September 11, 20XX
I went to inquire about this; this is what I learned.
Professor Siger's life began in the most unconventional of circumstances. Born in the prison's hospital to parents whose crimes remained shrouded in mystery, his origins were steeped in intrigue and uncertainty.
The turning point in young Siger's life occurred when an unknown government order arrived at the prison's doorstep. It declared that Siger, an innocent child caught in the web of his parents' misdeeds, would be confined to the very cell where his deceased parents had served their sentences. This decision raised eyebrows among the prison staff, as it defied all conventional wisdom regarding the upbringing of a child.
However, the prison warden took it upon himself to ensure that Siger received a proper upbringing. Instead of viewing the child as a burden, the warden adopted him and became both a father figure and mentor to him.
As Professor Siger continued to serve this egregious and inhumane life sentence within the confines of the infamous island prison, he transformed himself into an extraordinary individual, defying the oppressive circumstances that surrounded him. His quest for knowledge knew no bounds, and he voraciously devoured every book he could lay his hands on. The prison library, though modest, became his sanctuary, offering him a window into the world beyond the prison walls.
But it wasn't just the pursuit of knowledge that occupied his time. Siger recognized the importance of physical strength and discipline in this unforgiving environment. In the prison's rudimentary gymnasium, he honed his body, sculpting it into a powerful and resilient machine. The physical training served not only as a means of survival but also as a testament to his unyielding spirit.
Amidst the chaos and brutality of prison life, Siger developed his own form of meditation, a mental sanctuary that allowed him to escape the harsh reality, even if only for brief moments. This practice provided him with the mental fortitude to endure the daily hardships and uncertainties that came with his sentence.
One of the most remarkable aspects of Professor Siger's time in prison was his ability to transcend linguistic and cultural barriers. The island's unique cultural mix and supposed geographical location had exposed him to a diverse array of languages, and he became proficient in advanced forms of English, Spanish, Portuguese, Farsi, Urdu, and even sometimes deceased Latin. These linguistic skills not only facilitated his interactions with fellow inmates but also allowed him to explore a vast range of literary works from around the world.
Despite the grim surroundings, Siger's thirst for knowledge and his innate curiosity drew the attention of a variety of mentors within the prison. From hardened convicts who had learned their own life lessons to compassionate prison chaplains and religious theological missionaries who saw potential in him, these mentors imparted a basic symmetrical education that transcended the boundaries of the prison walls. The head warden, after years of denial and terrible paperwork, arranged for his release. He selected himself to be his parole officer as well.
In spare time after traveling the world and galactical expeditions, he acquired a citizenship in the continents of human colonized lands, the Mushroom Kingdom, and Mobius.
Chem Notes: (filled with academic musings)
Solvation
Solution = solute and a solvent. Homogenous Mixtures.
• Solute = usually the material present in the lower amount and usually the reactive component. It can be a solid, liquid, or gas.
• Solvent = material into which the solute is dissolved and is usually present in the larger amount
Solutions
Solution formation is the result of the interaction of the intermolecular forces of solute and solvent particles.
Saying: "Likes dissolve in likes," or ionic / polar with polar and nonpolar with nonpolar substances readily form solutions.
Solutions: Energy Picture
• For the solvent and solute to mix, you must overcome
1. Solute–Solute attractive forces
2. Solvent–Solvent attractive forces.
• Both processes are endothermic.
• At least some of the energy to do this comes from making new solute–solvent attractions, which is an exothermic process.
Energetics of Solution Formation:
The Enthalpy of Solution
• To make a solution, you need to do the following: all attractions between the solute particles
ΔHsolute is endothermic. Some attractions between solvent molecules, ΔHsolvent is endothermic.
3. Form new attractions between solute particles and solvent molecules; ΔHmix is exothermic.
ΔHsoln = ΔHsolute + ΔHsolvent + ΔHmix
Energy Changes and the Solution Process
Exothermic vs Endothermic
Solution Equilibrium: NaCl Dissolving in Water
(ΔHsol = +3.9 kJ/mol)
Solubility Terminology
• When one substance (solute) dissolves in another (solvent), it is said to be soluble.
