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H2O + HMnO4 + N2O4 = HNO3 + Mn(NO3)2

Input interpretation

H_2O water + HMnO4 + N_2O_4 dinitrogen tetroxide ⟶ HNO_3 nitric acid + Mn(NO_3)_2 manganese(II) nitrate
H_2O water + HMnO4 + N_2O_4 dinitrogen tetroxide ⟶ HNO_3 nitric acid + Mn(NO_3)_2 manganese(II) nitrate

Balanced equation

Balance the chemical equation algebraically: H_2O + HMnO4 + N_2O_4 ⟶ HNO_3 + Mn(NO_3)_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 HMnO4 + c_3 N_2O_4 ⟶ c_4 HNO_3 + c_5 Mn(NO_3)_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Mn and N: H: | 2 c_1 + c_2 = c_4 O: | c_1 + 4 c_2 + 4 c_3 = 3 c_4 + 6 c_5 Mn: | c_2 = c_5 N: | 2 c_3 = c_4 + 2 c_5 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 = 5/2 c_4 = 3 c_5 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 2 c_2 = 2 c_3 = 5 c_4 = 6 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2O + 2 HMnO4 + 5 N_2O_4 ⟶ 6 HNO_3 + 2 Mn(NO_3)_2
Balance the chemical equation algebraically: H_2O + HMnO4 + N_2O_4 ⟶ HNO_3 + Mn(NO_3)_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 HMnO4 + c_3 N_2O_4 ⟶ c_4 HNO_3 + c_5 Mn(NO_3)_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Mn and N: H: | 2 c_1 + c_2 = c_4 O: | c_1 + 4 c_2 + 4 c_3 = 3 c_4 + 6 c_5 Mn: | c_2 = c_5 N: | 2 c_3 = c_4 + 2 c_5 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 = 5/2 c_4 = 3 c_5 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 2 c_2 = 2 c_3 = 5 c_4 = 6 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2O + 2 HMnO4 + 5 N_2O_4 ⟶ 6 HNO_3 + 2 Mn(NO_3)_2

Structures

+ HMnO4 + ⟶ +
+ HMnO4 + ⟶ +

Names

water + HMnO4 + dinitrogen tetroxide ⟶ nitric acid + manganese(II) nitrate
water + HMnO4 + dinitrogen tetroxide ⟶ nitric acid + manganese(II) nitrate

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2O + HMnO4 + N_2O_4 ⟶ HNO_3 + Mn(NO_3)_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 + 2 HMnO4 + 5 N_2O_4 ⟶ 6 HNO_3 + 2 Mn(NO_3)_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 HMnO4 | 2 | -2 N_2O_4 | 5 | -5 HNO_3 | 6 | 6 Mn(NO_3)_2 | 2 | 2 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) HMnO4 | 2 | -2 | ([HMnO4])^(-2) N_2O_4 | 5 | -5 | ([N2O4])^(-5) HNO_3 | 6 | 6 | ([HNO3])^6 Mn(NO_3)_2 | 2 | 2 | ([Mn(NO3)2])^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 = ([H2O])^(-2) ([HMnO4])^(-2) ([N2O4])^(-5) ([HNO3])^6 ([Mn(NO3)2])^2 = (([HNO3])^6 ([Mn(NO3)2])^2)/(([H2O])^2 ([HMnO4])^2 ([N2O4])^5)
Construct the equilibrium constant, K, expression for: H_2O + HMnO4 + N_2O_4 ⟶ HNO_3 + Mn(NO_3)_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 + 2 HMnO4 + 5 N_2O_4 ⟶ 6 HNO_3 + 2 Mn(NO_3)_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 HMnO4 | 2 | -2 N_2O_4 | 5 | -5 HNO_3 | 6 | 6 Mn(NO_3)_2 | 2 | 2 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) HMnO4 | 2 | -2 | ([HMnO4])^(-2) N_2O_4 | 5 | -5 | ([N2O4])^(-5) HNO_3 | 6 | 6 | ([HNO3])^6 Mn(NO_3)_2 | 2 | 2 | ([Mn(NO3)2])^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 = ([H2O])^(-2) ([HMnO4])^(-2) ([N2O4])^(-5) ([HNO3])^6 ([Mn(NO3)2])^2 = (([HNO3])^6 ([Mn(NO3)2])^2)/(([H2O])^2 ([HMnO4])^2 ([N2O4])^5)

