S + Mg = MgS

S (mixed sulfur) + Mg (magnesium) ⟶ MgS (magnesium sulfide)

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

+ ⟶

mixed sulfur + magnesium ⟶ magnesium sulfide

Construct the equilibrium constant, K, expression for: S + Mg ⟶ MgS 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 + Mg ⟶ MgS 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 Mg | 1 | -1 MgS | 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) Mg | 1 | -1 | ([Mg])^(-1) MgS | 1 | 1 | [MgS] 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) ([Mg])^(-1) [MgS] = ([MgS])/([S] [Mg])

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

| mixed sulfur | magnesium | magnesium sulfide formula | S | Mg | MgS name | mixed sulfur | magnesium | magnesium sulfide IUPAC name | sulfur | magnesium |

| mixed sulfur | magnesium | magnesium sulfide molar mass | 32.06 g/mol | 24.305 g/mol | 56.36 g/mol phase | solid (at STP) | solid (at STP) | melting point | 112.8 °C | 648 °C | 2226 °C boiling point | 444.7 °C | 1090 °C | density | 2.07 g/cm^3 | 1.738 g/cm^3 | 2.68 g/cm^3 solubility in water | | reacts | reacts