8/3 c_3 = 4 c_4 = 1 c_5 = 4/3 Multiply by the least common denominator, 3, to eliminate fractional coefficients: c_1 = 15 c_2 = 8 c_3 = 12 c_4 = 3 c_5 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 15 H_2SO_4 + 8 Cr ⟶ 12 H_2O + 3 H_2S + 4 Cr_2(SO_4)_3

+ ⟶ + +

sulfuric acid + chromium ⟶ water + hydrogen sulfide + chromium sulfate

Construct the equilibrium constant, K, expression for: H_2SO_4 + Cr ⟶ H_2O + H_2S + Cr_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: 15 H_2SO_4 + 8 Cr ⟶ 12 H_2O + 3 H_2S + 4 Cr_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_2SO_4 | 15 | -15 Cr | 8 | -8 H_2O | 12 | 12 H_2S | 3 | 3 Cr_2(SO_4)_3 | 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 | 15 | -15 | ([H2SO4])^(-15) Cr | 8 | -8 | ([Cr])^(-8) H_2O | 12 | 12 | ([H2O])^12 H_2S | 3 | 3 | ([H2S])^3 Cr_2(SO_4)_3 | 4 | 4 | ([Cr2(SO4)3])^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])^(-15) ([Cr])^(-8) ([H2O])^12 ([H2S])^3 ([Cr2(SO4)3])^4 = (([H2O])^12 ([H2S])^3 ([Cr2(SO4)3])^4)/(([H2SO4])^15 ([Cr])^8)

Construct the rate of reaction expression for: H_2SO_4 + Cr ⟶ H_2O + H_2S + Cr_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: 15 H_2SO_4 + 8 Cr ⟶ 12 H_2O + 3 H_2S + 4 Cr_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_2SO_4 | 15 | -15 Cr | 8 | -8 H_2O | 12 | 12 H_2S | 3 | 3 Cr_2(SO_4)_3 | 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 | 15 | -15 | -1/15 (Δ[H2SO4])/(Δt) Cr | 8 | -8 | -1/8 (Δ[Cr])/(Δt) H_2O | 12 | 12 | 1/12 (Δ[H2O])/(Δt) H_2S | 3 | 3 | 1/3 (Δ[H2S])/(Δt) Cr_2(SO_4)_3 | 4 | 4 | 1/4 (Δ[Cr2(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 = -1/15 (Δ[H2SO4])/(Δt) = -1/8 (Δ[Cr])/(Δt) = 1/12 (Δ[H2O])/(Δt) = 1/3 (Δ[H2S])/(Δt) = 1/4 (Δ[Cr2(SO4)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | chromium | water | hydrogen sulfide | chromium sulfate formula | H_2SO_4 | Cr | H_2O | H_2S | Cr_2(SO_4)_3 Hill formula | H_2O_4S | Cr | H_2O | H_2S | Cr_2O_12S_3 name | sulfuric acid | chromium | water | hydrogen sulfide | chromium sulfate IUPAC name | sulfuric acid | chromium | water | hydrogen sulfide | chromium(+3) cation trisulfate

| sulfuric acid | chromium | water | hydrogen sulfide | chromium sulfate molar mass | 98.07 g/mol | 51.9961 g/mol | 18.015 g/mol | 34.08 g/mol | 392.2 g/mol phase | liquid (at STP) | solid (at STP) | liquid (at STP) | gas (at STP) | liquid (at STP) melting point | 10.371 °C | 1857 °C | 0 °C | -85 °C | boiling point | 279.6 °C | 2672 °C | 99.9839 °C | -60 °C | 330 °C density | 1.8305 g/cm^3 | 7.14 g/cm^3 | 1 g/cm^3 | 0.001393 g/cm^3 (at 25 °C) | 1.84 g/cm^3 solubility in water | very soluble | insoluble | | | surface tension | 0.0735 N/m | | 0.0728 N/m | | dynamic viscosity | 0.021 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | 1.239×10^-5 Pa s (at 25 °C) | odor | odorless | odorless | odorless | | odorless