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HNO3 + MnCl2 + PbO2 = H2O + Pb(NO3)2 + PbCl2 + Pb(MnO4)2

Input interpretation

HNO_3 nitric acid + MnCl_2 manganese(II) chloride + PbO_2 lead dioxide ⟶ H_2O water + Pb(NO_3)_2 lead(II) nitrate + PbCl_2 lead(II) chloride + Pb(MnO4)2
HNO_3 nitric acid + MnCl_2 manganese(II) chloride + PbO_2 lead dioxide ⟶ H_2O water + Pb(NO_3)_2 lead(II) nitrate + PbCl_2 lead(II) chloride + Pb(MnO4)2

Balanced equation

Balance the chemical equation algebraically: HNO_3 + MnCl_2 + PbO_2 ⟶ H_2O + Pb(NO_3)_2 + PbCl_2 + Pb(MnO4)2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 MnCl_2 + c_3 PbO_2 ⟶ c_4 H_2O + c_5 Pb(NO_3)_2 + c_6 PbCl_2 + c_7 Pb(MnO4)2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O, Cl, Mn and Pb: H: | c_1 = 2 c_4 N: | c_1 = 2 c_5 O: | 3 c_1 + 2 c_3 = c_4 + 6 c_5 + 8 c_7 Cl: | 2 c_2 = 2 c_6 Mn: | c_2 = 2 c_7 Pb: | c_3 = c_5 + c_6 + c_7 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_7 = 1 and solve the system of equations for the remaining coefficients: c_1 = 4 c_2 = 2 c_3 = 5 c_4 = 2 c_5 = 2 c_6 = 2 c_7 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 HNO_3 + 2 MnCl_2 + 5 PbO_2 ⟶ 2 H_2O + 2 Pb(NO_3)_2 + 2 PbCl_2 + Pb(MnO4)2
Balance the chemical equation algebraically: HNO_3 + MnCl_2 + PbO_2 ⟶ H_2O + Pb(NO_3)_2 + PbCl_2 + Pb(MnO4)2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 MnCl_2 + c_3 PbO_2 ⟶ c_4 H_2O + c_5 Pb(NO_3)_2 + c_6 PbCl_2 + c_7 Pb(MnO4)2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O, Cl, Mn and Pb: H: | c_1 = 2 c_4 N: | c_1 = 2 c_5 O: | 3 c_1 + 2 c_3 = c_4 + 6 c_5 + 8 c_7 Cl: | 2 c_2 = 2 c_6 Mn: | c_2 = 2 c_7 Pb: | c_3 = c_5 + c_6 + c_7 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_7 = 1 and solve the system of equations for the remaining coefficients: c_1 = 4 c_2 = 2 c_3 = 5 c_4 = 2 c_5 = 2 c_6 = 2 c_7 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 HNO_3 + 2 MnCl_2 + 5 PbO_2 ⟶ 2 H_2O + 2 Pb(NO_3)_2 + 2 PbCl_2 + Pb(MnO4)2

Structures

+ + ⟶ + + + Pb(MnO4)2
+ + ⟶ + + + Pb(MnO4)2

Names

nitric acid + manganese(II) chloride + lead dioxide ⟶ water + lead(II) nitrate + lead(II) chloride + Pb(MnO4)2
nitric acid + manganese(II) chloride + lead dioxide ⟶ water + lead(II) nitrate + lead(II) chloride + Pb(MnO4)2