• Salt is soluble in water.
• When one substance does not dissolve in another, it is said to be insoluble.
• Oil is insoluble in water.
• The maximum amount of solute that can be dissolved in a given amount of solvent is called the solubility. (e.g. Salt solubility in water
is 359 g/L)
• There usually is a limit to the solubility of one substance in another.
• Gases are always soluble in each other.
• Two liquids that are mutually soluble are said to be miscible.
• Alcohol and water are miscible.
• Oil and water are immiscible.
• The solubility of one substance in another varies with temperature and pressure.
Solubility Limit
• A solution that has the solute and solvent in dynamic equilibrium is said to be saturated.
• If you add more solute, it will not dissolve.
• The saturation concentration depends on the temperature and pressure of gases.
• A solution that has less solute than saturation is said to be unsaturated.
• More solute will dissolve at this temperature.
• A solution that has more solute than saturation is said to be supersaturated.
Temperature Dependence of Solubility of Solids in Water
• Solubility is generally given in grams of solute that will dissolve in 100 g of water.
• For most solids, the solubility of the solid increases as the temperature increases.
• When ΔHsolution is endothermic
• Solubility curves can be used to predict whether a solution with a particular amount of solute dissolved in water is
❑ saturated (on the line)
❑ unsaturated (below the line)
❑ supersaturated (above the line).
Temperature Dependence of Solubility of Solids in Water
• Solubility is generally given in grams of solute that will dissolve in 100 g of water.
• For most solids, the solubility of the solid increases as the temperature increases.
• When ΔHsolution is endothermic
• Solubility curves can be used to predict whether a solution with a particular amount of solute dissolved in water is
❑ saturated (on the line)
❑ unsaturated (below the line)
❑ supersaturated (above the line).
Temperature Dependence of Solubility of Gases in Water
• Gases have lower solubility in water than ionic or polar covalent solids because most are nonpolar molecules or atoms (e.g. He)
• For all gases, the solubility of the gas decreases as the temperature increases.
• The ΔHsolution is exothermic because you do not need to overcome solute–solute attractions.
Gas Solubility and Temperature
1. The types of intermolecular attractive forces
2. Nature's tendency toward mixing
The solubility of one substance in another depends on the following1. The types of intermolecular attractive forces
2. Nature's tendency toward mixing
The solubility of one substance in another depends on the following
1. The types of intermolecular attractive forces
2. Nature's tendency toward mixing
The solubility of one substance in another depends on the following
Energy changes in the formation of most solutions involve differences in attractive forces between the particles.
1. The types of intermolecular attractive forces
2. Nature's tendency toward mixing
The solubility of one substance in another depends on the following
• The gases mix because the energy of the system is lowered through the release of entropy.
• Entropy is the measure of energy dispersal throughout the system.
• Energy has a spontaneous drive to spread out over as large a volume as it is allowed.
• As each gas expands to fill the container, it spreads its energy out and increases its entropy.
Energy Changes and the Solution Process
There is an entropy change for the solution process.
Solution #1
Solution #2
Energy Changes and the Solution Process
ΔG = ΔH − TΔS
−ΔG
+ ΔG
Spontaneous:
Nonspontaneous:
+ ΔH
−ΔH
Endothermic:
Exothermic:
Concentration Units
Solution Concentrations
• Solutions have changing composition. To describe a solution, you need to describe the components and their relative amounts.
Concentration = amount of solute in a given amount of solution.
• The terms dilute and concentrated can be used as qualitative descriptions of the amount of solute in solution.
*Dilute = small amount, concentrated = large amount
Concentration Units for Solutions
Molarity, M
• Molarity (M or mol/L) is defined as the moles of solute per 1 liter of solution.
• Molarity describes how many molecules or atoms of solute are in each liter of solution.
• If a sugar solution concentration is 2.0 M, then 1 L of solution contains 2.0 mol of sugar; or 2 L = 4.0 mol sugar; or 0.5 L = 1.0 mol sugar.
Molality, m
• Molality (m or mol/kg) is defined as the moles of solute per 1 kilogram of solvent.
• Molality (m) is defined in terms of amount of solvent, not solution.
