Na2S + Y2 = S + NaY

Na_2S sodium sulfide + Y2 ⟶ S mixed sulfur + NaY

Balance the chemical equation algebraically: Na_2S + Y2 ⟶ S + NaY Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Na_2S + c_2 Y2 ⟶ c_3 S + c_4 NaY Set the number of atoms in the reactants equal to the number of atoms in the products for Na, S and Y: Na: | 2 c_1 = c_4 S: | c_1 = c_3 Y: | 2 c_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_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: | | Na_2S + Y2 ⟶ S + 2 NaY

+ Y2 ⟶ + NaY

sodium sulfide + Y2 ⟶ mixed sulfur + NaY

Construct the equilibrium constant, K, expression for: Na_2S + Y2 ⟶ S + NaY 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: Na_2S + Y2 ⟶ S + 2 NaY 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 Na_2S | 1 | -1 Y2 | 1 | -1 S | 1 | 1 NaY | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Na_2S | 1 | -1 | ([Na2S])^(-1) Y2 | 1 | -1 | ([Y2])^(-1) S | 1 | 1 | [S] NaY | 2 | 2 | ([NaY])^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 = ([Na2S])^(-1) ([Y2])^(-1) [S] ([NaY])^2 = ([S] ([NaY])^2)/([Na2S] [Y2])

Construct the rate of reaction expression for: Na_2S + Y2 ⟶ S + NaY 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: Na_2S + Y2 ⟶ S + 2 NaY 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 Na_2S | 1 | -1 Y2 | 1 | -1 S | 1 | 1 NaY | 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 Na_2S | 1 | -1 | -(Δ[Na2S])/(Δt) Y2 | 1 | -1 | -(Δ[Y2])/(Δt) S | 1 | 1 | (Δ[S])/(Δt) NaY | 2 | 2 | 1/2 (Δ[NaY])/(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[Na2S])/(Δt) = -(Δ[Y2])/(Δt) = (Δ[S])/(Δt) = 1/2 (Δ[NaY])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium sulfide | Y2 | mixed sulfur | NaY formula | Na_2S | Y2 | S | NaY Hill formula | Na_2S_1 | Y2 | S | NaY name | sodium sulfide | | mixed sulfur | IUPAC name | | | sulfur |

| sodium sulfide | Y2 | mixed sulfur | NaY molar mass | 78.04 g/mol | 177.8117 g/mol | 32.06 g/mol | 111.8956 g/mol phase | solid (at STP) | | solid (at STP) | melting point | 1172 °C | | 112.8 °C | boiling point | | | 444.7 °C | density | 1.856 g/cm^3 | | 2.07 g/cm^3 |