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H2O + Cl2 + Pb(NO3)2 = HCl + HNO3 + PbO2

Input interpretation

H_2O water + Cl_2 chlorine + Pb(NO_3)_2 lead(II) nitrate ⟶ HCl hydrogen chloride + HNO_3 nitric acid + PbO_2 lead dioxide
H_2O water + Cl_2 chlorine + Pb(NO_3)_2 lead(II) nitrate ⟶ HCl hydrogen chloride + HNO_3 nitric acid + PbO_2 lead dioxide

Balanced equation

Balance the chemical equation algebraically: H_2O + Cl_2 + Pb(NO_3)_2 ⟶ HCl + HNO_3 + PbO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 Cl_2 + c_3 Pb(NO_3)_2 ⟶ c_4 HCl + c_5 HNO_3 + c_6 PbO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Cl, N and Pb: H: | 2 c_1 = c_4 + c_5 O: | c_1 + 6 c_3 = 3 c_5 + 2 c_6 Cl: | 2 c_2 = c_4 N: | 2 c_3 = c_5 Pb: | c_3 = c_6 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 1 c_4 = 2 c_5 = 2 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2O + Cl_2 + Pb(NO_3)_2 ⟶ 2 HCl + 2 HNO_3 + PbO_2
Balance the chemical equation algebraically: H_2O + Cl_2 + Pb(NO_3)_2 ⟶ HCl + HNO_3 + PbO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 Cl_2 + c_3 Pb(NO_3)_2 ⟶ c_4 HCl + c_5 HNO_3 + c_6 PbO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Cl, N and Pb: H: | 2 c_1 = c_4 + c_5 O: | c_1 + 6 c_3 = 3 c_5 + 2 c_6 Cl: | 2 c_2 = c_4 N: | 2 c_3 = c_5 Pb: | c_3 = c_6 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 1 c_4 = 2 c_5 = 2 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2O + Cl_2 + Pb(NO_3)_2 ⟶ 2 HCl + 2 HNO_3 + PbO_2

Structures

+ + ⟶ + +
+ + ⟶ + +

Names

water + chlorine + lead(II) nitrate ⟶ hydrogen chloride + nitric acid + lead dioxide
water + chlorine + lead(II) nitrate ⟶ hydrogen chloride + nitric acid + lead dioxide

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2O + Cl_2 + Pb(NO_3)_2 ⟶ HCl + HNO_3 + PbO_2 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: 2 H_2O + Cl_2 + Pb(NO_3)_2 ⟶ 2 HCl + 2 HNO_3 + PbO_2 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 H_2O | 2 | -2 Cl_2 | 1 | -1 Pb(NO_3)_2 | 1 | -1 HCl | 2 | 2 HNO_3 | 2 | 2 PbO_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 2 | -2 | ([H2O])^(-2) Cl_2 | 1 | -1 | ([Cl2])^(-1) Pb(NO_3)_2 | 1 | -1 | ([Pb(NO3)2])^(-1) HCl | 2 | 2 | ([HCl])^2 HNO_3 | 2 | 2 | ([HNO3])^2 PbO_2 | 1 | 1 | [PbO2] 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 = ([H2O])^(-2) ([Cl2])^(-1) ([Pb(NO3)2])^(-1) ([HCl])^2 ([HNO3])^2 [PbO2] = (([HCl])^2 ([HNO3])^2 [PbO2])/(([H2O])^2 [Cl2] [Pb(NO3)2])
Construct the equilibrium constant, K, expression for: H_2O + Cl_2 + Pb(NO_3)_2 ⟶ HCl + HNO_3 + PbO_2 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: 2 H_2O + Cl_2 + Pb(NO_3)_2 ⟶ 2 HCl + 2 HNO_3 + PbO_2 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 H_2O | 2 | -2 Cl_2 | 1 | -1 Pb(NO_3)_2 | 1 | -1 HCl | 2 | 2 HNO_3 | 2 | 2 PbO_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 2 | -2 | ([H2O])^(-2) Cl_2 | 1 | -1 | ([Cl2])^(-1) Pb(NO_3)_2 | 1 | -1 | ([Pb(NO3)2])^(-1) HCl | 2 | 2 | ([HCl])^2 HNO_3 | 2 | 2 | ([HNO3])^2 PbO_2 | 1 | 1 | [PbO2] 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 = ([H2O])^(-2) ([Cl2])^(-1) ([Pb(NO3)2])^(-1) ([HCl])^2 ([HNO3])^2 [PbO2] = (([HCl])^2 ([HNO3])^2 [PbO2])/(([H2O])^2 [Cl2] [Pb(NO3)2])

