AP Chemistry - Solutions and Mixtures

3.7 Solutions & Mixtures

  • Enduring Understanding: SPQ-3 Interactions between intermolecular forces influence the solubility and separation of mixtures.
  • Learning Objective: SPQ-1.A Calculate the number of solute particles, volume, or molarity of solutions.
  • Essential Knowledge:
    • SPQ-3.A.1 Solutions, also sometimes called homogeneous mixtures, can be solids, liquids, or gases. In a solution, the macroscopic properties do not vary throughout the sample. In a heterogeneous mixture, the macroscopic properties depend on location in the mixture.
    • SPQ-3.A.2 Solution composition can be expressed in a variety of ways; molarity is the most common method used in the laboratory.
  • Equation: M = \frac{n{solute}}{L{solution}}
  • Solutions can be solids, liquids, or gases with uniform macroscopic properties.
  • Molarity is the most common concentration measure in the lab.
  • Properties of liquid solutions:
    • Components cannot be separated by filtering.
    • No components scatter visible light (Tyndall Effect).
    • Components can be separated by distillation or chromatography based on intermolecular interactions.
  • Ionic compounds dissociate into ions in solution.
  • The concentration of ions in a solution may not be the same as the original solution's molarity.
  • Example:
    • NaCl(s) \rightarrow Na^+(aq) + Cl^-(aq)
    • CaCl_2(s) \rightarrow Ca^{2+}(aq) + 2Cl^-(aq)
  • A 1 M CaCl_2 solution contains 1 mole of Ca^{2+} ions and 2 moles of Cl^- ions.
  • Calculating volume of a solution: L{solution} = \frac{moles{solute}}{M}
    • Example: Calculate the volume of a 1.25 M lithium chloride solution made with 13.3 g of lithium chloride.
      • Moles of LiCl = \frac{13.3 \text{ g } LiCl}{42.39 \text{ g/mol}} = 0.314 \text{ moles } LiCl
      • L_{solution} = \frac{0.314 \text{ moles } LiCl}{1.25 \text{ M}} = 0.251 \text{ L } LiCl \text{ solution}
  • Calculating ion concentration:
    • Example: Find the concentration of Cl^{1-} in a solution made by dissolving 10.0 g of ZnCl_2 in 500 mL of solution.
      • Moles of ZnCl2 = \frac{10.0 \text{ g } ZnCl2}{136.3 \text{ g/mol}} = 0.0734 \text{ moles } ZnCl_2
      • Since ZnCl2 \rightarrow Zn^{2+} + 2Cl^{1-}, there are 2 moles of Cl^{1-} per mole of ZnCl2.
      • Moles of Cl^{1-} = 0.0734 \text{ moles } ZnCl2 \times \frac{2 \text{ moles } Cl^{1-}}{1 \text{ mole } ZnCl2} = 0.147 \text{ moles } Cl^{1-}
      • M_{Cl^{1-}} = \frac{0.147 \text{ moles } Cl^{1-}}{0.500 \text{ L solution}} = 0.294 \text{ M } Cl^{1-}

3.8 Representations of Solutions

  • Enduring Understanding: SPQ-3 Interactions between intermolecular forces influence the solubility and separation of mixtures.
  • Learning Objective: SPQ-3.B Using particulate models for mixtures:
    • a. Represent interactions between components
    • b. Represent concentrations of components
  • Essential Knowledge: SPQ-3.B.1 Particulate representations of solutions communicate the structure and properties of solutions, by illustration of the relative concentrations of the components in the solution and drawings that show interactions among the components.
  • Colligative properties and calculations of molality, percent by mass, and percent by volume are not assessed on the AP Exam.
  • Intermolecular forces exist between solute particles, solvent particles, and solute-solvent particles.
  • These intermolecular forces can either promote or prevent the formation of a solution.
  • Miscibility: the ability of two substances to mix without separating.
  • "Like dissolves like":
    • Polar solvents dissolve polar solutes.
    • Nonpolar solvents dissolve nonpolar solutes.
  • A solution forms if:
    • Solvent-solute interactions > solvent-solvent and solute-solute interactions.
    • Solvent-solute interactions ≈ solvent-solvent and solute-solute interactions.
  • A solution will likely not form if solvent-solvent and solute-solute interactions > solvent-solute interactions.
  • Concentration in particulate diagrams is shown via relative amounts of solute in solution.
  • More particles ⇒ higher concentration.
  • Ionic substances dissociate and exist as ions in solution.
  • To determine which solvent is most effective:
    • Ethanol (C2H5OH):
      • Ethanol is part hydrocarbon (nonpolar) and part polar at the -OH hydroxyl group.
      • Since the hydrocarbon portion is relatively small, the very polar -0H group will dominate. Ethanol can form hydrogen bonds with water and is therefore more miscible in water.
    • Potassium chloride (KCl):
      • KCl is an ionic compound.
      • The strong charges on K+ and Cl- would attract strongly to the polar partial charges in water and form ion-dipole interactions. KCl is miscible in water.

