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HNO3 + Mn(NO3)2 + NaBiO3 = H2O + NaNO3 + Bi(NO3)3 + HMnO3

Input interpretation

HNO_3 nitric acid + Mn(NO_3)_2 manganese(II) nitrate + NaBiO_3 sodium bismuthate ⟶ H_2O water + NaNO_3 sodium nitrate + Bi(NO3)3 + HMnO3
HNO_3 nitric acid + Mn(NO_3)_2 manganese(II) nitrate + NaBiO_3 sodium bismuthate ⟶ H_2O water + NaNO_3 sodium nitrate + Bi(NO3)3 + HMnO3

Balanced equation

Balance the chemical equation algebraically: HNO_3 + Mn(NO_3)_2 + NaBiO_3 ⟶ H_2O + NaNO_3 + Bi(NO3)3 + HMnO3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 Mn(NO_3)_2 + c_3 NaBiO_3 ⟶ c_4 H_2O + c_5 NaNO_3 + c_6 Bi(NO3)3 + c_7 HMnO3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O, Mn, Bi and Na: H: | c_1 = 2 c_4 + c_7 N: | c_1 + 2 c_2 = c_5 + 3 c_6 O: | 3 c_1 + 6 c_2 + 3 c_3 = c_4 + 3 c_5 + 9 c_6 + 3 c_7 Mn: | c_2 = c_7 Bi: | c_3 = c_6 Na: | c_3 = 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 4 c_2 = 1 c_3 = 3/2 c_4 = 3/2 c_5 = 3/2 c_6 = 3/2 c_7 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 8 c_2 = 2 c_3 = 3 c_4 = 3 c_5 = 3 c_6 = 3 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 HNO_3 + 2 Mn(NO_3)_2 + 3 NaBiO_3 ⟶ 3 H_2O + 3 NaNO_3 + 3 Bi(NO3)3 + 2 HMnO3
Balance the chemical equation algebraically: HNO_3 + Mn(NO_3)_2 + NaBiO_3 ⟶ H_2O + NaNO_3 + Bi(NO3)3 + HMnO3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 Mn(NO_3)_2 + c_3 NaBiO_3 ⟶ c_4 H_2O + c_5 NaNO_3 + c_6 Bi(NO3)3 + c_7 HMnO3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O, Mn, Bi and Na: H: | c_1 = 2 c_4 + c_7 N: | c_1 + 2 c_2 = c_5 + 3 c_6 O: | 3 c_1 + 6 c_2 + 3 c_3 = c_4 + 3 c_5 + 9 c_6 + 3 c_7 Mn: | c_2 = c_7 Bi: | c_3 = c_6 Na: | c_3 = 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 4 c_2 = 1 c_3 = 3/2 c_4 = 3/2 c_5 = 3/2 c_6 = 3/2 c_7 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 8 c_2 = 2 c_3 = 3 c_4 = 3 c_5 = 3 c_6 = 3 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 HNO_3 + 2 Mn(NO_3)_2 + 3 NaBiO_3 ⟶ 3 H_2O + 3 NaNO_3 + 3 Bi(NO3)3 + 2 HMnO3

Structures

+ + ⟶ + + Bi(NO3)3 + HMnO3
+ + ⟶ + + Bi(NO3)3 + HMnO3

Names

nitric acid + manganese(II) nitrate + sodium bismuthate ⟶ water + sodium nitrate + Bi(NO3)3 + HMnO3
nitric acid + manganese(II) nitrate + sodium bismuthate ⟶ water + sodium nitrate + Bi(NO3)3 + HMnO3