• It does not vary with temperature because it is based on masses, not volumes.
Parts Solute in Parts Solution
Parts can be measured by mass or volume.
• Parts are generally measured in the same units.
• By mass in grams, kilograms, pounds (lb), etc.
• By volume in mL, L, gallons (gal), etc.
• Percentage = parts of solute in every 100 parts solution.
• If a solution is 0.9% by mass, then there are 0.9 g of solute in every 100 g of solution (or 0.9 kg solute in every 100 kg solution).
• Parts per million = parts of solute in every 1 million parts solution.
• If a solution is 36 ppm by volume, then there are 36 mL of solute in 1 million mL of solution.
Mole Fraction, χa
• A mole fraction is the fraction of the moles of one component in the total moles of all the components of the solution.
• Total of all the mole fractions in a solution = 1.
χa = moles of substance a / moles of substance a + moles of substance b
• Mole fraction has no units.
• The mole percentage is the percentage of the moles of one component in the total moles of all the components of the solution.
mol % = mole fraction (χa) × 100%
Practice Problem: Calculating Concentrations
You prepare a solution by dissolving 50.4 g sucrose (C12H22O11) in 0.332 kg of water. The final volume of the solution is 355 mL. Calculate the concentration of the solution in each unit.
a. molarity b. molality c. percent by mass d. mole fraction
Molarity Practice
Assuming that seawater is an aqueous solution of NaCl, what is its molarity? The density of seawater is 1.025 g/mL at 20 °C, and the NaCl concentration is 3.50 mass
percent.
Molality Problem
What is the molality of a solution prepared by dissolving 0.385 g of cholesterol, C27H46O, in 40.0 g chloroform, CHCl3?
What mass of sucrose (C12H22O11), in g, is in 355 mL (12 fl oz) of a soft drink that is 11.5% sucrose by mass? (Assume a density of 1.04 g/mL).
Practice Problem: Using Parts by Mass in Calculations
The drinking water in Flint, Michigan had a lead concentration of 25 ppb. What is this in molarity? Assume the density of the drinking water is 1.0 g / mL. Atomic mass Pb is 207.2g/mol
Practice Problem: Using ppm and ppb
Vapor Pressure and Raoult's Law
Dynamic Equilibrium of Liquids
• In a closed container, once the rates of vaporization and condensation are equal, the total amount of vapor and liquid will not change.
The pressure exerted by the vapor when it is in dynamic equilibrium with its liquid is called the vapor pressure.
Vapor Pressure versus Temperature
• When the temperature of a liquid reaches a point where its vapor pressure is the same as the external pressure, vapor bubbles can form anywhere in the liquid, not just on the surface. (boiling point)
• Increasing the temperature increases the number of molecules able to escape the liquid.
• The net result is that as the temperature increases, the vapor pressure increases.
•Colligative properties are properties whose value depends only on the number of solute particles and not on what they are.
Value of the property depends on the concentration of the solution.
Vapor Pressure of Solutions
• The vapor pressure of a solvent above a solution is lower than the vapor pressure of the pure solvent.
• The solute particles replace some of the solvent molecules at the surface.
• The pure solvent establishes a liquid vapor equilibrium.
• Addition of a nonvolatile solute reduces the rate of vaporization
• A concentrated solution will draw pure solvent vapor into it becauseof this tendency to mix.
• The result is reduction in vapor pressure.
The vapor pressure of a solvent in a solution is always lower than the vapor pressure of a pure solvent.
Vapor Pressure Lowering (Raoult's Law)
• The vapor pressure of a solvent in a solution is always lower than the vapor pressure of the pure solvent.
• The vapor pressure of the solution is directly proportional to the amount of the solvent in the solution.
(Mole Fraction)
• The difference between the vapor pressure of the pure solvent and the vapor pressure of the solvent in solution is called the vapor pressure lowering.
ΔP = P°solvent – Psolution
Psolvent in solution = χsolvent ∙ P°solvent
Vapor-Pressure Lowering of Solutions: Raoult's Law
Psoln = Psolv Xsolv
Vapor-Pressure Lowering of Solutions: Raoult's Law
Calculate the vapor pressure at 25 °C of a solution containing 55.3 g glucose (C6H12O6) and 285.2 g water. The vapor pressure of pure water at 25 °C is 23.8 torr. MM glucose is 180.2 g/mol.
