H2S + CrO3 = S + Cr(OH)3

H_2S hydrogen sulfide + CrO_3 chromium trioxide ⟶ S mixed sulfur + Cr(OH)3

Balance the chemical equation algebraically: H_2S + CrO_3 ⟶ S + Cr(OH)3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2S + c_2 CrO_3 ⟶ c_3 S + c_4 Cr(OH)3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, S, Cr and O: H: | 2 c_1 = 3 c_4 S: | c_1 = c_3 Cr: | c_2 = c_4 O: | 3 c_2 = 3 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3/2 c_2 = 1 c_3 = 3/2 c_4 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 3 c_2 = 2 c_3 = 3 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2S + 2 CrO_3 ⟶ 3 S + 2 Cr(OH)3

+ ⟶ + Cr(OH)3

hydrogen sulfide + chromium trioxide ⟶ mixed sulfur + Cr(OH)3

Construct the equilibrium constant, K, expression for: H_2S + CrO_3 ⟶ S + Cr(OH)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_2S + 2 CrO_3 ⟶ 3 S + 2 Cr(OH)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_2S | 3 | -3 CrO_3 | 2 | -2 S | 3 | 3 Cr(OH)3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2S | 3 | -3 | ([H2S])^(-3) CrO_3 | 2 | -2 | ([CrO3])^(-2) S | 3 | 3 | ([S])^3 Cr(OH)3 | 2 | 2 | ([Cr(OH)3])^2 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 = ([H2S])^(-3) ([CrO3])^(-2) ([S])^3 ([Cr(OH)3])^2 = (([S])^3 ([Cr(OH)3])^2)/(([H2S])^3 ([CrO3])^2)

Construct the rate of reaction expression for: H_2S + CrO_3 ⟶ S + Cr(OH)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_2S + 2 CrO_3 ⟶ 3 S + 2 Cr(OH)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_2S | 3 | -3 CrO_3 | 2 | -2 S | 3 | 3 Cr(OH)3 | 2 | 2 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_2S | 3 | -3 | -1/3 (Δ[H2S])/(Δt) CrO_3 | 2 | -2 | -1/2 (Δ[CrO3])/(Δt) S | 3 | 3 | 1/3 (Δ[S])/(Δt) Cr(OH)3 | 2 | 2 | 1/2 (Δ[Cr(OH)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[H2S])/(Δt) = -1/2 (Δ[CrO3])/(Δt) = 1/3 (Δ[S])/(Δt) = 1/2 (Δ[Cr(OH)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen sulfide | chromium trioxide | mixed sulfur | Cr(OH)3 formula | H_2S | CrO_3 | S | Cr(OH)3 Hill formula | H_2S | CrO_3 | S | H3CrO3 name | hydrogen sulfide | chromium trioxide | mixed sulfur | IUPAC name | hydrogen sulfide | trioxochromium | sulfur |

| hydrogen sulfide | chromium trioxide | mixed sulfur | Cr(OH)3 molar mass | 34.08 g/mol | 99.993 g/mol | 32.06 g/mol | 103.02 g/mol phase | gas (at STP) | solid (at STP) | solid (at STP) | melting point | -85 °C | 196 °C | 112.8 °C | boiling point | -60 °C | | 444.7 °C | density | 0.001393 g/cm^3 (at 25 °C) | | 2.07 g/cm^3 | solubility in water | | very soluble | | dynamic viscosity | 1.239×10^-5 Pa s (at 25 °C) | | | odor | | odorless | |