Equilibrium constant

Construct the equilibrium constant, K, expression for: HNO_3 + Mn(NO_3)_2 + NaBiO_3 ⟶ H_2O + NaNO_3 + Bi(NO3)3 + HMnO3 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: 8 HNO_3 + 2 Mn(NO_3)_2 + 3 NaBiO_3 ⟶ 3 H_2O + 3 NaNO_3 + 3 Bi(NO3)3 + 2 HMnO3 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 | 8 | -8 Mn(NO_3)_2 | 2 | -2 NaBiO_3 | 3 | -3 H_2O | 3 | 3 NaNO_3 | 3 | 3 Bi(NO3)3 | 3 | 3 HMnO3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HNO_3 | 8 | -8 | ([HNO3])^(-8) Mn(NO_3)_2 | 2 | -2 | ([Mn(NO3)2])^(-2) NaBiO_3 | 3 | -3 | ([NaBiO3])^(-3) H_2O | 3 | 3 | ([H2O])^3 NaNO_3 | 3 | 3 | ([NaNO3])^3 Bi(NO3)3 | 3 | 3 | ([Bi(NO3)3])^3 HMnO3 | 2 | 2 | ([HMnO3])^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])^(-8) ([Mn(NO3)2])^(-2) ([NaBiO3])^(-3) ([H2O])^3 ([NaNO3])^3 ([Bi(NO3)3])^3 ([HMnO3])^2 = (([H2O])^3 ([NaNO3])^3 ([Bi(NO3)3])^3 ([HMnO3])^2)/(([HNO3])^8 ([Mn(NO3)2])^2 ([NaBiO3])^3)
Construct the equilibrium constant, K, expression for: HNO_3 + Mn(NO_3)_2 + NaBiO_3 ⟶ H_2O + NaNO_3 + Bi(NO3)3 + HMnO3 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: 8 HNO_3 + 2 Mn(NO_3)_2 + 3 NaBiO_3 ⟶ 3 H_2O + 3 NaNO_3 + 3 Bi(NO3)3 + 2 HMnO3 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 | 8 | -8 Mn(NO_3)_2 | 2 | -2 NaBiO_3 | 3 | -3 H_2O | 3 | 3 NaNO_3 | 3 | 3 Bi(NO3)3 | 3 | 3 HMnO3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HNO_3 | 8 | -8 | ([HNO3])^(-8) Mn(NO_3)_2 | 2 | -2 | ([Mn(NO3)2])^(-2) NaBiO_3 | 3 | -3 | ([NaBiO3])^(-3) H_2O | 3 | 3 | ([H2O])^3 NaNO_3 | 3 | 3 | ([NaNO3])^3 Bi(NO3)3 | 3 | 3 | ([Bi(NO3)3])^3 HMnO3 | 2 | 2 | ([HMnO3])^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])^(-8) ([Mn(NO3)2])^(-2) ([NaBiO3])^(-3) ([H2O])^3 ([NaNO3])^3 ([Bi(NO3)3])^3 ([HMnO3])^2 = (([H2O])^3 ([NaNO3])^3 ([Bi(NO3)3])^3 ([HMnO3])^2)/(([HNO3])^8 ([Mn(NO3)2])^2 ([NaBiO3])^3)

