HNO3 + MnSO4 + NaBiO3 = H2O + Na2SO4 + NaNO3 + HMnO4 + Bi(NO3)3

HNO_3 nitric acid + MnSO_4 manganese(II) sulfate + NaBiO_3 sodium bismuthate ⟶ H_2O water + Na_2SO_4 sodium sulfate + NaNO_3 sodium nitrate + HMnO4 + Bi(NO3)3

Balance the chemical equation algebraically: HNO_3 + MnSO_4 + NaBiO_3 ⟶ H_2O + Na_2SO_4 + NaNO_3 + HMnO4 + Bi(NO3)3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 MnSO_4 + c_3 NaBiO_3 ⟶ c_4 H_2O + c_5 Na_2SO_4 + c_6 NaNO_3 + c_7 HMnO4 + c_8 Bi(NO3)3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O, Mn, S, Bi and Na: H: | c_1 = 2 c_4 + c_7 N: | c_1 = c_6 + 3 c_8 O: | 3 c_1 + 4 c_2 + 3 c_3 = c_4 + 4 c_5 + 3 c_6 + 4 c_7 + 9 c_8 Mn: | c_2 = c_7 S: | c_2 = c_5 Bi: | c_3 = c_8 Na: | c_3 = 2 c_5 + 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_6 = 1 and solve the system of equations for the remaining coefficients: c_1 = 16 c_2 = 2 c_3 = 5 c_4 = 7 c_5 = 2 c_6 = 1 c_7 = 2 c_8 = 5 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 16 HNO_3 + 2 MnSO_4 + 5 NaBiO_3 ⟶ 7 H_2O + 2 Na_2SO_4 + NaNO_3 + 2 HMnO4 + 5 Bi(NO3)3

+ + ⟶ + + + HMnO4 + Bi(NO3)3

nitric acid + manganese(II) sulfate + sodium bismuthate ⟶ water + sodium sulfate + sodium nitrate + HMnO4 + Bi(NO3)3

Construct the equilibrium constant, K, expression for: HNO_3 + MnSO_4 + NaBiO_3 ⟶ H_2O + Na_2SO_4 + NaNO_3 + HMnO4 + Bi(NO3)3 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: 16 HNO_3 + 2 MnSO_4 + 5 NaBiO_3 ⟶ 7 H_2O + 2 Na_2SO_4 + NaNO_3 + 2 HMnO4 + 5 Bi(NO3)3 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 | 16 | -16 MnSO_4 | 2 | -2 NaBiO_3 | 5 | -5 H_2O | 7 | 7 Na_2SO_4 | 2 | 2 NaNO_3 | 1 | 1 HMnO4 | 2 | 2 Bi(NO3)3 | 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 | 16 | -16 | ([HNO3])^(-16) MnSO_4 | 2 | -2 | ([MnSO4])^(-2) NaBiO_3 | 5 | -5 | ([NaBiO3])^(-5) H_2O | 7 | 7 | ([H2O])^7 Na_2SO_4 | 2 | 2 | ([Na2SO4])^2 NaNO_3 | 1 | 1 | [NaNO3] HMnO4 | 2 | 2 | ([HMnO4])^2 Bi(NO3)3 | 5 | 5 | ([Bi(NO3)3])^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])^(-16) ([MnSO4])^(-2) ([NaBiO3])^(-5) ([H2O])^7 ([Na2SO4])^2 [NaNO3] ([HMnO4])^2 ([Bi(NO3)3])^5 = (([H2O])^7 ([Na2SO4])^2 [NaNO3] ([HMnO4])^2 ([Bi(NO3)3])^5)/(([HNO3])^16 ([MnSO4])^2 ([NaBiO3])^5)

Construct the rate of reaction expression for: HNO_3 + MnSO_4 + NaBiO_3 ⟶ H_2O + Na_2SO_4 + NaNO_3 + HMnO4 + Bi(NO3)3 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: 16 HNO_3 + 2 MnSO_4 + 5 NaBiO_3 ⟶ 7 H_2O + 2 Na_2SO_4 + NaNO_3 + 2 HMnO4 + 5 Bi(NO3)3 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 | 16 | -16 MnSO_4 | 2 | -2 NaBiO_3 | 5 | -5 H_2O | 7 | 7 Na_2SO_4 | 2 | 2 NaNO_3 | 1 | 1 HMnO4 | 2 | 2 Bi(NO3)3 | 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 | 16 | -16 | -1/16 (Δ[HNO3])/(Δt) MnSO_4 | 2 | -2 | -1/2 (Δ[MnSO4])/(Δt) NaBiO_3 | 5 | -5 | -1/5 (Δ[NaBiO3])/(Δt) H_2O | 7 | 7 | 1/7 (Δ[H2O])/(Δt) Na_2SO_4 | 2 | 2 | 1/2 (Δ[Na2SO4])/(Δt) NaNO_3 | 1 | 1 | (Δ[NaNO3])/(Δt) HMnO4 | 2 | 2 | 1/2 (Δ[HMnO4])/(Δt) Bi(NO3)3 | 5 | 5 | 1/5 (Δ[Bi(NO3)3])/(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 = -1/16 (Δ[HNO3])/(Δt) = -1/2 (Δ[MnSO4])/(Δt) = -1/5 (Δ[NaBiO3])/(Δt) = 1/7 (Δ[H2O])/(Δt) = 1/2 (Δ[Na2SO4])/(Δt) = (Δ[NaNO3])/(Δt) = 1/2 (Δ[HMnO4])/(Δt) = 1/5 (Δ[Bi(NO3)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitric acid | manganese(II) sulfate | sodium bismuthate | water | sodium sulfate | sodium nitrate | HMnO4 | Bi(NO3)3 formula | HNO_3 | MnSO_4 | NaBiO_3 | H_2O | Na_2SO_4 | NaNO_3 | HMnO4 | Bi(NO3)3 Hill formula | HNO_3 | MnSO_4 | BiNaO_3 | H_2O | Na_2O_4S | NNaO_3 | HMnO4 | BiN3O9 name | nitric acid | manganese(II) sulfate | sodium bismuthate | water | sodium sulfate | sodium nitrate | | IUPAC name | nitric acid | manganese(+2) cation sulfate | sodium oxido-dioxobismuth | water | disodium sulfate | sodium nitrate | |

| nitric acid | manganese(II) sulfate | sodium bismuthate | water | sodium sulfate | sodium nitrate | HMnO4 | Bi(NO3)3 molar mass | 63.012 g/mol | 150.99 g/mol | 279.967 g/mol | 18.015 g/mol | 142.04 g/mol | 84.994 g/mol | 119.94 g/mol | 394.99 g/mol phase | liquid (at STP) | solid (at STP) | | liquid (at STP) | solid (at STP) | solid (at STP) | | melting point | -41.6 °C | 710 °C | | 0 °C | 884 °C | 306 °C | | boiling point | 83 °C | | | 99.9839 °C | 1429 °C | | | density | 1.5129 g/cm^3 | 3.25 g/cm^3 | | 1 g/cm^3 | 2.68 g/cm^3 | 2.26 g/cm^3 | | solubility in water | miscible | soluble | insoluble | | soluble | 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 | | | |