Solutions Chemistry Notes

Solutions

Objectives

• Describe energy changes during the solution process (solute-solute, solvent-solvent, solute-solvent attractive forces) and the role of disorder.
• Define mass percentage, parts per million, mole fraction, molarity, and molality.
• Calculate concentrations using these units.
• Define solution-related terms: solvent, solute, hydration, miscible, saturated, etc.
• Convert between concentration units (given solution density).
• Determine if a mixture is saturated, supersaturated, or unsaturated, and calculate undissolved solid amount.
• Relate solubility to molecular structures and intermolecular forces; predict relative solubility in specific solvents.
• Describe effects of pressure and temperature on solubility of solids and gases, including Henry's Law.
• Describe effects of dissolved particle concentration on vapor pressure, boiling point, freezing point, and osmotic pressure; calculate colligative properties from concentration data.
• Estimate the van't Hoff i factor from a compound's formula.
• Determine concentration and molar mass of nonvolatile nonelectrolytes or electrolytes from colligative properties.
• Predict the lowest/highest freezing or boiling point among compounds (including electrolytes) given their molality.

Solution Vocabulary

• Solution: Solute + Solvent
• A uniform or homogenous mixture.

Examples of Different Types of Solutions

• Solid in solid: Brass (zinc and copper mixture)
• Solid in liquid: Sugar water
• Liquid in solid: Mercury in silver (dental amalgam)
• Liquid in liquid: Gasoline (hydrocarbon mixture)
• Gas in solid: Hydrogen in platinum
• Gas in liquid: Carbonated soft drinks (CO₂ in water)
• Gas in gas: Air (O₂ in N₂)

\"Like Dissolves Like\"

• Solvents dissolve solutes with similar Intermolecular Forces (IMFs).
  • Polar solvents dissolve ionic and polar solutes (permanent charges).
  • Nonpolar solvents dissolve nonpolar solutes (instantaneous charges).

Choosing the Best Solvent

• Examples:
  • Ammonia (NH₃) - Water (H₂O)
  • Hexane (C₆H₁₄) - C₈H₁₈
  • CaCl₂ - Water

Saturation Vocabulary Roundup

• Unsaturated: Less than the maximum solute amount is dissolved.
• Saturated: The maximum solute amount is dissolved; solid remains at the bottom. Equilibrium exists.
• Supersaturated: More than the maximum solute amount is dissolved; unstable.

Thermodynamics of Solution Formation

• Steps:
  1. Break solvent-solvent interactions.
  2. Break solute-solute interactions.
  3. Form solute-solvent interactions.
• Pure solute and solvent → Solution
• $ΔH<em>{solution} = ΔH</em>1 + ΔH<em>2 + ΔH</em>3$
• $ΔS$ is so large that $ΔG < 0$ even when $ΔH > 0$.

Supersaturated Solutions

• Unstable; created by \"tricking\" the solution via heating to dissolve more solute.
• Crystallization is induced by a seed crystal or tapping.

More Solution Vocabulary

• Miscible: Two liquids completely soluble in each other (similar IMFs), e.g., acetic acid and water (hydrogen bonding).
• Immiscible: Two liquids not soluble (dissimilar IMFs), e.g., oil and water (London dispersion forces and hydrogen bonding).

Solubility and Temperature

• Graphs show the solubility of different compounds at different temperatures.
• Solubility is expressed as grams of solute per 100 g of water.
• Example compounds: $KNO<em>3$, sucrose ($C</em>{12}H<em>{22}O</em>{11}$), $NaNO<em>3$, $CaCl</em>2$, $NaCl$, $KBr$, $KCl$, $KClO<em>3$, $K</em>2Cr<em>2O</em>7$, $Ce<em>2(SO</em>4)_3$

Solids vs. Gases

• Solids: Solubility generally increases with increasing temperature.
• Gases: Solubility generally decreases with increasing temperature.
  • Gases include methane, oxygen, carbon monoxide, nitrogen, helium.

Solubility and Pressure

• Solids: Solubility is generally not affected by pressure.
• Gases: Solubility generally increases with increasing pressure.

Henry's Law

• The linear relationship between pressure and gas solubility:
  • $S<em>g = kP</em>g$
  • $S_g$ = solubility of the gas in the solution
  • $P_g$ = partial pressure of the gas over the solution
  • $k$ = Henry's law constant (varies with each solute-solvent pair)
• As pressure doubles, solubility doubles.

Example: Henry's Law

• A sealed carbonated soda has a CO₂ partial pressure of 4.0 atm at 25°C; the CO₂ concentration is 0.14 M.
  • Calculate Henry's Law constant for CO₂ in water at 25°C.
  • Find the CO₂ concentration after opening when it equilibrates at a partial pressure of $3.0 × 10^{-4}$ atm.

