Solutions - Notes

Solutions

• A solution is a homogeneous mixture of two or more substances in a single phase.
• The component present in the largest amount is the solvent, and the other components are the solutes.

Common Types of Solutions

• Solutions can be combinations of solid and liquid, gas and liquid, or other combinations, as shown in Table 13.1.

Homogeneous Mixtures and Spontaneous Mixing

• Most homogeneous materials we encounter are solutions, such as air and seawater.
• Nature tends toward spontaneous mixing.
• Uniform mixing is generally more energetically favorable.

The Solution Process

• Solutes dissolve in solvents through solvation.
• "Like dissolves like": Polar solvents dissolve polar solutes, and non-polar solvents dissolve non-polar solutes.
• Miscible liquids mix to an appreciable extent to form a solution.
• Immiscible liquids do not mix and remain as separate layers.
• Dipole-dipole attraction and hydrogen bonding are key interactions.
• Ion-dipole attraction relates to the enthalpy of hydration, denoted as $\Delta_{hydration} H$.
• Ion-ion attraction is defined by the lattice enthalpy, denoted as $\Delta_{lattice} H$.

Miscibility Examples

• Non-polar octane (C8H18) forms a less dense layer.
• A solution of copper sulfate (CuSO4) in water is shown.
• Non-polar carbon tetrachloride (CCl4) forms a denser layer.
• A homogeneous mixture of nonpolar CCl4 and C8H18 has a greater density than water

Solubility

• Nonpolar solutes dissolve in nonpolar solvents (e.g., Hexane, $C<em>6H</em>{14}$).
• Polar and ionic solutes dissolve in polar solvents (e.g., $H<em>2O$, $CH</em>3OH$, $C<em>2H</em>5OH$).
• Hydrogen bonding solutes dissolve in hydrogen bonding solvents (e.g., $H<em>2O$, $CH</em>3OH$, $C<em>2H</em>5OH$).

Like Dissolves Like

1. Nonpolar solutes dissolve in nonpolar solvents.
2. Polar and ionic solutes dissolve in polar solvents.
3. Hydrogen bonding solutes dissolve in hydrogen bonding solvents.

• A substance is soluble in a solvent with similar intermolecular forces (IMFs).

Solubility Demonstration

• Nonpolar iodine (I2) isn't soluble in polar water (H2O) but is soluble in nonpolar carbon tetrachloride (CCl4).
• Shaking a test tube with I2, H2O, and CCl4 results in I2 dissolving in CCl4.

Solubility Rules for Ionic Compounds in Water (Chapter 4)

• General Soluble Ions:
  • $Li^+, Na^+, K^+, NH_4^+$: No exceptions.
  • $NO<em>3^-$, $C</em>2H<em>3O</em>2^-$: No exceptions.
  • $Cl^-, Br^-, I^-$: Insoluble when paired with $Ag^+, Hg_2^{2+}, Pb^{2+}$.
  • SO_4^{2-}$: Insoluble when paired with Sr^{2+}, Ba^{2+}, Pb^{2+}, Ag^+, Ca^{2+}.
• Generally Insoluble Ions:
  • OH^-, S^{2-}$: Soluble when paired with $Li^+, Na^+, K^+, NH_4^+$. $S^{2-}$ is also soluble when paired with $Ca^{2+}, Sr^{2+}, Ba^{2+}$.
    • $OH^-$ is slightly soluble when paired with $Ca^{2+}, Sr^{2+}, Ba^{2+}$.
  • CO3^{2-}, PO4^{3-}$: Soluble when paired with Li^+, Na^+, K^+, NH_4^+.

Application of Solubility Rules

• Will a solution form?
  1. CaCl2$and$H2O: Yes
  2. KBr$and$C6H{14}: No
  3. I2$and$C6H_{14}: Yes
  4. CCl4$and$H2O: No
  5. CH3OH$and$H2O: Yes
  6. CH3OH$and$C6H_{14}: Yes

Molality Calculation

• Molality formula:
  m = \frac{\text{moles of solute}}{\text{kg of solvent}}
  \text{moles of solute} = \frac{\text{grams}}{\text{molar mass}}
  \text{kg of solvent} = \frac{\text{grams}}{\text{molar mass}} \times \text{kg of solvent}

Molality vs. Molarity

• Molality (m):
  • Definition: moles of solute per kg of solvent.
  • Expressed as: molal.
  • Symbol: m
• Molarity (M):
  • Definition: moles of solute per liter of solution.
  • Expressed as: molar.
  • Symbol: M
• Key Difference:
  • Molality uses kg of solvent while molarity uses liters of solution.

Visualizing Molality vs Molarity

• 0. 100 molal solution:
  • Water added to flask = 1.00 kg
  • Volume of solution > 1.00 L
• 0. 100 molar solution:
  • Water added to flask < 1.00 L
  • Volume of solution = 1.00 L

Solution Concentration Terms

Molality Calculation Example

• Calculate the molality of a solution made by dissolving 4.50 g of Naphthalene (C{10}H8$) in 95.5 g of CCl4. Given the molar mass of$C{10}H8 is 128.2 g/mol.