Rate of reaction

Construct the rate of reaction expression for: H_2O + HMnO4 + N_2O_4 ⟶ HNO_3 + Mn(NO_3)_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 + 2 HMnO4 + 5 N_2O_4 ⟶ 6 HNO_3 + 2 Mn(NO_3)_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 HMnO4 | 2 | -2 N_2O_4 | 5 | -5 HNO_3 | 6 | 6 Mn(NO_3)_2 | 2 | 2 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) HMnO4 | 2 | -2 | -1/2 (Δ[HMnO4])/(Δt) N_2O_4 | 5 | -5 | -1/5 (Δ[N2O4])/(Δt) HNO_3 | 6 | 6 | 1/6 (Δ[HNO3])/(Δt) Mn(NO_3)_2 | 2 | 2 | 1/2 (Δ[Mn(NO3)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 = -1/2 (Δ[H2O])/(Δt) = -1/2 (Δ[HMnO4])/(Δt) = -1/5 (Δ[N2O4])/(Δt) = 1/6 (Δ[HNO3])/(Δt) = 1/2 (Δ[Mn(NO3)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2O + HMnO4 + N_2O_4 ⟶ HNO_3 + Mn(NO_3)_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 + 2 HMnO4 + 5 N_2O_4 ⟶ 6 HNO_3 + 2 Mn(NO_3)_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 HMnO4 | 2 | -2 N_2O_4 | 5 | -5 HNO_3 | 6 | 6 Mn(NO_3)_2 | 2 | 2 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) HMnO4 | 2 | -2 | -1/2 (Δ[HMnO4])/(Δt) N_2O_4 | 5 | -5 | -1/5 (Δ[N2O4])/(Δt) HNO_3 | 6 | 6 | 1/6 (Δ[HNO3])/(Δt) Mn(NO_3)_2 | 2 | 2 | 1/2 (Δ[Mn(NO3)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 = -1/2 (Δ[H2O])/(Δt) = -1/2 (Δ[HMnO4])/(Δt) = -1/5 (Δ[N2O4])/(Δt) = 1/6 (Δ[HNO3])/(Δt) = 1/2 (Δ[Mn(NO3)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| water | HMnO4 | dinitrogen tetroxide | nitric acid | manganese(II) nitrate formula | H_2O | HMnO4 | N_2O_4 | HNO_3 | Mn(NO_3)_2 Hill formula | H_2O | HMnO4 | N_2O_4 | HNO_3 | MnN_2O_6 name | water | | dinitrogen tetroxide | nitric acid | manganese(II) nitrate IUPAC name | water | | | nitric acid | manganese(2+) dinitrate
| water | HMnO4 | dinitrogen tetroxide | nitric acid | manganese(II) nitrate formula | H_2O | HMnO4 | N_2O_4 | HNO_3 | Mn(NO_3)_2 Hill formula | H_2O | HMnO4 | N_2O_4 | HNO_3 | MnN_2O_6 name | water | | dinitrogen tetroxide | nitric acid | manganese(II) nitrate IUPAC name | water | | | nitric acid | manganese(2+) dinitrate

Substance properties

| water | HMnO4 | dinitrogen tetroxide | nitric acid | manganese(II) nitrate molar mass | 18.015 g/mol | 119.94 g/mol | 92.01 g/mol | 63.012 g/mol | 178.95 g/mol phase | liquid (at STP) | | gas (at STP) | liquid (at STP) | melting point | 0 °C | | -15 °C | -41.6 °C | boiling point | 99.9839 °C | | 21.2 °C | 83 °C | density | 1 g/cm^3 | | 1.45 g/cm^3 (at 20 °C) | 1.5129 g/cm^3 | 1.536 g/cm^3 solubility in water | | | reacts | miscible | surface tension | 0.0728 N/m | | 0.0275 N/m | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | 4.18×10^-4 Pa s (at 20 °C) | 7.6×10^-4 Pa s (at 25 °C) | odor | odorless | | | |
| water | HMnO4 | dinitrogen tetroxide | nitric acid | manganese(II) nitrate molar mass | 18.015 g/mol | 119.94 g/mol | 92.01 g/mol | 63.012 g/mol | 178.95 g/mol phase | liquid (at STP) | | gas (at STP) | liquid (at STP) | melting point | 0 °C | | -15 °C | -41.6 °C | boiling point | 99.9839 °C | | 21.2 °C | 83 °C | density | 1 g/cm^3 | | 1.45 g/cm^3 (at 20 °C) | 1.5129 g/cm^3 | 1.536 g/cm^3 solubility in water | | | reacts | miscible | surface tension | 0.0728 N/m | | 0.0275 N/m | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | 4.18×10^-4 Pa s (at 20 °C) | 7.6×10^-4 Pa s (at 25 °C) | odor | odorless | | | |

Units

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