Equilibrium constant

Construct the equilibrium constant, K, expression for: HNO_3 + MnCl_2 + PbO_2 ⟶ H_2O + Pb(NO_3)_2 + PbCl_2 + Pb(MnO4)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: 4 HNO_3 + 2 MnCl_2 + 5 PbO_2 ⟶ 2 H_2O + 2 Pb(NO_3)_2 + 2 PbCl_2 + Pb(MnO4)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 HNO_3 | 4 | -4 MnCl_2 | 2 | -2 PbO_2 | 5 | -5 H_2O | 2 | 2 Pb(NO_3)_2 | 2 | 2 PbCl_2 | 2 | 2 Pb(MnO4)2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HNO_3 | 4 | -4 | ([HNO3])^(-4) MnCl_2 | 2 | -2 | ([MnCl2])^(-2) PbO_2 | 5 | -5 | ([PbO2])^(-5) H_2O | 2 | 2 | ([H2O])^2 Pb(NO_3)_2 | 2 | 2 | ([Pb(NO3)2])^2 PbCl_2 | 2 | 2 | ([PbCl2])^2 Pb(MnO4)2 | 1 | 1 | [Pb(MnO4)2] 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 = ([HNO3])^(-4) ([MnCl2])^(-2) ([PbO2])^(-5) ([H2O])^2 ([Pb(NO3)2])^2 ([PbCl2])^2 [Pb(MnO4)2] = (([H2O])^2 ([Pb(NO3)2])^2 ([PbCl2])^2 [Pb(MnO4)2])/(([HNO3])^4 ([MnCl2])^2 ([PbO2])^5)
Construct the equilibrium constant, K, expression for: HNO_3 + MnCl_2 + PbO_2 ⟶ H_2O + Pb(NO_3)_2 + PbCl_2 + Pb(MnO4)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: 4 HNO_3 + 2 MnCl_2 + 5 PbO_2 ⟶ 2 H_2O + 2 Pb(NO_3)_2 + 2 PbCl_2 + Pb(MnO4)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 HNO_3 | 4 | -4 MnCl_2 | 2 | -2 PbO_2 | 5 | -5 H_2O | 2 | 2 Pb(NO_3)_2 | 2 | 2 PbCl_2 | 2 | 2 Pb(MnO4)2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HNO_3 | 4 | -4 | ([HNO3])^(-4) MnCl_2 | 2 | -2 | ([MnCl2])^(-2) PbO_2 | 5 | -5 | ([PbO2])^(-5) H_2O | 2 | 2 | ([H2O])^2 Pb(NO_3)_2 | 2 | 2 | ([Pb(NO3)2])^2 PbCl_2 | 2 | 2 | ([PbCl2])^2 Pb(MnO4)2 | 1 | 1 | [Pb(MnO4)2] 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 = ([HNO3])^(-4) ([MnCl2])^(-2) ([PbO2])^(-5) ([H2O])^2 ([Pb(NO3)2])^2 ([PbCl2])^2 [Pb(MnO4)2] = (([H2O])^2 ([Pb(NO3)2])^2 ([PbCl2])^2 [Pb(MnO4)2])/(([HNO3])^4 ([MnCl2])^2 ([PbO2])^5)

