#### Input interpretation

KI potassium iodide + Bi(NO3)3 ⟶ KNO_3 potassium nitrate + BiI_3 bismuth(III) iodide

#### Balanced equation

Balance the chemical equation algebraically: KI + Bi(NO3)3 ⟶ KNO_3 + BiI_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KI + c_2 Bi(NO3)3 ⟶ c_3 KNO_3 + c_4 BiI_3 Set the number of atoms in the reactants equal to the number of atoms in the products for I, K, Bi, N and O: I: | c_1 = 3 c_4 K: | c_1 = c_3 Bi: | c_2 = c_4 N: | 3 c_2 = c_3 O: | 9 c_2 = 3 c_3 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 = 3 c_2 = 1 c_3 = 3 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 KI + Bi(NO3)3 ⟶ 3 KNO_3 + BiI_3

#### Structures

+ Bi(NO3)3 ⟶ +

#### Names

potassium iodide + Bi(NO3)3 ⟶ potassium nitrate + bismuth(III) iodide

#### Equilibrium constant

Construct the equilibrium constant, K, expression for: KI + Bi(NO3)3 ⟶ KNO_3 + BiI_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: 3 KI + Bi(NO3)3 ⟶ 3 KNO_3 + BiI_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 KI | 3 | -3 Bi(NO3)3 | 1 | -1 KNO_3 | 3 | 3 BiI_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KI | 3 | -3 | ([KI])^(-3) Bi(NO3)3 | 1 | -1 | ([Bi(NO3)3])^(-1) KNO_3 | 3 | 3 | ([KNO3])^3 BiI_3 | 1 | 1 | [BiI3] 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 = ([KI])^(-3) ([Bi(NO3)3])^(-1) ([KNO3])^3 [BiI3] = (([KNO3])^3 [BiI3])/(([KI])^3 [Bi(NO3)3])

#### Rate of reaction

Construct the rate of reaction expression for: KI + Bi(NO3)3 ⟶ KNO_3 + BiI_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: 3 KI + Bi(NO3)3 ⟶ 3 KNO_3 + BiI_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 KI | 3 | -3 Bi(NO3)3 | 1 | -1 KNO_3 | 3 | 3 BiI_3 | 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 KI | 3 | -3 | -1/3 (Δ[KI])/(Δt) Bi(NO3)3 | 1 | -1 | -(Δ[Bi(NO3)3])/(Δt) KNO_3 | 3 | 3 | 1/3 (Δ[KNO3])/(Δt) BiI_3 | 1 | 1 | (Δ[BiI3])/(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 = -1/3 (Δ[KI])/(Δt) = -(Δ[Bi(NO3)3])/(Δt) = 1/3 (Δ[KNO3])/(Δt) = (Δ[BiI3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

#### Chemical names and formulas

| potassium iodide | Bi(NO3)3 | potassium nitrate | bismuth(III) iodide formula | KI | Bi(NO3)3 | KNO_3 | BiI_3 Hill formula | IK | BiN3O9 | KNO_3 | BiI_3 name | potassium iodide | | potassium nitrate | bismuth(III) iodide IUPAC name | potassium iodide | | potassium nitrate | triiodobismuthane

#### Substance properties

| potassium iodide | Bi(NO3)3 | potassium nitrate | bismuth(III) iodide molar mass | 166.0028 g/mol | 394.99 g/mol | 101.1 g/mol | 589.69381 g/mol phase | solid (at STP) | | solid (at STP) | solid (at STP) melting point | 681 °C | | 334 °C | 408 °C boiling point | 1330 °C | | | density | 3.123 g/cm^3 | | | 5.78 g/cm^3 solubility in water | | | soluble | dynamic viscosity | 0.0010227 Pa s (at 732.9 °C) | | | odor | | | odorless |

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