(NH4)2S + CoCl3 = NH4Cl + Co2S3

(NH_4)_2S diammonium sulfide + CoCl3 ⟶ NH_4Cl ammonium chloride + Co2S3

Balance the chemical equation algebraically: (NH_4)_2S + CoCl3 ⟶ NH_4Cl + Co2S3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 (NH_4)_2S + c_2 CoCl3 ⟶ c_3 NH_4Cl + c_4 Co2S3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, S, Co and Cl: H: | 8 c_1 = 4 c_3 N: | 2 c_1 = c_3 S: | c_1 = 3 c_4 Co: | c_2 = 2 c_4 Cl: | 3 c_2 = c_3 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 (NH_4)_2S + 2 CoCl3 ⟶ 6 NH_4Cl + Co2S3

+ CoCl3 ⟶ + Co2S3

diammonium sulfide + CoCl3 ⟶ ammonium chloride + Co2S3

Construct the equilibrium constant, K, expression for: (NH_4)_2S + CoCl3 ⟶ NH_4Cl + Co2S3 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 (NH_4)_2S + 2 CoCl3 ⟶ 6 NH_4Cl + Co2S3 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 (NH_4)_2S | 3 | -3 CoCl3 | 2 | -2 NH_4Cl | 6 | 6 Co2S3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression (NH_4)_2S | 3 | -3 | ([(NH4)2S])^(-3) CoCl3 | 2 | -2 | ([CoCl3])^(-2) NH_4Cl | 6 | 6 | ([NH4Cl])^6 Co2S3 | 1 | 1 | [Co2S3] 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 = ([(NH4)2S])^(-3) ([CoCl3])^(-2) ([NH4Cl])^6 [Co2S3] = (([NH4Cl])^6 [Co2S3])/(([(NH4)2S])^3 ([CoCl3])^2)

Construct the rate of reaction expression for: (NH_4)_2S + CoCl3 ⟶ NH_4Cl + Co2S3 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 (NH_4)_2S + 2 CoCl3 ⟶ 6 NH_4Cl + Co2S3 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 (NH_4)_2S | 3 | -3 CoCl3 | 2 | -2 NH_4Cl | 6 | 6 Co2S3 | 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 (NH_4)_2S | 3 | -3 | -1/3 (Δ[(NH4)2S])/(Δt) CoCl3 | 2 | -2 | -1/2 (Δ[CoCl3])/(Δt) NH_4Cl | 6 | 6 | 1/6 (Δ[NH4Cl])/(Δt) Co2S3 | 1 | 1 | (Δ[Co2S3])/(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[(NH4)2S])/(Δt) = -1/2 (Δ[CoCl3])/(Δt) = 1/6 (Δ[NH4Cl])/(Δt) = (Δ[Co2S3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| diammonium sulfide | CoCl3 | ammonium chloride | Co2S3 formula | (NH_4)_2S | CoCl3 | NH_4Cl | Co2S3 Hill formula | H_8N_2S | Cl3Co | ClH_4N | Co2S3 name | diammonium sulfide | | ammonium chloride |

| diammonium sulfide | CoCl3 | ammonium chloride | Co2S3 molar mass | 68.14 g/mol | 165.3 g/mol | 53.49 g/mol | 214 g/mol phase | liquid (at STP) | | solid (at STP) | melting point | -18 °C | | 340 °C | density | 0.997 g/cm^3 | | 1.5256 g/cm^3 | solubility in water | very soluble | | soluble |