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K2SO4 + Pb(NO3)2 = KNO3 + PbSO4

Input interpretation

K_2SO_4 potassium sulfate + Pb(NO_3)_2 lead(II) nitrate ⟶ KNO_3 potassium nitrate + PbSO_4 lead(II) sulfate
K_2SO_4 potassium sulfate + Pb(NO_3)_2 lead(II) nitrate ⟶ KNO_3 potassium nitrate + PbSO_4 lead(II) sulfate

Balanced equation

Balance the chemical equation algebraically: K_2SO_4 + Pb(NO_3)_2 ⟶ KNO_3 + PbSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 K_2SO_4 + c_2 Pb(NO_3)_2 ⟶ c_3 KNO_3 + c_4 PbSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for K, O, S, N and Pb: K: | 2 c_1 = c_3 O: | 4 c_1 + 6 c_2 = 3 c_3 + 4 c_4 S: | c_1 = c_4 N: | 2 c_2 = c_3 Pb: | 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: | | K_2SO_4 + Pb(NO_3)_2 ⟶ 2 KNO_3 + PbSO_4
Balance the chemical equation algebraically: K_2SO_4 + Pb(NO_3)_2 ⟶ KNO_3 + PbSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 K_2SO_4 + c_2 Pb(NO_3)_2 ⟶ c_3 KNO_3 + c_4 PbSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for K, O, S, N and Pb: K: | 2 c_1 = c_3 O: | 4 c_1 + 6 c_2 = 3 c_3 + 4 c_4 S: | c_1 = c_4 N: | 2 c_2 = c_3 Pb: | 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: | | K_2SO_4 + Pb(NO_3)_2 ⟶ 2 KNO_3 + PbSO_4

Structures

+ ⟶ +
+ ⟶ +

Names

potassium sulfate + lead(II) nitrate ⟶ potassium nitrate + lead(II) sulfate
potassium sulfate + lead(II) nitrate ⟶ potassium nitrate + lead(II) sulfate

Equilibrium constant

Construct the equilibrium constant, K, expression for: K_2SO_4 + Pb(NO_3)_2 ⟶ KNO_3 + PbSO_4 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: K_2SO_4 + Pb(NO_3)_2 ⟶ 2 KNO_3 + PbSO_4 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 K_2SO_4 | 1 | -1 Pb(NO_3)_2 | 1 | -1 KNO_3 | 2 | 2 PbSO_4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression K_2SO_4 | 1 | -1 | ([K2SO4])^(-1) Pb(NO_3)_2 | 1 | -1 | ([Pb(NO3)2])^(-1) KNO_3 | 2 | 2 | ([KNO3])^2 PbSO_4 | 1 | 1 | [PbSO4] 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 = ([K2SO4])^(-1) ([Pb(NO3)2])^(-1) ([KNO3])^2 [PbSO4] = (([KNO3])^2 [PbSO4])/([K2SO4] [Pb(NO3)2])
Construct the equilibrium constant, K, expression for: K_2SO_4 + Pb(NO_3)_2 ⟶ KNO_3 + PbSO_4 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: K_2SO_4 + Pb(NO_3)_2 ⟶ 2 KNO_3 + PbSO_4 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 K_2SO_4 | 1 | -1 Pb(NO_3)_2 | 1 | -1 KNO_3 | 2 | 2 PbSO_4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression K_2SO_4 | 1 | -1 | ([K2SO4])^(-1) Pb(NO_3)_2 | 1 | -1 | ([Pb(NO3)2])^(-1) KNO_3 | 2 | 2 | ([KNO3])^2 PbSO_4 | 1 | 1 | [PbSO4] 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 = ([K2SO4])^(-1) ([Pb(NO3)2])^(-1) ([KNO3])^2 [PbSO4] = (([KNO3])^2 [PbSO4])/([K2SO4] [Pb(NO3)2])

Rate of reaction

Construct the rate of reaction expression for: K_2SO_4 + Pb(NO_3)_2 ⟶ KNO_3 + PbSO_4 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: K_2SO_4 + Pb(NO_3)_2 ⟶ 2 KNO_3 + PbSO_4 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 K_2SO_4 | 1 | -1 Pb(NO_3)_2 | 1 | -1 KNO_3 | 2 | 2 PbSO_4 | 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 K_2SO_4 | 1 | -1 | -(Δ[K2SO4])/(Δt) Pb(NO_3)_2 | 1 | -1 | -(Δ[Pb(NO3)2])/(Δt) KNO_3 | 2 | 2 | 1/2 (Δ[KNO3])/(Δt) PbSO_4 | 1 | 1 | (Δ[PbSO4])/(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[K2SO4])/(Δt) = -(Δ[Pb(NO3)2])/(Δt) = 1/2 (Δ[KNO3])/(Δt) = (Δ[PbSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: K_2SO_4 + Pb(NO_3)_2 ⟶ KNO_3 + PbSO_4 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: K_2SO_4 + Pb(NO_3)_2 ⟶ 2 KNO_3 + PbSO_4 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 K_2SO_4 | 1 | -1 Pb(NO_3)_2 | 1 | -1 KNO_3 | 2 | 2 PbSO_4 | 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 K_2SO_4 | 1 | -1 | -(Δ[K2SO4])/(Δt) Pb(NO_3)_2 | 1 | -1 | -(Δ[Pb(NO3)2])/(Δt) KNO_3 | 2 | 2 | 1/2 (Δ[KNO3])/(Δt) PbSO_4 | 1 | 1 | (Δ[PbSO4])/(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[K2SO4])/(Δt) = -(Δ[Pb(NO3)2])/(Δt) = 1/2 (Δ[KNO3])/(Δt) = (Δ[PbSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| potassium sulfate | lead(II) nitrate | potassium nitrate | lead(II) sulfate formula | K_2SO_4 | Pb(NO_3)_2 | KNO_3 | PbSO_4 Hill formula | K_2O_4S | N_2O_6Pb | KNO_3 | O_4PbS name | potassium sulfate | lead(II) nitrate | potassium nitrate | lead(II) sulfate IUPAC name | dipotassium sulfate | plumbous dinitrate | potassium nitrate |
| potassium sulfate | lead(II) nitrate | potassium nitrate | lead(II) sulfate formula | K_2SO_4 | Pb(NO_3)_2 | KNO_3 | PbSO_4 Hill formula | K_2O_4S | N_2O_6Pb | KNO_3 | O_4PbS name | potassium sulfate | lead(II) nitrate | potassium nitrate | lead(II) sulfate IUPAC name | dipotassium sulfate | plumbous dinitrate | potassium nitrate |

Substance properties

| potassium sulfate | lead(II) nitrate | potassium nitrate | lead(II) sulfate molar mass | 174.25 g/mol | 331.2 g/mol | 101.1 g/mol | 303.3 g/mol phase | | solid (at STP) | solid (at STP) | solid (at STP) melting point | | 470 °C | 334 °C | 1087 °C density | | | | 6.29 g/cm^3 solubility in water | soluble | | soluble | slightly soluble odor | | odorless | odorless |
| potassium sulfate | lead(II) nitrate | potassium nitrate | lead(II) sulfate molar mass | 174.25 g/mol | 331.2 g/mol | 101.1 g/mol | 303.3 g/mol phase | | solid (at STP) | solid (at STP) | solid (at STP) melting point | | 470 °C | 334 °C | 1087 °C density | | | | 6.29 g/cm^3 solubility in water | soluble | | soluble | slightly soluble odor | | odorless | odorless |

Units

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