Rate of reaction

Construct the rate of reaction expression for: HNO_3 + MnCl_2 + PbO_2 ⟶ H_2O + Pb(NO_3)_2 + PbCl_2 + Pb(MnO4)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: 4 HNO_3 + 2 MnCl_2 + 5 PbO_2 ⟶ 2 H_2O + 2 Pb(NO_3)_2 + 2 PbCl_2 + Pb(MnO4)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 HNO_3 | 4 | -4 MnCl_2 | 2 | -2 PbO_2 | 5 | -5 H_2O | 2 | 2 Pb(NO_3)_2 | 2 | 2 PbCl_2 | 2 | 2 Pb(MnO4)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 HNO_3 | 4 | -4 | -1/4 (Δ[HNO3])/(Δt) MnCl_2 | 2 | -2 | -1/2 (Δ[MnCl2])/(Δt) PbO_2 | 5 | -5 | -1/5 (Δ[PbO2])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) Pb(NO_3)_2 | 2 | 2 | 1/2 (Δ[Pb(NO3)2])/(Δt) PbCl_2 | 2 | 2 | 1/2 (Δ[PbCl2])/(Δt) Pb(MnO4)2 | 1 | 1 | (Δ[Pb(MnO4)2])/(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 = -1/4 (Δ[HNO3])/(Δt) = -1/2 (Δ[MnCl2])/(Δt) = -1/5 (Δ[PbO2])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/2 (Δ[Pb(NO3)2])/(Δt) = 1/2 (Δ[PbCl2])/(Δt) = (Δ[Pb(MnO4)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: HNO_3 + MnCl_2 + PbO_2 ⟶ H_2O + Pb(NO_3)_2 + PbCl_2 + Pb(MnO4)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: 4 HNO_3 + 2 MnCl_2 + 5 PbO_2 ⟶ 2 H_2O + 2 Pb(NO_3)_2 + 2 PbCl_2 + Pb(MnO4)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 HNO_3 | 4 | -4 MnCl_2 | 2 | -2 PbO_2 | 5 | -5 H_2O | 2 | 2 Pb(NO_3)_2 | 2 | 2 PbCl_2 | 2 | 2 Pb(MnO4)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 HNO_3 | 4 | -4 | -1/4 (Δ[HNO3])/(Δt) MnCl_2 | 2 | -2 | -1/2 (Δ[MnCl2])/(Δt) PbO_2 | 5 | -5 | -1/5 (Δ[PbO2])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) Pb(NO_3)_2 | 2 | 2 | 1/2 (Δ[Pb(NO3)2])/(Δt) PbCl_2 | 2 | 2 | 1/2 (Δ[PbCl2])/(Δt) Pb(MnO4)2 | 1 | 1 | (Δ[Pb(MnO4)2])/(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 = -1/4 (Δ[HNO3])/(Δt) = -1/2 (Δ[MnCl2])/(Δt) = -1/5 (Δ[PbO2])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/2 (Δ[Pb(NO3)2])/(Δt) = 1/2 (Δ[PbCl2])/(Δt) = (Δ[Pb(MnO4)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| nitric acid | manganese(II) chloride | lead dioxide | water | lead(II) nitrate | lead(II) chloride | Pb(MnO4)2 formula | HNO_3 | MnCl_2 | PbO_2 | H_2O | Pb(NO_3)_2 | PbCl_2 | Pb(MnO4)2 Hill formula | HNO_3 | Cl_2Mn | O_2Pb | H_2O | N_2O_6Pb | Cl_2Pb | Mn2O8Pb name | nitric acid | manganese(II) chloride | lead dioxide | water | lead(II) nitrate | lead(II) chloride | IUPAC name | nitric acid | dichloromanganese | | water | plumbous dinitrate | dichlorolead |
| nitric acid | manganese(II) chloride | lead dioxide | water | lead(II) nitrate | lead(II) chloride | Pb(MnO4)2 formula | HNO_3 | MnCl_2 | PbO_2 | H_2O | Pb(NO_3)_2 | PbCl_2 | Pb(MnO4)2 Hill formula | HNO_3 | Cl_2Mn | O_2Pb | H_2O | N_2O_6Pb | Cl_2Pb | Mn2O8Pb name | nitric acid | manganese(II) chloride | lead dioxide | water | lead(II) nitrate | lead(II) chloride | IUPAC name | nitric acid | dichloromanganese | | water | plumbous dinitrate | dichlorolead |

Substance properties

| nitric acid | manganese(II) chloride | lead dioxide | water | lead(II) nitrate | lead(II) chloride | Pb(MnO4)2 molar mass | 63.012 g/mol | 125.8 g/mol | 239.2 g/mol | 18.015 g/mol | 331.2 g/mol | 278.1 g/mol | 445.1 g/mol phase | liquid (at STP) | solid (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) | solid (at STP) | melting point | -41.6 °C | 652 °C | 290 °C | 0 °C | 470 °C | 501 °C | boiling point | 83 °C | | | 99.9839 °C | | 950 °C | density | 1.5129 g/cm^3 | 2.98 g/cm^3 | 9.58 g/cm^3 | 1 g/cm^3 | | 5.85 g/cm^3 | solubility in water | miscible | | insoluble | | | | surface tension | | | | 0.0728 N/m | | | dynamic viscosity | 7.6×10^-4 Pa s (at 25 °C) | | | 8.9×10^-4 Pa s (at 25 °C) | | | odor | | | | odorless | odorless | |
| nitric acid | manganese(II) chloride | lead dioxide | water | lead(II) nitrate | lead(II) chloride | Pb(MnO4)2 molar mass | 63.012 g/mol | 125.8 g/mol | 239.2 g/mol | 18.015 g/mol | 331.2 g/mol | 278.1 g/mol | 445.1 g/mol phase | liquid (at STP) | solid (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) | solid (at STP) | melting point | -41.6 °C | 652 °C | 290 °C | 0 °C | 470 °C | 501 °C | boiling point | 83 °C | | | 99.9839 °C | | 950 °C | density | 1.5129 g/cm^3 | 2.98 g/cm^3 | 9.58 g/cm^3 | 1 g/cm^3 | | 5.85 g/cm^3 | solubility in water | miscible | | insoluble | | | | surface tension | | | | 0.0728 N/m | | | dynamic viscosity | 7.6×10^-4 Pa s (at 25 °C) | | | 8.9×10^-4 Pa s (at 25 °C) | | | odor | | | | odorless | odorless | |

Units

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