3.9 Separation of Solutions and Mixtures - Chromatography

  • Enduring Understanding: SPQ-3 Interactions between intermolecular forces influence the solubility and separation of mixtures.
  • Learning Objective: SPQ-3.C Explain the relationship between the solubility of ionic and molecular compounds in aqueous and nonaqueous solvents and the intermolecular interactions between particles.
  • Essential Knowledge:
    • SPQ-3.A.1 The components of a liquid solution cannot be separated by filtration.
    • They can, however, be separated using processes that take advantage of differences in the intermolecular interactions of the components.
    • Chromatography (paper, thin-layer, and column) separates chemical species by taking advantage of the differential strength of intermolecular interactions between and among the components of the solution (the mobile phase) and with the surface components of the stationary phase.
    • Distillation separates chemical species by taking advantage of the differential strength of intermolecular interactions between and among the components and the effects these interactions have on the vapor pressures of the components in the mixture.
  • Equation: Rf = \frac{d{dye}}{d_{solvent}}
    • R_f – retention factor unique per solute (dye)
    • d_{ink} – farthest distance the dye travelled
    • d_{solvent} – farthest distance the solvent travelled
  • Chromatography separates mixtures based on polarity differences (solubility).
  • Types:
    • Paper chromatography (most common in AP Chemistry)
    • Thin layer chromatography
    • Column Chromatography
  • Paper Chromatography Methodology:
    1. Draw a line (pencil) near the end of the paper strip.
    2. Place a drop of the sample on the line.
    3. Place the paper in a sealed container with a shallow layer of solvent, ensuring the bottom of the paper touches the solvent but the sample line does not.
    4. Allow time for separation.
    5. Remove paper before solvent reaches the top.
    6. Measure the height of the leading edge of the solvent and each dye.
  • Paper Chromatography Analysis:
    • The same compound moves at the same rate relative to the same solvent in different trials.
    • Different compounds have slightly different polarities, so the R_f factor differs.
    • The more similar the sample's polarity to the solvent, the farther it travels.
    • Polar water: polar samples travel far, nonpolar samples travel a short distance.
    • Nonpolar benzene: polar samples travel a short distance, nonpolar samples travel far.
    • Identification via comparing R_f values, NOT DISTANCES.
    • Stationary phase: paper, mobile phase: solvent.
  • Thin Layer Chromatography:
    • Similar to paper chromatography but separation occurs on a thin layer of silica or alumina on a plastic sheet.
    • Can separate colorless samples using UV light and a fluorescent solvent.
    • Frequently used with amino acids.
  • Thin Layer Chromatography Analysis:
    • The same compound moves at the same rate relative to the solvent on different trials.
    • Different compounds have slightly different polarities, so the R_f factor differs.
    • Typically, the more nonpolar the sample, the farther it travels.
    • Typically, the more polar the sample, the shorter it travels.
    • Identification via comparing R_f values.
  • Column Chromatography:
    1. Place steel wool at the bottom of a burette to prevent gel from escaping.
    2. Fill a burette with very polar silica or alumina gel (usually).
    3. Place the mixture at the top, flush with nonpolar solvent repeatedly.
    4. Collect separated phases in beakers or flasks.
  • Column Chromatography Analysis:
    • Most polar parts travel slowest, least polar travel fastest.
    • Once one part is separated, a new solvent can speed up the movement of remaining parts.
    • Meant for separation more than analysis.
  • Distillation:
    • Separates substances based on differences in boiling points and intermolecular forces.
  • Applications:
    * Distillation of fermented beverages
    * Desalination of salt water
    * Separation of crude oil into fuels and other petroleum products (fractional distillation).
  • Fractional distillation is better for boiling points that are close together; it allows vapor to condense and revaporize for better purification.
  • With all chromatography, recognize which part of the system interacts with the materials being tested.
  • Consider intermolecular forces for all components.