  • Moles of solute = 4.50 g / 128.2 g/mol = 0.0351 mole
  • Molality (m) = 0.0351 mol / 0.0955 kg = 0.368 mol/kg

Molality Calculation Example 2

• How many grams of C2H5OH$(molar mass 46.07 g/mol) must be dissolved in 500.mL of$H_2O to give a 0.450 molal solution?
  • Answer: 10.4g
    0.450 \text{ molal} = \frac{\text{moles of } C2H5OH}{0.500 \text{ kg of } H2O} \text{moles of } C2H5OH = 0.450 \times 0.500 = 0.225 \text{ moles} \text{grams of } C2H_5OH = 0.225 \text{ moles} \times 46.07 \text{ g/mol} = 10.36575 \text{ g} \approx 10.4 \text{ g}

Molality Calculation Example 3

• Calculate the molality of a 28% aqueous NH3$solution; the molar mass of$NH3 is 17.0 g/mol.
  • Answer: 23 molal

Colligative Properties of Solutions

1. Vapor pressure lowering
2. Boiling point elevation
3. Freezing point depression
4. Osmotic pressure

• Formulas:

  \Delta T{fp} = K{fp} \cdot m{solution} \Delta Tb = Kb \cdot m{solution}

• Be able to calculate boiling point elevation (\Delta T{bP}$) and freezing point depression ($\Delta T{fP}) of a solution.

Colligative Properties

• Physical properties of solution that depend only on the relative number of solute & solvent particles
  • Vapor Pressure
  • Boiling Point
  • Freezing Point
  • Osmotic Pressure

Changes in Vapor Pressure: Raoult’s Law

• Vapor pressure: pressure exerted by the vapor when a liquid in a closed container is at equilibrium with the vapor.
• Vapor pressure of solution is decreased by the presence of a solute.
• More solute particles present in a solution will result in lower vapor pressure of the solution.

Freezing Point Depression

• When a nonvolatile solute is added to a solvent, the temperature at which the resulting solution freezes is lower than the freezing point of the pure solvent.

Boiling Point Elevation

• When a nonvolatile solute is added to a solvent, the temperature at which the resulting solution boils is higher than the boiling point of the pure solvent.

Boiling Point Elevation & Freezing Point Depression

• The temperature of the normal boiling point of a solution is increased.

  \Delta Tb = Kb \cdot m_{solution}

• The temperature of the normal freezing point of a solution is decreased.

  \Delta Tf = Kf \cdot m_{solution}

• Where the K’s are the respective boiling and freezing point constants and m_{solution} is the molality of the solution.

Calculations

• Using the following formulas, derived from Raoult’s Law:

  \Delta T{fp} = K{fp} \cdot m{solution} \Delta Tb = Kb \cdot m{solution}

• Be able to calculate the boiling point elevation (\Delta T{bP}$) and freezing point depression ($\Delta T{fP}) of a solution.

Boiling Point Elevation Question #1

• You dissolve 29.3 g of NaCl (molar mass = 58.5 g/mol) in 500. grams water. What is the boiling point of this solution? (Kbp for water = 0.512 deg/molal)

  1. 100.512 °C
  2. 98.976 °C
  3. 101.536 °C
  4. 1.024 °C
  • Answer: 100.512 °C

Freezing Point Depression Question #2

• E´rythritol is a compound that occurs naturally in algae and fungi. It is about twice as sweet as sucrose. A solution of 2.50 g of erythritol in 50.0 g of water freezes at -0.762 °C. (The freezing point depression constant for water = 1.86 degrees/molal.) What is the molar mass of the compound?

  1. 26.9 g/mol
  2. 35.5 g/mol
  3. 122 g/mol
  4. 224 g/mol
  • Answer: 122 g/mol

Boiling Point Elevation Question #3

• What mass of ethylene glycol (HOC2H4OH, molar mass is 62.0 g/mol) must be added to 125 g of water to raise the boiling point by 1.0 °C? (Kbp for water = 0.512 deg/molal)

  1. 95 g
  2. 244 g
  3. 0 g
  4. 0 g
  • Answer: 15 grams

Osmosis

• A semipermeable membrane allows only the movement of solvent molecules.
• Solvent molecules move from pure solvent to solution in an attempt to make both have the same concentration of solvent.

Process of Osmosis

• Illustrates movement of water across a semi-permeable membrane from an area of high water concentration to lower water concentration.

Osmotic Pressure

• The amount of pressure needed to keep osmotic flow from taking place is called the osmotic pressure.

• The osmotic pressure, \Pi, is directly proportional to the molarity of the solute particles.

  \Pi = MRT$$

  • R = 0.08206 (atm∙L)/(mol∙K)

Osmosis & Tonicity

• Osmosis of solvent from one solution to another will occur as they try to equalize one another’s concentration.
• At the point where they have equal osmotic pressures, they are said to be Isotonic.

Osmosis at the Particulate Level

• Illustrates movement of water and hydrated ions across a semipermeable membrane.

Reverse Osmosis: Water Desalination

• Applying pressure to seawater forces water molecules through a semipermeable membrane, separating them from concentrated solution (salt).