H2O + CrCl3 + (NH4)2S = H2S + NH4Cl + Cr(OH)3

H_2O water + CrCl_3 chromic chloride + (NH_4)_2S diammonium sulfide ⟶ H_2S hydrogen sulfide + NH_4Cl ammonium chloride + Cr(OH)3

Balance the chemical equation algebraically: H_2O + CrCl_3 + (NH_4)_2S ⟶ H_2S + NH_4Cl + Cr(OH)3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 CrCl_3 + c_3 (NH_4)_2S ⟶ c_4 H_2S + c_5 NH_4Cl + 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, Cl, Cr, N and S: H: | 2 c_1 + 8 c_3 = 2 c_4 + 4 c_5 + 3 c_6 O: | c_1 = 3 c_6 Cl: | 3 c_2 = c_5 Cr: | c_2 = c_6 N: | 2 c_3 = c_5 S: | c_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 c_2 = 1 c_3 = 3/2 c_4 = 3/2 c_5 = 3 c_6 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 6 c_2 = 2 c_3 = 3 c_4 = 3 c_5 = 6 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 H_2O + 2 CrCl_3 + 3 (NH_4)_2S ⟶ 3 H_2S + 6 NH_4Cl + 2 Cr(OH)3

+ + ⟶ + + Cr(OH)3

water + chromic chloride + diammonium sulfide ⟶ hydrogen sulfide + ammonium chloride + Cr(OH)3

Construct the equilibrium constant, K, expression for: H_2O + CrCl_3 + (NH_4)_2S ⟶ H_2S + NH_4Cl + 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: 6 H_2O + 2 CrCl_3 + 3 (NH_4)_2S ⟶ 3 H_2S + 6 NH_4Cl + 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 | 6 | -6 CrCl_3 | 2 | -2 (NH_4)_2S | 3 | -3 H_2S | 3 | 3 NH_4Cl | 6 | 6 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 | 6 | -6 | ([H2O])^(-6) CrCl_3 | 2 | -2 | ([CrCl3])^(-2) (NH_4)_2S | 3 | -3 | ([(NH4)2S])^(-3) H_2S | 3 | 3 | ([H2S])^3 NH_4Cl | 6 | 6 | ([NH4Cl])^6 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])^(-6) ([CrCl3])^(-2) ([(NH4)2S])^(-3) ([H2S])^3 ([NH4Cl])^6 ([Cr(OH)3])^2 = (([H2S])^3 ([NH4Cl])^6 ([Cr(OH)3])^2)/(([H2O])^6 ([CrCl3])^2 ([(NH4)2S])^3)

Construct the rate of reaction expression for: H_2O + CrCl_3 + (NH_4)_2S ⟶ H_2S + NH_4Cl + 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: 6 H_2O + 2 CrCl_3 + 3 (NH_4)_2S ⟶ 3 H_2S + 6 NH_4Cl + 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 | 6 | -6 CrCl_3 | 2 | -2 (NH_4)_2S | 3 | -3 H_2S | 3 | 3 NH_4Cl | 6 | 6 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 | 6 | -6 | -1/6 (Δ[H2O])/(Δt) CrCl_3 | 2 | -2 | -1/2 (Δ[CrCl3])/(Δt) (NH_4)_2S | 3 | -3 | -1/3 (Δ[(NH4)2S])/(Δt) H_2S | 3 | 3 | 1/3 (Δ[H2S])/(Δt) NH_4Cl | 6 | 6 | 1/6 (Δ[NH4Cl])/(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 = -1/6 (Δ[H2O])/(Δt) = -1/2 (Δ[CrCl3])/(Δt) = -1/3 (Δ[(NH4)2S])/(Δt) = 1/3 (Δ[H2S])/(Δt) = 1/6 (Δ[NH4Cl])/(Δt) = 1/2 (Δ[Cr(OH)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | chromic chloride | diammonium sulfide | hydrogen sulfide | ammonium chloride | Cr(OH)3 formula | H_2O | CrCl_3 | (NH_4)_2S | H_2S | NH_4Cl | Cr(OH)3 Hill formula | H_2O | Cl_3Cr | H_8N_2S | H_2S | ClH_4N | H3CrO3 name | water | chromic chloride | diammonium sulfide | hydrogen sulfide | ammonium chloride | IUPAC name | water | trichlorochromium | diammonium sulfide | hydrogen sulfide | ammonium chloride |

| water | chromic chloride | diammonium sulfide | hydrogen sulfide | ammonium chloride | Cr(OH)3 molar mass | 18.015 g/mol | 158.3 g/mol | 68.14 g/mol | 34.08 g/mol | 53.49 g/mol | 103.02 g/mol phase | liquid (at STP) | solid (at STP) | liquid (at STP) | gas (at STP) | solid (at STP) | melting point | 0 °C | 1152 °C | -18 °C | -85 °C | 340 °C | boiling point | 99.9839 °C | | | -60 °C | | density | 1 g/cm^3 | 2.87 g/cm^3 | 0.997 g/cm^3 | 0.001393 g/cm^3 (at 25 °C) | 1.5256 g/cm^3 | solubility in water | | slightly soluble | very 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) | | odor | odorless | | | | |