Chem 1412 - Chapter 12

Chapter 1: Introduction

• Solutions and Volume Prediction:

  • Predicting which solution has the highest volume depends on the number of solute particles.

  • The van't Hoff factor $i$ is crucial for this prediction.

• Van't Hoff Factor:

  • For covalent compounds dissolving in water, $i = 1$ because they produce no ions (non-electrolytes or molecular compounds).

  • Ionic compounds dissociate into ions, affecting the van't Hoff factor.

• Methanol Example:

  • Methanol (a liquid) dissolves in water due to its polarity but doesn't form ions, so $i = 1$.

• Special Case: Polyatomic Positive Ions:

  • Ammonium ($NH<em>4^+$) is a common polyatomic cation in ionic compounds like ammonium chloride ($NH</em>4Cl$).

  • $NH<em>4Cl$ dissociates into $NH</em>4^+$ and $Cl^-$ ions, so $i = 2$.

• Calculating Total Moles of Solute:

  • If concentration and $i$ are known, the total number of moles of solute can be calculated.

  • The solution with the highest number of solute particles has the highest boiling point.

• Boiling Point and Solute Particles:

  • Pure water's boiling point is $100^\circ C$.

  • Adding any solute raises the boiling point.

  • The solution with the greatest number of moles of solute has the highest boiling point.

• Freezing Point Depression:

  • Pure water's freezing point is $0^\circ C$.

  • Adding solute lowers the freezing point.

  • The more solute particles, the lower the freezing point below zero.

• Vapor Pressure:

  • Vapor pressure is determined by the number of vapor molecules.

  • More vapor molecules mean higher vapor pressure.

  • At a lower temperature, there are fewer water molecules in the gas phase.

  • Higher temperature leads to greater vapor pressure.

Chapter 2: Highest Boiling Point

• Van't Hoff Factor Revisited:

  • Water has no van't Hoff factor in the context of solute effects.

  • Nonelectrolytes (covalent compounds) have $i = 1$.

  • Magnesium chloride ($MgCl_2$) dissociates into $Mg^{2+}$ and $2Cl^-$, so $i = 3$.

• Boiling Point and Vapor Pressure Relationship:

  • Higher boiling point implies lower vapor pressure due to fewer molecules transitioning to the gas phase.

  • Water has the highest freezing point, lowest boiling point and highest vapor pressure when compared to solutions with solutes.

• Colligative Properties:

  • Boiling point elevation and freezing point depression are colligative properties.

  • Osmotic pressure and vapor pressure are two other colligative properties. All are on the formula sheet.

• Osmotic Pressure:

  • Water flows from an area of lower solute concentration to higher solute concentration to equalize concentrations.

  • The greater the concentration disparity, the higher the osmotic pressure.

  • Formula: $\Pi = i \cdot M \cdot R \cdot T$, where $\Pi$ is osmotic pressure, $i$ is the van't Hoff factor, $M$ is molarity, $R$ is the gas constant, and $T$ is temperature in Kelvin.

• Vapor Pressure (Raoult's Law):

  • The pressure of a component changes by its mole fraction.

  • Formula: $P = X \cdot P<em>0$, where $P$ is the vapor pressure of the solution, $X$ is the mole fraction of the solvent, and $P</em>0$ is the vapor pressure of the pure solvent.

  • The greater the number of solute moles, the greater the change in pressure.

  • This relationship is described by Raoult's Law.

Chapter 3: Freezing Point Change

• Calculating Changes in Temperature:

  • $\Delta T$ (delta T) represents the change in temperature (final - initial).

  • For boiling point elevation, the new boiling point is $100 + \Delta T$ (in Celsius).

• Freezing Point Depression Calculation:

  • The freezing point constant for water is $1.86 ^\circ C/m$.

  • The equation is set up the same way as boiling point elevation, but temperature goes down from zero.

• Using the Equations:

  • You may be asked to calculate $i$, the number of grams of substance, or the molar mass given the change in temperature.

• Freezing Point Example:

  • The new freezing point is negative (e.g., $-6.95 ^\circ C$).

Chapter 4: Number Of Moles

• Osmotic Pressure and Moles:

  • Using the osmotic pressure equation to find the number of moles of solute.

• Non-Electrolyte Solute:

  • For a nonelectrolyte solute, $i = 1$.

• Osmotic Pressure Calculation:

  • Osmotic pressure is given (e.g., $5.5$ millimeters of mercury) and needs to be converted to atmospheres to match the gas constant units ($760$ mmHg = $1$ atm).

• Molar Mass:

  • Molar mass is the number of grams per mole.

Chapter 5: The Right Expressions

• Mass of Solute:

  • Finding molality and molarity requires calculating the mass of the solute.

• Molecular Weight:

  • Molecular weight (MW) or molar mass is essential for calculations.

• Equilibrium Reactions:

  • Generic reaction: $aA \rightarrow bB$, where A is the reactant and B is the product.

  • Reactant (A) concentration decreases over time, while product (B) concentration increases.

• Rate Expression:

  • Rate expression relates the change in concentration over time.

  • For reactants: negative sign indicates decreasing concentration.

  • For products: positive sign indicates increasing concentration.

• Stoichiometry:

  • $N<em>2(g) + 3H</em>2(g) \rightarrow 2NH_3(g)$

    • Rate of disappearance of nitrogen, rate of disappearance of hydrogen, and rate of appearance of ammonia are related by stoichiometry.

    • If you know the rate of one, you can calculate the others.

Chapter 6: Amount Of Energy

• Reaction Rate Units:

  • Concentration (Molarity) per time (seconds).

  • Units are typically $M/s$, often written as $M \cdot s^{-1}$.

• Collision Theory:

  • Not every collision between molecules results in product formation. Molecules must collide with enough energy to break existing bonds.

  • Bonds in reactants must be broken before new bonds can form.

• Factors Affecting Reaction Rate:

  • Number of collisions: More collisions increase the likelihood of product formation.

  • Physical state of reactants: Related to the orientation of molecules during collisions.

  • Concentration of reactants: Higher concentration leads to more collisions and a faster reaction rate.

  • Temperature: Higher temperature increases kinetic energy, leading to more collisions and a faster rate.

• Catalysts:

  • Catalysts speed up reactions by creating a new reaction pathway with lower energy requirements.

  • Catalysts are not consumed in the reaction, and their concentration remains constant.

• Energy Diagrams:

  • Energy diagrams illustrate the energy changes during a reaction.

  • $\Delta H$ (delta H) is the heat of reaction. Positive $\Delta H$ indicates endothermic reaction; negative $\Delta H$ indicates exothermic reaction.

• Activation Energy:

  • Activation energy ($E_a$) is the energy barrier that reactants must overcome to form products.

  • Reactants have some initial energy; the difference between this energy and the highest point on the energy diagram is the activation energy.

Chapter 7: Conclusion

• Endothermic vs. Exothermic Reactions:

  • Endothermic: Products have more energy than reactants (positive $\Delta H$).

  • Exothermic: Products have less energy than reactants (negative $\Delta H$).

• Transition State:

  • The transition state represents the point where reactants are transitioning to products.

• Catalyst Effect:

  • Catalysts lower the activation energy by creating a new reaction pathway.

  • This means molecules need less energy to become product molecules, speeding up the reaction.