Rate of reaction

Construct the rate of reaction expression for: H_2O + Cl_2 + Pb(NO_3)_2 ⟶ HCl + HNO_3 + PbO_2 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: 2 H_2O + Cl_2 + Pb(NO_3)_2 ⟶ 2 HCl + 2 HNO_3 + PbO_2 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 H_2O | 2 | -2 Cl_2 | 1 | -1 Pb(NO_3)_2 | 1 | -1 HCl | 2 | 2 HNO_3 | 2 | 2 PbO_2 | 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 H_2O | 2 | -2 | -1/2 (Δ[H2O])/(Δt) Cl_2 | 1 | -1 | -(Δ[Cl2])/(Δt) Pb(NO_3)_2 | 1 | -1 | -(Δ[Pb(NO3)2])/(Δt) HCl | 2 | 2 | 1/2 (Δ[HCl])/(Δt) HNO_3 | 2 | 2 | 1/2 (Δ[HNO3])/(Δt) PbO_2 | 1 | 1 | (Δ[PbO2])/(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 = -1/2 (Δ[H2O])/(Δt) = -(Δ[Cl2])/(Δt) = -(Δ[Pb(NO3)2])/(Δt) = 1/2 (Δ[HCl])/(Δt) = 1/2 (Δ[HNO3])/(Δt) = (Δ[PbO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2O + Cl_2 + Pb(NO_3)_2 ⟶ HCl + HNO_3 + PbO_2 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: 2 H_2O + Cl_2 + Pb(NO_3)_2 ⟶ 2 HCl + 2 HNO_3 + PbO_2 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 H_2O | 2 | -2 Cl_2 | 1 | -1 Pb(NO_3)_2 | 1 | -1 HCl | 2 | 2 HNO_3 | 2 | 2 PbO_2 | 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 H_2O | 2 | -2 | -1/2 (Δ[H2O])/(Δt) Cl_2 | 1 | -1 | -(Δ[Cl2])/(Δt) Pb(NO_3)_2 | 1 | -1 | -(Δ[Pb(NO3)2])/(Δt) HCl | 2 | 2 | 1/2 (Δ[HCl])/(Δt) HNO_3 | 2 | 2 | 1/2 (Δ[HNO3])/(Δt) PbO_2 | 1 | 1 | (Δ[PbO2])/(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 = -1/2 (Δ[H2O])/(Δt) = -(Δ[Cl2])/(Δt) = -(Δ[Pb(NO3)2])/(Δt) = 1/2 (Δ[HCl])/(Δt) = 1/2 (Δ[HNO3])/(Δt) = (Δ[PbO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| water | chlorine | lead(II) nitrate | hydrogen chloride | nitric acid | lead dioxide formula | H_2O | Cl_2 | Pb(NO_3)_2 | HCl | HNO_3 | PbO_2 Hill formula | H_2O | Cl_2 | N_2O_6Pb | ClH | HNO_3 | O_2Pb name | water | chlorine | lead(II) nitrate | hydrogen chloride | nitric acid | lead dioxide IUPAC name | water | molecular chlorine | plumbous dinitrate | hydrogen chloride | nitric acid |
| water | chlorine | lead(II) nitrate | hydrogen chloride | nitric acid | lead dioxide formula | H_2O | Cl_2 | Pb(NO_3)_2 | HCl | HNO_3 | PbO_2 Hill formula | H_2O | Cl_2 | N_2O_6Pb | ClH | HNO_3 | O_2Pb name | water | chlorine | lead(II) nitrate | hydrogen chloride | nitric acid | lead dioxide IUPAC name | water | molecular chlorine | plumbous dinitrate | hydrogen chloride | nitric acid |

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