HNO3 + MnSO4 + KBiO3 = H2O + H2SO4 + KMnO4 + KNO3 + BiONO3

HNO_3 nitric acid + MnSO_4 manganese(II) sulfate + KBiO3 ⟶ H_2O water + H_2SO_4 sulfuric acid + KMnO_4 potassium permanganate + KNO_3 potassium nitrate + NO_4Bi bismuth oxynitrate

Balance the chemical equation algebraically: HNO_3 + MnSO_4 + KBiO3 ⟶ H_2O + H_2SO_4 + KMnO_4 + KNO_3 + NO_4Bi Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 MnSO_4 + c_3 KBiO3 ⟶ c_4 H_2O + c_5 H_2SO_4 + c_6 KMnO_4 + c_7 KNO_3 + c_8 NO_4Bi Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O, Mn, S, K and Bi: H: | c_1 = 2 c_4 + 2 c_5 N: | c_1 = c_7 + c_8 O: | 3 c_1 + 4 c_2 + 3 c_3 = c_4 + 4 c_5 + 4 c_6 + 3 c_7 + 4 c_8 Mn: | c_2 = c_6 S: | c_2 = c_5 K: | c_3 = c_6 + c_7 Bi: | c_3 = c_8 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 = 5/2 c_4 = 1 c_5 = 1 c_6 = 1 c_7 = 3/2 c_8 = 5/2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 8 c_2 = 2 c_3 = 5 c_4 = 2 c_5 = 2 c_6 = 2 c_7 = 3 c_8 = 5 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 HNO_3 + 2 MnSO_4 + 5 KBiO3 ⟶ 2 H_2O + 2 H_2SO_4 + 2 KMnO_4 + 3 KNO_3 + 5 NO_4Bi

+ + KBiO3 ⟶ + + + +

nitric acid + manganese(II) sulfate + KBiO3 ⟶ water + sulfuric acid + potassium permanganate + potassium nitrate + bismuth oxynitrate

Construct the equilibrium constant, K, expression for: HNO_3 + MnSO_4 + KBiO3 ⟶ H_2O + H_2SO_4 + KMnO_4 + KNO_3 + NO_4Bi 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 MnSO_4 + 5 KBiO3 ⟶ 2 H_2O + 2 H_2SO_4 + 2 KMnO_4 + 3 KNO_3 + 5 NO_4Bi 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 MnSO_4 | 2 | -2 KBiO3 | 5 | -5 H_2O | 2 | 2 H_2SO_4 | 2 | 2 KMnO_4 | 2 | 2 KNO_3 | 3 | 3 NO_4Bi | 5 | 5 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) MnSO_4 | 2 | -2 | ([MnSO4])^(-2) KBiO3 | 5 | -5 | ([KBiO3])^(-5) H_2O | 2 | 2 | ([H2O])^2 H_2SO_4 | 2 | 2 | ([H2SO4])^2 KMnO_4 | 2 | 2 | ([KMnO4])^2 KNO_3 | 3 | 3 | ([KNO3])^3 NO_4Bi | 5 | 5 | ([N1O4Bi1])^5 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) ([MnSO4])^(-2) ([KBiO3])^(-5) ([H2O])^2 ([H2SO4])^2 ([KMnO4])^2 ([KNO3])^3 ([N1O4Bi1])^5 = (([H2O])^2 ([H2SO4])^2 ([KMnO4])^2 ([KNO3])^3 ([N1O4Bi1])^5)/(([HNO3])^8 ([MnSO4])^2 ([KBiO3])^5)

Construct the rate of reaction expression for: HNO_3 + MnSO_4 + KBiO3 ⟶ H_2O + H_2SO_4 + KMnO_4 + KNO_3 + NO_4Bi 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 MnSO_4 + 5 KBiO3 ⟶ 2 H_2O + 2 H_2SO_4 + 2 KMnO_4 + 3 KNO_3 + 5 NO_4Bi 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 MnSO_4 | 2 | -2 KBiO3 | 5 | -5 H_2O | 2 | 2 H_2SO_4 | 2 | 2 KMnO_4 | 2 | 2 KNO_3 | 3 | 3 NO_4Bi | 5 | 5 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) MnSO_4 | 2 | -2 | -1/2 (Δ[MnSO4])/(Δt) KBiO3 | 5 | -5 | -1/5 (Δ[KBiO3])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) H_2SO_4 | 2 | 2 | 1/2 (Δ[H2SO4])/(Δt) KMnO_4 | 2 | 2 | 1/2 (Δ[KMnO4])/(Δt) KNO_3 | 3 | 3 | 1/3 (Δ[KNO3])/(Δt) NO_4Bi | 5 | 5 | 1/5 (Δ[N1O4Bi1])/(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[MnSO4])/(Δt) = -1/5 (Δ[KBiO3])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/2 (Δ[H2SO4])/(Δt) = 1/2 (Δ[KMnO4])/(Δt) = 1/3 (Δ[KNO3])/(Δt) = 1/5 (Δ[N1O4Bi1])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitric acid | manganese(II) sulfate | KBiO3 | water | sulfuric acid | potassium permanganate | potassium nitrate | bismuth oxynitrate formula | HNO_3 | MnSO_4 | KBiO3 | H_2O | H_2SO_4 | KMnO_4 | KNO_3 | NO_4Bi Hill formula | HNO_3 | MnSO_4 | BiKO3 | H_2O | H_2O_4S | KMnO_4 | KNO_3 | BiNO_4 name | nitric acid | manganese(II) sulfate | | water | sulfuric acid | potassium permanganate | potassium nitrate | bismuth oxynitrate IUPAC name | nitric acid | manganese(+2) cation sulfate | | water | sulfuric acid | potassium permanganate | potassium nitrate | nitric acid oxobismuthinyl ester

| nitric acid | manganese(II) sulfate | KBiO3 | water | sulfuric acid | potassium permanganate | potassium nitrate | bismuth oxynitrate molar mass | 63.012 g/mol | 150.99 g/mol | 296.076 g/mol | 18.015 g/mol | 98.07 g/mol | 158.03 g/mol | 101.1 g/mol | 286.983 g/mol phase | liquid (at STP) | solid (at STP) | | liquid (at STP) | liquid (at STP) | solid (at STP) | solid (at STP) | melting point | -41.6 °C | 710 °C | | 0 °C | 10.371 °C | 240 °C | 334 °C | boiling point | 83 °C | | | 99.9839 °C | 279.6 °C | | | density | 1.5129 g/cm^3 | 3.25 g/cm^3 | | 1 g/cm^3 | 1.8305 g/cm^3 | 1 g/cm^3 | | solubility in water | miscible | soluble | | | very soluble | | soluble | surface tension | | | | 0.0728 N/m | 0.0735 N/m | | | dynamic viscosity | 7.6×10^-4 Pa s (at 25 °C) | | | 8.9×10^-4 Pa s (at 25 °C) | 0.021 Pa s (at 25 °C) | | | odor | | | | odorless | odorless | odorless | odorless |