Cl2 + Na2S = S + NaCl

Cl_2 chlorine + Na_2S sodium sulfide ⟶ S mixed sulfur + NaCl sodium chloride

Balance the chemical equation algebraically: Cl_2 + Na_2S ⟶ S + NaCl Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cl_2 + c_2 Na_2S ⟶ c_3 S + c_4 NaCl Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, Na and S: Cl: | 2 c_1 = c_4 Na: | 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 + Na_2S ⟶ S + 2 NaCl

+ ⟶ +

chlorine + sodium sulfide ⟶ mixed sulfur + sodium chloride

Construct the equilibrium constant, K, expression for: Cl_2 + Na_2S ⟶ S + NaCl 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 + Na_2S ⟶ S + 2 NaCl 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 Na_2S | 1 | -1 S | 1 | 1 NaCl | 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) Na_2S | 1 | -1 | ([Na2S])^(-1) S | 1 | 1 | [S] NaCl | 2 | 2 | ([NaCl])^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) ([Na2S])^(-1) [S] ([NaCl])^2 = ([S] ([NaCl])^2)/([Cl2] [Na2S])

Construct the rate of reaction expression for: Cl_2 + Na_2S ⟶ S + NaCl 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 + Na_2S ⟶ S + 2 NaCl 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 Na_2S | 1 | -1 S | 1 | 1 NaCl | 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) Na_2S | 1 | -1 | -(Δ[Na2S])/(Δt) S | 1 | 1 | (Δ[S])/(Δt) NaCl | 2 | 2 | 1/2 (Δ[NaCl])/(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[Na2S])/(Δt) = (Δ[S])/(Δt) = 1/2 (Δ[NaCl])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| chlorine | sodium sulfide | mixed sulfur | sodium chloride formula | Cl_2 | Na_2S | S | NaCl Hill formula | Cl_2 | Na_2S_1 | S | ClNa name | chlorine | sodium sulfide | mixed sulfur | sodium chloride IUPAC name | molecular chlorine | | sulfur | sodium chloride

| chlorine | sodium sulfide | mixed sulfur | sodium chloride molar mass | 70.9 g/mol | 78.04 g/mol | 32.06 g/mol | 58.44 g/mol phase | gas (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | -101 °C | 1172 °C | 112.8 °C | 801 °C boiling point | -34 °C | | 444.7 °C | 1413 °C density | 0.003214 g/cm^3 (at 0 °C) | 1.856 g/cm^3 | 2.07 g/cm^3 | 2.16 g/cm^3 solubility in water | | | | soluble odor | | | | odorless