Curve Fitting

• Scientific data often match a standard curve shape (line, parabola, exponential, or logarithmic).
• Historically, lines were easiest to work with; data would be mathematically manipulated to convert curves to lines.
• The slope of the line often has meaning.

Conditions for Dissolving Maximum Solute

• Gases: Low temperature, high pressure
• Solids: High temperature, pressure doesn't matter

Concentration Units

• Molarity (M)
• Molality (m)
• Percent
• ppm (parts per million)
• ppb (parts per billion)
• Normality
• Osmolarity
• Mole Fraction

Molarity (M)

• $M = \frac{moles \ of \ solute}{liters \ of \ solution}$

Molarity Example

• How many grams of glucose ($C<em>6H</em>{12}O_6$, molar mass 180.18 g/mol) are needed to make 250 mL of 0.15 M aqueous solution?

Molality (m)

• $m = \frac{moles \ of \ solute}{kilograms \ of \ solvent}$
• Needed for freezing point depression lab.

Molality Example

• How many grams of glucose ($C<em>6H</em>{12}O<em>6$) are needed to dissolve in 563 grams of ethanol ($C</em>2H_5OH$) to prepare a 0.0240 m solution?

Percent by Mass

• $mass \% = \frac{mass \ of \ solute}{total \ mass \ of \ solution} × 100$

Mole Fraction (X)

• $X = \frac{moles \ of \ solute}{total \ moles \ of \ solution}$

Example: Mole Fraction, Mass Percent

• A solution contains 0.100 mol NaCl in 8.60 mol water. Find the mole fraction and mass percent of NaCl (molar mass of NaCl = 58.44 g).

Density of Solution

• $D = \frac{mass \ of \ solution}{volume \ of \ solution}$

Concentration Conversions

• Convert concentration from one set of units to another (e.g., molarity to molality); density is often given.
• Look at the denominator unit (not density). Pick an "easy" amount to work with based on this.
• Perform calculations based on this amount.
  • Molarity: 1 L of solution
  • Molality: 1 kg of solvent
  • Mass %: 100 g of solution
• Some problems give a fixed amount to begin with (mass of solute and solvent) instead of concentration. In this case, you don't need to make assumptions.

3-2-1 Table for Conversions

• 3 Masses: Mass of solute, mass of solvent, mass of solution
• 2 Moles: Moles of solute, moles of solvent
• 1 Volume: Volume of solution
• Fill in any pieces of the table that you can to find a clear path from given information to the target concentration unit.

Conversion Example

• An 8.00 mass % aqueous solution of ammonia has a density of 0.9651 g/mL. Calculate the molality, molarity, and mole fraction.

Colligative Properties

• Depend on the concentration of solution, not the nature of the solute or solvent.
  • Freezing point depression
  • Boiling point elevation
  • Vapor pressure lowering
  • Osmotic pressure

Freezing Point Depression

• $ΔT<em>f = T</em>{f,solvent} - T<em>{f,solution} = iK</em>fm$
  • $i$ = van't Hoff factor
  • $K_f$ = freezing point depression constant
  • $m$ = molality

Van't Hoff i Factor

• $i = \frac{Moles \ of \ particles \ in \ solution}{Moles \ of \ solute \ dissolved}$
• Examples:
  • Glucose $C<em>6H</em>{12}O_6(s) \rightarrow i = 1$
  • $NaCl(s) \rightarrow i = 2$
  • $BaCl_2(s) \rightarrow i = 3$
  • $AlCl_3(s) \rightarrow i = 4$

$K_f$

• Freezing point depression constant depends on the solvent, not the solute.

Boiling Point Elevation

• $ΔT<em>b = T</em>{b,solution} - T<em>{b,solvent} = iK</em>bm$
  • Boiling point works in the opposite direction from freezing point. Add $ΔT<em>b$ to $T</em>b$.
  • The biggest $i×m$ has the highest boiling point.

Example: Freezing and Boiling Points

• What are the boiling point and freezing point of a solution made by dissolving 1000 grams of ethylene glycol (antifreeze, $C<em>2H</em>6O_2$) in a car radiator containing 4450 grams of water?
  • $K_f$ (water) = 1.86 °C/m
  • $K_b$ (water) = 0.52 °C/m

Comparing Freezing Points

• Which aqueous solution will have the lowest freezing point?
  • Pure water
  • 0.2 m sucrose
  • 0.2 m NaCl
  • 0.15 m $K<em>2SO</em>4$

Molar Mass by Freezing Point Depression

• $MM = \frac{mass \ of \ unknown \ (g) × K<em>f}{mass \ of \ solvent \ (kg) × ΔT</em>f}$

Example: Molar Mass

• 1.22 g of a white solid (suspected pure cocaine) is dissolved in 15.60 g of benzene; the freezing point is lowered by 1.32 °C. Calculate the molar mass of the solid (Kf for benzene = 5.12 °C/m).