Vapor-Pressure Lowering of Solutions:
Raoult's Law for Two Volatile Liquids
Ptotal = PA + PB = (P°A XA) + (P°B XB)Vapor-Pressure Lowering of Solutions:
Raoult's Law for Two Volatile Liquids
Ptotal = PA + PB = (P°A XA) + (P°B XB)
Colligative Properties of Solutions
• Vapor-pressure lowering
• Boiling-point elevation
• Freezing-point depression
• Osmotic pressure
Boiling-Point Elevation and Freezing-
Point Depression of Solutions
Vapor Pressure Lowering Causes
Boiling/Freezing Temp Change
• The freezing point of a solution is lower than the freezing point of the pure solvent.
• Therefore, the melting point of the solid solution is lower.
(Tfreezing,solvent – Tfreezing,solution) = ΔTf = mc ∙ kf
The proportionality constant is called the freezing point depression constant, kf.
• The value of kf depends on the solvent.
• The units of k are ° Pressure Lowering Causes
Boiling/Freezing Temp Change
• The freezing point of a solution is lower than the freezing point of the pure solvent.
• Therefore, the melting point of the solid solution is lower.
(Tfreezing,solvent – Tfreezing,solution) = ΔTf = mc ∙ kf
The proportionality constant is called the freezing point depression constant, kf.
• The value of kf depends on the solvent.
• The units of k are °C/m.
Vapor Pressure Lowering Causes
Boiling/Freezing Temp Change
• The boiling point of a solution is higher than the boiling point of the pure solvent.
• Therefore, the boiling point of the solid solution is higher.
(Tboiling,solution – Tboiling,solvent) = ΔTb = mc ∙ kb
The proportionality constant is called the boiling point elevation constant, kb.
• The value of kb depends on the solvent.
• The units of k are °C/m.
Values for Various Solvents
Van't Hoff Factors
• Ionic compounds produce multiple solute particles for each formula unit.
• The theoretical van't Hoff factor, i, is the ratio of moles of solute particles to moles of formula units dissolved.
Moles of particles in solution
Moles of formula units dissolved
i =Van't Hoff Factors
• Ionic compounds produce multiple solute particles for each formula unit.
• The theoretical van't Hoff factor, i, is the ratio of moles of solute particles to moles of formula units dissolved.
Moles of particles in solution
Moles of formula units dissolved
i =H2ONaCl
H2O
mc =
mc =m = 1.0
m = 1.0
mc = i * m
Colligative Molality
CH3OH(l)
NaCl(s)
CaCl2(s)
Ca3(PO4)2(s)
Colligative Molality
(Tboiling,solution – Tboiling,solvent) = ΔTb = mc ∙ kb
(Tfreezing,solvent – Tfreezing,solution) = ΔTf = mc ∙ kf
mc = im
Practice Problem: Freezing Point Depression
How much sodium chloride is necessary to lower the freezing point of 355mL of water to -2.5°C?
Practice Problem: Boiling Point Elevation
How much sodium chloride is necessary to increase the boiling point of 652 mL of water to 105.0°C?
Osmosis and Osmotic Pressure
Osmosis: The passage of solvent through a semipermeable membrane from the less concentrated side to the more concentrated side
Osmotic Pressure (Π): The amount of pressure necessary to cause osmosis to stop, or the amount of pressure necessary to achieve an equilibrium passage of solvent molecules through a semipermeable membrane
Π = MRTi
Osmosis and Cells
An isosmotic (isotonic) solution has the same osmotic pressure as the solution inside the cell; as a result, there is no net flow of water into or out of the cell.
A hyperosmotic (hypertonic) solution has a higher osmotic pressure than the solution inside the cell; as a result, there is a net flow of water out of the cell, causing it to shrivel.
A hyposmotic (hypotonic) solution has a lower osmotic pressure than the solution inside the cell; as a result, there is a net flow of water into the cell, causing it to swell.
Reverse Osmosis and Drinking Water