Chemistry 120: Colligative Properties and Solutions Notes and the Van't Hoff Factor, Boiling Point Elevation, Freezing Point Depression, and Osmotic Pressure

Course Logistics and Announcements • ALEKS assignment: Due this coming Sunday at 10:00 pm. • Weekly Practice Assignments (WPA): Also due this Sunday at 10:00 pm. • iClicker Participation: iClicker points are officially being counted for the course grade. Students receive half credit for simply participating in the polling. • Background Survey: Dr. Martinez requests students to "Tell me about yourself" and explicitly share personal concerns regarding the course. • Mock Quiz: A sample quiz is available on Canvas designed to ensure technical readiness and that all systems work correctly before graded assessments. • Quiz 1 Schedule: The quiz opens on Sunday at 12:00 pm (noon) and will close on Monday at 10:00 pm. # Quiz 1 Overview and Learning Objectives • Quiz 1 Coverage Topics: 1. Solutions: Differences between saturated, unsaturated, and supersaturated solutions. 2. The solution formation process. 3. Predicting the solubility of various compounds. 4. Vapor pressure lowering. 5. Freezing point depression. 6. Boiling point elevation. 7. Osmotic pressure. • Student Learning Objectives: 1. Define the Van’t Hoff factor ($i$). 2. Determine the Van’t Hoff factor for any specific solute. 3. Define and calculate boiling point elevation ($\Delta T_b$) for any solution. 4. Define and calculate freezing point depression ($\Delta T_f$) for any solution. 5. Define osmosis, semipermeable membranes, and osmotic pressure ($\pi$). 6. Identify the direction of solvent molecule flow during the process of osmosis. # Introduction to Colligative Properties and the Van’t Hoff Factor • Comparison of Glucose and Sodium Chloride Solutions at $25\,^\circ C$: 1. Glucose Solution: 1 mole of glucose dissolved in 5 moles of $H_2O$ results in a solution vapor pressure ($P_{soln}$) of $19.8\,torr$. 2. Sodium Chloride Solution: 1 mole of $NaCl$ dissolved in 5 moles of $H_2O$ results in a solution vapor pressure ($P_{soln}$) of $17.0\,torr$. 3. Reasoning: The difference in vapor pressure occurs because vapor pressure depends on the number of particles in the solution, not just the number of moles of the original chemical unit. • Defining the Van’t Hoff Factor ($i$): The relationship between the total moles of solute dissolved and the total moles of particles present in the final solution. • Electrolyte Dissociation Examples: 1. Sodium Chloride: $NaCl(s) \rightarrow Na^+(aq) + Cl^-(aq)$. Because it dissociates into two separate particles, $i = 2$. 2. Iron(III) Nitrate: $Fe(NO_3)<em>3(s) \rightarrow Fe^{3+}(aq) + 3NO_3^-(aq)$. Because it dissociates into four separate particles (one iron ion and three nitrate ions), $i = 4$. # Boiling Point Elevation ($\Delta T_b$) • Conceptual Definition: The addition of a nonvolatile solute to a pure solvent results in the lowering of the solvent's vapor pressure. Consequently, the solution must be heated to a higher temperature than the pure solvent to reach its boiling point. • Mathematical Formula: $\Delta T_b = i K_b m</em>{solute}$ • Variable Definitions: 1. $\Delta T_b$: The change in the boiling point temperature (measured in $\,^\circ C$). 2. $i$: The Van’t Hoff factor. 3. $K_b$: The molal boiling point elevation constant ($K_b$) in units of $\,^\circ C/m$, which is specific to the solvent used. 4. $m$: The molality of the solute, defined as $mol/kg$. # Freezing Point Depression ($\Delta T_f$) • Conceptual Definition: Adding a nonvolatile solute to a solvent lowers the vapor pressure. This causes the solution to require cooling to a temperature lower than the pure solvent's freezing point before the transition to a solid state occurs. • Mathematical Formula: $\Delta T_f = -i K_f m_{solute}$ • Variable Definitions: 1. $\Delta T_f$: The change in freezing point temperature (measured in $\,^\circ C$). 2. $i$: The Van’t Hoff factor. 3. $K_f$: The molal freezing point depression constant in units of $\,^\circ C/m$, specific to the solvent. 4. $m$: The molality of the solute in $mol/kg$. # Osmosis and Osmotic Pressure ($\pi$) • Definitions: 1. Osmosis: The specific flow of a solvent through a semipermeable membrane into a solution. 2. Semipermeable Membrane: A selective barrier that allows the passage of solvent molecules but prevents the passage of solute molecules. 3. Osmotic Pressure ($\pi$): The precise amount of pressure that must be applied to the solution side to halt the process of osmosis. • Mathematical Formula: $\pi = i M R T$ • Variable Definitions: 1. $M$: Molarity (moles of solute per liter of solution). 2. $R$: The Universal gas constant, defined as $0.08206\,L \cdot atm / K \cdot mol$. 3. $T$: Absolute temperature measured in Kelvin ($K$). # Practice Problems and Quantitative Analysis • Clicker Question (Vapor Pressure): Calculate the vapor pressure for a solution made by dissolving $145\,g$ of calcium nitrate ($Ca(NO_3)_2$, $MM = 164.12\,g/mol$) in $13.89\,moles$ of water. Pure water vapor pressure at $30\,^\circ C$ is $31.8\,torr$. Options: A. $29.9\,torr$, B. $28.2\,torr$, C. $89.7\,torr$, D. $26.7\,torr$. • t-Butanol Freezing Point Calculation: The pure freezing point of t-butanol is $25.50\,^\circ C$ and its $K_f$ is $9.1\,^\circ C \cdot kg/mol$. t-butanol ($74.12\,g/mol$) absorbs water from the air. If a $10.0\,g$ sample freezes at $24.59\,^\circ C$, determine the kilograms of water present in the sample. • Clicker Question (Boiling Point): What is the boiling point of an aqueous solution containing $0.8\,moles$ of ammonium sulfide ($(NH_4)_2S$) in $125\,g$ of water? Normal boiling point is $100.\,^\circ C$ and $K_b = 0.512\,^\circ C/m$. Options: A. $9.83\,^\circ C$, B. $100.\,^\circ C$, C. $90.2\,^\circ C$, D. $110.\,^\circ C$. • Catalase Molar Mass Calculation: An aqueous solution of $10.00\,g$ of catalase (a liver enzyme) has a volume of $1.00\,L$ at $27\,^\circ C$. The measured osmotic pressure is $9.74 \times 10^{-4}\,atm$. Calculate the molar mass of catalase. • Clicker Question (Osmotic Pressure): An aqueous solution contains $0.029\,moles$ of acetaldehyde with a volume of $2.45\,L$ at $30\,^\circ C$. What is the osmotic pressure? Options: A. $0.297\,atm$, B. $0.600\,atm$, C. $0.729\,atm$, D. $0.150\,atm$. # Reverse Osmosis and Applications • Reverse Osmosis Definition: This process occurs when external pressure exceeds the osmotic pressure of a solution, causing a net flow of solvent through a semipermeable membrane from the solution side toward the pure solvent side. • Real-World Applications: 1. Desalination of seawater. 2. Treatment of industrial wastewater. 3. Deionized (DI) water pretreatment systems. 4. Production of purified drinking water.