H2O + H2S + K2CrO4 = S + KOH + Cr(OH)3

H_2O water + H_2S hydrogen sulfide + K_2CrO_4 potassium chromate ⟶ S mixed sulfur + KOH potassium hydroxide + Cr(OH)3

Balance the chemical equation algebraically: H_2O + H_2S + K_2CrO_4 ⟶ S + KOH + Cr(OH)3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 H_2S + c_3 K_2CrO_4 ⟶ c_4 S + c_5 KOH + c_6 Cr(OH)3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Cr and K: H: | 2 c_1 + 2 c_2 = c_5 + 3 c_6 O: | c_1 + 4 c_3 = c_5 + 3 c_6 S: | c_2 = c_4 Cr: | c_3 = c_6 K: | 2 c_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 = 3/2 c_3 = 1 c_4 = 3/2 c_5 = 2 c_6 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 2 c_2 = 3 c_3 = 2 c_4 = 3 c_5 = 4 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2O + 3 H_2S + 2 K_2CrO_4 ⟶ 3 S + 4 KOH + 2 Cr(OH)3

+ + ⟶ + + Cr(OH)3

water + hydrogen sulfide + potassium chromate ⟶ mixed sulfur + potassium hydroxide + Cr(OH)3

Construct the equilibrium constant, K, expression for: H_2O + H_2S + K_2CrO_4 ⟶ S + KOH + 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: 2 H_2O + 3 H_2S + 2 K_2CrO_4 ⟶ 3 S + 4 KOH + 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_2O | 2 | -2 H_2S | 3 | -3 K_2CrO_4 | 2 | -2 S | 3 | 3 KOH | 4 | 4 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_2O | 2 | -2 | ([H2O])^(-2) H_2S | 3 | -3 | ([H2S])^(-3) K_2CrO_4 | 2 | -2 | ([K2CrO4])^(-2) S | 3 | 3 | ([S])^3 KOH | 4 | 4 | ([KOH])^4 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 = ([H2O])^(-2) ([H2S])^(-3) ([K2CrO4])^(-2) ([S])^3 ([KOH])^4 ([Cr(OH)3])^2 = (([S])^3 ([KOH])^4 ([Cr(OH)3])^2)/(([H2O])^2 ([H2S])^3 ([K2CrO4])^2)

Construct the rate of reaction expression for: H_2O + H_2S + K_2CrO_4 ⟶ S + KOH + 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: 2 H_2O + 3 H_2S + 2 K_2CrO_4 ⟶ 3 S + 4 KOH + 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_2O | 2 | -2 H_2S | 3 | -3 K_2CrO_4 | 2 | -2 S | 3 | 3 KOH | 4 | 4 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_2O | 2 | -2 | -1/2 (Δ[H2O])/(Δt) H_2S | 3 | -3 | -1/3 (Δ[H2S])/(Δt) K_2CrO_4 | 2 | -2 | -1/2 (Δ[K2CrO4])/(Δt) S | 3 | 3 | 1/3 (Δ[S])/(Δt) KOH | 4 | 4 | 1/4 (Δ[KOH])/(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 = -1/2 (Δ[H2O])/(Δt) = -1/3 (Δ[H2S])/(Δt) = -1/2 (Δ[K2CrO4])/(Δt) = 1/3 (Δ[S])/(Δt) = 1/4 (Δ[KOH])/(Δt) = 1/2 (Δ[Cr(OH)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | hydrogen sulfide | potassium chromate | mixed sulfur | potassium hydroxide | Cr(OH)3 formula | H_2O | H_2S | K_2CrO_4 | S | KOH | Cr(OH)3 Hill formula | H_2O | H_2S | CrK_2O_4 | S | HKO | H3CrO3 name | water | hydrogen sulfide | potassium chromate | mixed sulfur | potassium hydroxide | IUPAC name | water | hydrogen sulfide | dipotassium dioxido-dioxochromium | sulfur | potassium hydroxide |

| water | hydrogen sulfide | potassium chromate | mixed sulfur | potassium hydroxide | Cr(OH)3 molar mass | 18.015 g/mol | 34.08 g/mol | 194.19 g/mol | 32.06 g/mol | 56.105 g/mol | 103.02 g/mol phase | liquid (at STP) | gas (at STP) | solid (at STP) | solid (at STP) | solid (at STP) | melting point | 0 °C | -85 °C | 971 °C | 112.8 °C | 406 °C | boiling point | 99.9839 °C | -60 °C | | 444.7 °C | 1327 °C | density | 1 g/cm^3 | 0.001393 g/cm^3 (at 25 °C) | 2.73 g/cm^3 | 2.07 g/cm^3 | 2.044 g/cm^3 | solubility in water | | | soluble | | soluble | surface tension | 0.0728 N/m | | | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | 1.239×10^-5 Pa s (at 25 °C) | | | 0.001 Pa s (at 550 °C) | odor | odorless | | odorless | | |