3.10 Solubility

  • Enduring Understanding: SPQ-3 Interactions between intermolecular forces influence the solubility and separation of mixtures.
  • Learning Objective: SPQ-3.C Explain the relationship between the solubility of ionic and molecular compounds in aqueous and nonaqueous solvents, and the intermolecular interactions between particles.
  • Essential Knowledge: SPQ-3.C.2 Substances with similar intermolecular interactions tend to be miscible or soluble in one another
  • Solubility: extent to which a solute dissolves in a solvent.
    • Highly soluble: a lot dissolves
    • Slightly (sparingly) soluble: very little dissolves
    • Insoluble: none dissolves
  • Water:
    • A common solvent due to its ability to dissolve many substances.
    • Aqueous solution: water as the solvent.
    • Highly polar molecule with 2 sets of lone pairs on oxygen ⇒ partial negative charge on oxygen, partial positive charge on hydrogens.
    • Bent/angular molecular geometry with a bond angle of 104.5°.
  • Hydration: water molecules surround ions to dissolve them.
    • Water molecules orient with their partially positive ends closest to negative ions and partially negative ends closest to positive ions.
    • This attraction is often referred to as an ion-dipole.
  • Water also dissolves non-ionic substances if they are polar and can form hydrogen bonds (e.g., acetic acid).
  • "Like dissolves like": substances with similar IMFs to the solvent will dissolve.
  • Steps for solution formation:
    1. Solute particles must separate (energy required)
    2. Solvent particles must separate (energy required)
    3. Solute and solvent particles must come back together (energy released)
  • Miscible: two substances can mix together (e.g., vinegar and water).
  • Immiscible: two substances cannot mix together (e.g., oil and water).

3.11 Spectroscopy and the Electromagnetic Spectrum

  • Enduring Understanding: SAP-8 Spectroscopy can determine the structure and concentration in a mixture of a chemical species.
  • Learning Objective: SAP-8.A Explain the relationship between a region of the electromagnetic spectrum and the types of molecular or electronic transitions associated with that region.
  • Essential Knowledge: SAP-8.A.1 Differences in absorption or emission of photons in different spectral regions are related to the different types of molecular motion or electronic transition:
    • Microwave radiation is associated with transitions in molecular rotational levels.
    • Infrared radiation is associated with transitions in molecular vibrational levels.
    • Ultraviolet/visible radiation is associated with transitions in electronic energy levels.
  • Spectroscopy is the study of how matter interacts with electromagnetic radiation.
  • Molecules can move in different ways:
    • Translational
      • Movement from one place to another
    • Rotational
      • Spinning in place
    • Vibrational
      • Moving in place, the movement of the atoms within the molecule relative to one another, such as bending, stretching and other internal movements within the molecule.
  • Microwave Rotational Spectroscopy:
    • Microwave radiation is lower in energy than visible light.
    • Causes molecules to rotate due to the interaction of the dipole moments of the molecules interacting with the electromagnetic field of the microwave photons.
    • Microwave radiation is associated with transitions in molecular rotational levels.
  • Infrared Vibrational Spectroscopy:
    • Infrared (IR) spectroscopy measures the vibration of the atoms and allows the determination of the functional groups present in a molecule by analyzing absorption, emission, and reflection.
    • Lighter atoms and stronger bonds tend to vibrate at higher frequencies.
    • Infrared radiation is associated with transitions in molecular vibrational levels.
  • Ultraviolet - Visible Light Spectroscopy:
    • Visible light spectroscopy is concerned with the part of the electromagnetic spectrum that we can see… the colors in the rainbow, the continuum from red to violet, from low to high energy, ~400-700 nm.
    • The ultraviolet portion of the electromagnetic spectrum is higher in energy as the wavelengths are shorter (~50-400 nm) and therefore the frequency is higher.
    • Photons of colored light are absorbed by a compound causing electrons to move from their ground state to a higher energy "excited" state.
    • Ultraviolet/visible radiation is associated with transitions in electronic energy levels.
  • By measuring the amount of light leaving (transmitted from) a sample and comparing it to the amount of light that entered the sample we can find the amount of light that was absorbed by the sample.
  • Completed using a device called a spectrophotometer.
  • By knowing the amount of light absorbed, one can determine the concentration of a colored substance within a solution.

3.12 The Photoelectric Effect

  • Enduring Understanding: SAP-8 Spectroscopy can determine the structure and concentration in a mixture of a chemical species.

  • Learning Objective: SAP-8.B Explain the properties of an absorbed or emitted photon in relationship to an electronic transition in an atom or molecule.

  • Essential Knowledge:

    • SAP-8.B.1 When a photon is absorbed (or emitted) by an atom or molecule, the energy of the species is increased (or decreased) by an amount equal to the energy of the photon.
    • SAP-8.B.2 The wavelength of the electromagnetic wave is related to its frequency and the speed of light by the equation: c = λν.
    • The energy of a photon is related to the frequency of the electromagnetic wave through Planck’s equation: E = hν.

