S + Pb = PbS

S mixed sulfur + Pb lead ⟶ PbS lead sulfide

Balance the chemical equation algebraically: S + Pb ⟶ PbS Add stoichiometric coefficients, c_i, to the reactants and products: c_1 S + c_2 Pb ⟶ c_3 PbS Set the number of atoms in the reactants equal to the number of atoms in the products for S and Pb: S: | c_1 = c_3 Pb: | 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 + Pb ⟶ PbS

+ ⟶

mixed sulfur + lead ⟶ lead sulfide

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

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

| mixed sulfur | lead | lead sulfide formula | S | Pb | PbS name | mixed sulfur | lead | lead sulfide IUPAC name | sulfur | lead |

| mixed sulfur | lead | lead sulfide molar mass | 32.06 g/mol | 207.2 g/mol | 239.3 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) melting point | 112.8 °C | 327.4 °C | 1114 °C boiling point | 444.7 °C | 1740 °C | 1344 °C density | 2.07 g/cm^3 | 11.34 g/cm^3 | 7.5 g/cm^3 solubility in water | | insoluble | insoluble dynamic viscosity | | 0.00183 Pa s (at 38 °C) |