Pb(NO3)2 + K2S = KNO3 + PbS

Pb(NO_3)_2 lead(II) nitrate + K2S ⟶ KNO_3 potassium nitrate + PbS lead sulfide

Balance the chemical equation algebraically: Pb(NO_3)_2 + K2S ⟶ KNO_3 + PbS Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Pb(NO_3)_2 + c_2 K2S ⟶ c_3 KNO_3 + c_4 PbS Set the number of atoms in the reactants equal to the number of atoms in the products for N, O, Pb, K and S: N: | 2 c_1 = c_3 O: | 6 c_1 = 3 c_3 Pb: | c_1 = c_4 K: | 2 c_2 = c_3 S: | 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 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Pb(NO_3)_2 + K2S ⟶ 2 KNO_3 + PbS

+ K2S ⟶ +

lead(II) nitrate + K2S ⟶ potassium nitrate + lead sulfide

Construct the equilibrium constant, K, expression for: Pb(NO_3)_2 + K2S ⟶ KNO_3 + 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: Pb(NO_3)_2 + K2S ⟶ 2 KNO_3 + 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 Pb(NO_3)_2 | 1 | -1 K2S | 1 | -1 KNO_3 | 2 | 2 PbS | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Pb(NO_3)_2 | 1 | -1 | ([Pb(NO3)2])^(-1) K2S | 1 | -1 | ([K2S])^(-1) KNO_3 | 2 | 2 | ([KNO3])^2 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 = ([Pb(NO3)2])^(-1) ([K2S])^(-1) ([KNO3])^2 [PbS] = (([KNO3])^2 [PbS])/([Pb(NO3)2] [K2S])

Construct the rate of reaction expression for: Pb(NO_3)_2 + K2S ⟶ KNO_3 + 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: Pb(NO_3)_2 + K2S ⟶ 2 KNO_3 + 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 Pb(NO_3)_2 | 1 | -1 K2S | 1 | -1 KNO_3 | 2 | 2 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 Pb(NO_3)_2 | 1 | -1 | -(Δ[Pb(NO3)2])/(Δt) K2S | 1 | -1 | -(Δ[K2S])/(Δt) KNO_3 | 2 | 2 | 1/2 (Δ[KNO3])/(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[Pb(NO3)2])/(Δt) = -(Δ[K2S])/(Δt) = 1/2 (Δ[KNO3])/(Δt) = (Δ[PbS])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| lead(II) nitrate | K2S | potassium nitrate | lead sulfide formula | Pb(NO_3)_2 | K2S | KNO_3 | PbS Hill formula | N_2O_6Pb | K2S | KNO_3 | PbS name | lead(II) nitrate | | potassium nitrate | lead sulfide IUPAC name | plumbous dinitrate | | potassium nitrate |

| lead(II) nitrate | K2S | potassium nitrate | lead sulfide molar mass | 331.2 g/mol | 110.26 g/mol | 101.1 g/mol | 239.3 g/mol phase | solid (at STP) | | solid (at STP) | solid (at STP) melting point | 470 °C | | 334 °C | 1114 °C boiling point | | | | 1344 °C density | | | | 7.5 g/cm^3 solubility in water | | | soluble | insoluble odor | odorless | | odorless |