Cl2 + (NH4)2S = S + NH4Cl

Cl_2 chlorine + (NH_4)_2S diammonium sulfide ⟶ S mixed sulfur + NH_4Cl ammonium chloride

Balance the chemical equation algebraically: Cl_2 + (NH_4)_2S ⟶ S + NH_4Cl Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cl_2 + c_2 (NH_4)_2S ⟶ c_3 S + c_4 NH_4Cl Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, N and S: Cl: | 2 c_1 = c_4 H: | 8 c_2 = 4 c_4 N: | 2 c_2 = c_4 S: | 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Cl_2 + (NH_4)_2S ⟶ S + 2 NH_4Cl

+ ⟶ +

chlorine + diammonium sulfide ⟶ mixed sulfur + ammonium chloride

Construct the equilibrium constant, K, expression for: Cl_2 + (NH_4)_2S ⟶ S + NH_4Cl 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: Cl_2 + (NH_4)_2S ⟶ S + 2 NH_4Cl 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 Cl_2 | 1 | -1 (NH_4)_2S | 1 | -1 S | 1 | 1 NH_4Cl | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Cl_2 | 1 | -1 | ([Cl2])^(-1) (NH_4)_2S | 1 | -1 | ([(NH4)2S])^(-1) S | 1 | 1 | [S] NH_4Cl | 2 | 2 | ([NH4Cl])^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 = ([Cl2])^(-1) ([(NH4)2S])^(-1) [S] ([NH4Cl])^2 = ([S] ([NH4Cl])^2)/([Cl2] [(NH4)2S])

Construct the rate of reaction expression for: Cl_2 + (NH_4)_2S ⟶ S + NH_4Cl 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: Cl_2 + (NH_4)_2S ⟶ S + 2 NH_4Cl 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 Cl_2 | 1 | -1 (NH_4)_2S | 1 | -1 S | 1 | 1 NH_4Cl | 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 Cl_2 | 1 | -1 | -(Δ[Cl2])/(Δt) (NH_4)_2S | 1 | -1 | -(Δ[(NH4)2S])/(Δt) S | 1 | 1 | (Δ[S])/(Δt) NH_4Cl | 2 | 2 | 1/2 (Δ[NH4Cl])/(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 = -(Δ[Cl2])/(Δt) = -(Δ[(NH4)2S])/(Δt) = (Δ[S])/(Δt) = 1/2 (Δ[NH4Cl])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| chlorine | diammonium sulfide | mixed sulfur | ammonium chloride formula | Cl_2 | (NH_4)_2S | S | NH_4Cl Hill formula | Cl_2 | H_8N_2S | S | ClH_4N name | chlorine | diammonium sulfide | mixed sulfur | ammonium chloride IUPAC name | molecular chlorine | diammonium sulfide | sulfur | ammonium chloride

| chlorine | diammonium sulfide | mixed sulfur | ammonium chloride molar mass | 70.9 g/mol | 68.14 g/mol | 32.06 g/mol | 53.49 g/mol phase | gas (at STP) | liquid (at STP) | solid (at STP) | solid (at STP) melting point | -101 °C | -18 °C | 112.8 °C | 340 °C boiling point | -34 °C | | 444.7 °C | density | 0.003214 g/cm^3 (at 0 °C) | 0.997 g/cm^3 | 2.07 g/cm^3 | 1.5256 g/cm^3 solubility in water | | very soluble | | soluble