  • Photoelectric Effect: when light shines on the surface of metal, electrons can be ejected from the surface.

  • Light has wave-like and particle-like properties: light is composed of photons with energy E = hν.

  • By measuring the amount of energy needed to remove the electrons, we can deduce how tightly the electrons are being held in the atom, known as the binding energy.

  • Greater energy values indicate the electrons that are closest to the nucleus or that the nucleus is a higher charge.

  • The amount of energy needed to remove an electron is measured by the threshold frequency, ν_0.

  • The amount of energy needed to eject an electron can also be thought of in terms of the longest wavelength that will still eject an electron, called the threshold wavelength, λMAX, and any waves that are shorter than the max will have enough energy to eject electrons.

  • Energy is proportional to frequency, but inversely proportional to the wavelength.

    • E = hν

    • E = \text{Energy (J)}

    • h = \text{Plank’s Constant}, 6.626x10^{-34} \text{ Js}

    • ν = \text{frequency (Hz, s}^{-1})

    • Since c=νλ

    • E = \frac{hc}{λ}

    • E = \text{Energy (J)}

    • h = \text{Plank’s Constant}, 6.626x10^{-34} \text{ Js}

    • c = \text{speed of light}, 3.00x10^8 \text{ m/s}

    • λ = \text{wavelength (m)}

  • 1x10-9m = 1 nm

  • E{photon} = KE{electron} +Ф Phi, is the work function for different materials and is the energy to remove the electron.

  • Ф = \frac{hc}{λMAX} = hν_0

  • Summary of the Photoelectric Effect

    • The energy of the photons (light) must meet the minimum energy. This is given in terms of being a higher frequency than the threshold frequency, ν0, or having a shorter wavelength that the λMAX. If the minimum energy is not met, electrons will not be emitted.
    • The rate of emission of the photoelectrons is known as the photoelectric current. Photoelectric current is proportional to the intensity of the light.
    • If the minimum energy is met to eject electrons, the kinetic energy of the photoelectrons is dependent on the energy of the light used to eject the electrons.

3.13 Beer-Lambert Law

  • Enduring Understanding: SAP-8 Spectroscopy can determine the structure and concentration in a mixture of a chemical species.
  • Learning Objective: SAP-8.C Explain the amount of light absorbed by a solution of molecules or ions in relationship to the concentration, path length, and molar absorptivity.
  • Essential Knowledge:
    • SAP-8.C.1 The Beer-Lambert law relates the absorption of light by a solution to three variables according to the equation: A = ԑbc.
    • The molar absorptivity ԑ describes how intensely a sample of molecules or ions absorbs light of a specific wavelength. The path length b and concentration c are proportional to the number of absorbing species.
    • SAP-8.C.2 In most experiments the path length and wavelength of light are held constant. In such cases, the absorbance is proportional only to the concentration of absorbing molecules or ions.
  • The measure of the light that is stopped by or absorbed by a solution is referred to as the absorbance.
  • The more concentrated the solution is, the less light can pass through the solution.
  • Molarity is the moles of solute divided by the volume of solution.
    • M = \frac{\text{moles of solute}}{\text{Liters of solution}}
    • Molarity has the units moles/Liters.
  • Different colors of solutions absorb different colors (or wavelengths) of light. We want to choose complementary colors. If we are using a red solution, we should choose to use green light with a wavelength of 560-520 nm to measure it.
  • For colored solutions, absorbance can be used to measure the concentration of solutions.
    • First, you need to determine the best wavelength to use to measure your sample. To do this you will place your sample into a spectrophotometer and generate a graph of absorbance vs. wavelength. The best choice for a wavelength is one were the absorbance is close to 1.
    • Then, you create a calibration graph with standard solution concentrations and their corresponding absorbance value. This graph should be linear, and the slope of the line will give you the molar absorptivity constant. The more concentrated a solution is the more light is absorbed by the solution.
  • Beer-Lambert Law describes this relationship as A = ԑ b c.
    • A = \text{Absorbance}
      • Absorbance is unitless.
    • ԑ = \text{molar absorptivity constant (this is the slope of the graph) (1/M*cm)}
    • b = \text{path length (usually 1 cm)}
    • c = \text{concentration (Molarity, M)}
  • The path length term, b, is the width of the cuvette that the sample is placed in. The standard path length is 1 cm. This is usually held constant.
  • When you calibrate the spectrophotometer you should start with a “blank” the “blank” is your solvent only, usually water.
    • By calibrating the spectrophotometer with the blank it will remove the data from the solvent and therefore only outputs the absorbance of the solute. (It is analogous to using the “tare” button on a digital scale.)