Rate of reaction

Construct the rate of reaction expression for: HNO_3 + Mn(NO_3)_2 + NaBiO_3 ⟶ H_2O + NaNO_3 + Bi(NO3)3 + HMnO3 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: 8 HNO_3 + 2 Mn(NO_3)_2 + 3 NaBiO_3 ⟶ 3 H_2O + 3 NaNO_3 + 3 Bi(NO3)3 + 2 HMnO3 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 | 8 | -8 Mn(NO_3)_2 | 2 | -2 NaBiO_3 | 3 | -3 H_2O | 3 | 3 NaNO_3 | 3 | 3 Bi(NO3)3 | 3 | 3 HMnO3 | 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 HNO_3 | 8 | -8 | -1/8 (Δ[HNO3])/(Δt) Mn(NO_3)_2 | 2 | -2 | -1/2 (Δ[Mn(NO3)2])/(Δt) NaBiO_3 | 3 | -3 | -1/3 (Δ[NaBiO3])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) NaNO_3 | 3 | 3 | 1/3 (Δ[NaNO3])/(Δt) Bi(NO3)3 | 3 | 3 | 1/3 (Δ[Bi(NO3)3])/(Δt) HMnO3 | 2 | 2 | 1/2 (Δ[HMnO3])/(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 = -1/8 (Δ[HNO3])/(Δt) = -1/2 (Δ[Mn(NO3)2])/(Δt) = -1/3 (Δ[NaBiO3])/(Δt) = 1/3 (Δ[H2O])/(Δt) = 1/3 (Δ[NaNO3])/(Δt) = 1/3 (Δ[Bi(NO3)3])/(Δt) = 1/2 (Δ[HMnO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: HNO_3 + Mn(NO_3)_2 + NaBiO_3 ⟶ H_2O + NaNO_3 + Bi(NO3)3 + HMnO3 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: 8 HNO_3 + 2 Mn(NO_3)_2 + 3 NaBiO_3 ⟶ 3 H_2O + 3 NaNO_3 + 3 Bi(NO3)3 + 2 HMnO3 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 | 8 | -8 Mn(NO_3)_2 | 2 | -2 NaBiO_3 | 3 | -3 H_2O | 3 | 3 NaNO_3 | 3 | 3 Bi(NO3)3 | 3 | 3 HMnO3 | 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 HNO_3 | 8 | -8 | -1/8 (Δ[HNO3])/(Δt) Mn(NO_3)_2 | 2 | -2 | -1/2 (Δ[Mn(NO3)2])/(Δt) NaBiO_3 | 3 | -3 | -1/3 (Δ[NaBiO3])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) NaNO_3 | 3 | 3 | 1/3 (Δ[NaNO3])/(Δt) Bi(NO3)3 | 3 | 3 | 1/3 (Δ[Bi(NO3)3])/(Δt) HMnO3 | 2 | 2 | 1/2 (Δ[HMnO3])/(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 = -1/8 (Δ[HNO3])/(Δt) = -1/2 (Δ[Mn(NO3)2])/(Δt) = -1/3 (Δ[NaBiO3])/(Δt) = 1/3 (Δ[H2O])/(Δt) = 1/3 (Δ[NaNO3])/(Δt) = 1/3 (Δ[Bi(NO3)3])/(Δt) = 1/2 (Δ[HMnO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| nitric acid | manganese(II) nitrate | sodium bismuthate | water | sodium nitrate | Bi(NO3)3 | HMnO3 formula | HNO_3 | Mn(NO_3)_2 | NaBiO_3 | H_2O | NaNO_3 | Bi(NO3)3 | HMnO3 Hill formula | HNO_3 | MnN_2O_6 | BiNaO_3 | H_2O | NNaO_3 | BiN3O9 | HMnO3 name | nitric acid | manganese(II) nitrate | sodium bismuthate | water | sodium nitrate | | IUPAC name | nitric acid | manganese(2+) dinitrate | sodium oxido-dioxobismuth | water | sodium nitrate | |
| nitric acid | manganese(II) nitrate | sodium bismuthate | water | sodium nitrate | Bi(NO3)3 | HMnO3 formula | HNO_3 | Mn(NO_3)_2 | NaBiO_3 | H_2O | NaNO_3 | Bi(NO3)3 | HMnO3 Hill formula | HNO_3 | MnN_2O_6 | BiNaO_3 | H_2O | NNaO_3 | BiN3O9 | HMnO3 name | nitric acid | manganese(II) nitrate | sodium bismuthate | water | sodium nitrate | | IUPAC name | nitric acid | manganese(2+) dinitrate | sodium oxido-dioxobismuth | water | sodium nitrate | |

Substance properties

| nitric acid | manganese(II) nitrate | sodium bismuthate | water | sodium nitrate | Bi(NO3)3 | HMnO3 molar mass | 63.012 g/mol | 178.95 g/mol | 279.967 g/mol | 18.015 g/mol | 84.994 g/mol | 394.99 g/mol | 103.94 g/mol phase | liquid (at STP) | | | liquid (at STP) | solid (at STP) | | melting point | -41.6 °C | | | 0 °C | 306 °C | | boiling point | 83 °C | | | 99.9839 °C | | | density | 1.5129 g/cm^3 | 1.536 g/cm^3 | | 1 g/cm^3 | 2.26 g/cm^3 | | solubility in water | miscible | | insoluble | | soluble | | 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) | 0.003 Pa s (at 250 °C) | | odor | | | | odorless | | |
| nitric acid | manganese(II) nitrate | sodium bismuthate | water | sodium nitrate | Bi(NO3)3 | HMnO3 molar mass | 63.012 g/mol | 178.95 g/mol | 279.967 g/mol | 18.015 g/mol | 84.994 g/mol | 394.99 g/mol | 103.94 g/mol phase | liquid (at STP) | | | liquid (at STP) | solid (at STP) | | melting point | -41.6 °C | | | 0 °C | 306 °C | | boiling point | 83 °C | | | 99.9839 °C | | | density | 1.5129 g/cm^3 | 1.536 g/cm^3 | | 1 g/cm^3 | 2.26 g/cm^3 | | solubility in water | miscible | | insoluble | | soluble | | 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) | 0.003 Pa s (at 250 °C) | | odor | | | | odorless | | |

Units

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