H2S + CrCl3 = HCl + Cr2S3

H_2S hydrogen sulfide + CrCl_3 chromic chloride ⟶ HCl hydrogen chloride + Cr_2S_3 chromium(III) sulfide

Balance the chemical equation algebraically: H_2S + CrCl_3 ⟶ HCl + Cr_2S_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2S + c_2 CrCl_3 ⟶ c_3 HCl + c_4 Cr_2S_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, S, Cl and Cr: H: | 2 c_1 = c_3 S: | c_1 = 3 c_4 Cl: | 3 c_2 = c_3 Cr: | c_2 = 2 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 6 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2S + 2 CrCl_3 ⟶ 6 HCl + Cr_2S_3

+ ⟶ +

hydrogen sulfide + chromic chloride ⟶ hydrogen chloride + chromium(III) sulfide

Construct the equilibrium constant, K, expression for: H_2S + CrCl_3 ⟶ HCl + Cr_2S_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 CrCl_3 ⟶ 6 HCl + Cr_2S_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 CrCl_3 | 2 | -2 HCl | 6 | 6 Cr_2S_3 | 1 | 1 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) CrCl_3 | 2 | -2 | ([CrCl3])^(-2) HCl | 6 | 6 | ([HCl])^6 Cr_2S_3 | 1 | 1 | [Cr2S3] 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) ([CrCl3])^(-2) ([HCl])^6 [Cr2S3] = (([HCl])^6 [Cr2S3])/(([H2S])^3 ([CrCl3])^2)

Construct the rate of reaction expression for: H_2S + CrCl_3 ⟶ HCl + Cr_2S_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 CrCl_3 ⟶ 6 HCl + Cr_2S_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 CrCl_3 | 2 | -2 HCl | 6 | 6 Cr_2S_3 | 1 | 1 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) CrCl_3 | 2 | -2 | -1/2 (Δ[CrCl3])/(Δt) HCl | 6 | 6 | 1/6 (Δ[HCl])/(Δt) Cr_2S_3 | 1 | 1 | (Δ[Cr2S3])/(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[CrCl3])/(Δt) = 1/6 (Δ[HCl])/(Δt) = (Δ[Cr2S3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen sulfide | chromic chloride | hydrogen chloride | chromium(III) sulfide formula | H_2S | CrCl_3 | HCl | Cr_2S_3 Hill formula | H_2S | Cl_3Cr | ClH | Cr_2S_3 name | hydrogen sulfide | chromic chloride | hydrogen chloride | chromium(III) sulfide IUPAC name | hydrogen sulfide | trichlorochromium | hydrogen chloride | chromium(+3) cation trisulfide