S + Na = Na2S

S (mixed sulfur) + Na (sodium) ⟶ Na_2S (sodium sulfide)

Balance the chemical equation algebraically: S + Na ⟶ Na_2S Add stoichiometric coefficients, c_i, to the reactants and products: c_1 S + c_2 Na ⟶ c_3 Na_2S Set the number of atoms in the reactants equal to the number of atoms in the products for S and Na: S: | c_1 = c_3 Na: | c_2 = 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 = 2 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | S + 2 Na ⟶ Na_2S

+ ⟶

mixed sulfur + sodium ⟶ sodium sulfide

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

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

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

| mixed sulfur | sodium | sodium sulfide molar mass | 32.06 g/mol | 22.98976928 g/mol | 78.04 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) melting point | 112.8 °C | 97.8 °C | 1172 °C boiling point | 444.7 °C | 883 °C | density | 2.07 g/cm^3 | 0.968 g/cm^3 | 1.856 g/cm^3 solubility in water | | decomposes | dynamic viscosity | | 1.413×10^-5 Pa s (at 527 °C) |