TOPIC A: STATES OF MATTER AND SOLUTIONS

States of matter All matter has two distinct characteristics. It has mass and it occupies space. The properties associated with the three states of matter, and the behaviors of the particles that make them up, are summarized below

The particulate diagrams below represent the relative positions and movements of the particles in the three states of matter. Increasing Energy Solids: categories: (1) crystalline - a regular, ordered, repeatable 3-D structure of particles is found (2) amorphous - the arrangement of particles is not regular or ordered.

The particles in the solid (1) have very little energy, (2) move very little in relation to one another. (vibrating in fixed positions) Liquids: Liquids have particles that are very close together, the particles in liquids are: constantly moving and colliding with one another, have significantly greater energy, move a lot in relation to one another The properties of solids and liquids Properties of solids and liquids such as viscosity, surface tension, hardness depend on the extent of the attractions between the particles. Example: a liquid where the particles are attracted to one another with very strong inter-particular forces is likely to be more viscous than one where the force of attraction is weaker.

Heating and cooling curves: Different states of matter have particles with differing energies, converting between them requires a change in energy. The changes in energy associated with phase changes can be quantified in heating and cooling curves.

Gases and kinetic molecular theory Gases: made up of particles that have (relatively) large amounts of energy. no definite shape or volume will expand to fill as much space as possible As a result of the large amount of empty space in a volume of gas, gases are easily compressed. Pressure: A pressure is exerted when the gas particles collide with the walls of any container it is held in. Pressure can be measured in a number of units, for example; 1.00 atm = 760 mmHg = 760 Torr

Kinetic molecular theory 1. Gases are composed of tiny particles (atoms or molecules) whose size is negligible compared to the average distance between them. therefore the total volume that the gas fills is almost all, empty space. And gases are compressible 2. The gas particles move randomly, in straight lines, in all directions and at various speeds. 3. The forces of attraction or repulsion between two gas particles are negligible, except when they collide.

4. When particles collide with one another, the collisions are elastic (no kinetic energy is lost). 5. The average kinetic energy of a molecule is proportional to the Kelvin temperature. ( all calculations involving gases should be carried out with temperatures converted to K ) These assumptions do have limitations. gases can be liquefied if cooled enough “real” gas particles do attract one another to some extent (otherwise the particles would never stick to one another and therefore never condense to form a liquid)

Pressure and Volume relationships: Boyle’s Law Boyle’s Law – at constant temperature, pressure is inversely proportional to volume. PV = k ( k is a constant) If the volume is increased the gas particles collide with the walls of the container less frequently and the pressure is reduced. Working formula: P 1 V 1 = P 2 V 2 P1 and V1 are the original conditions and P2 and V2 are the new conditions

Practice Problems: 1. If a 1.23 L sample of a gas at 53.0 torr is put under pressure up to a value of 240. torr at a constant temperature, what is the new volume? 2. The pressure on a 411 mL sample of gas is decreased from 812 mmHg to 790 mmHg. What will the new volume of the gas be?

Volume and Temperature relationships: Charles’ Law Charles’ Law states that, at constant pressure, volume is directly proportional to temperature. If the temperature is increased the gas particles gain kinetic energy, collide with the walls more frequently & with more force and occupy more space. Working formula: V1 and T1 are the original conditions and V2 and T2 are the new conditions.

Practice Problems: 1. An 11.0 L sample of a gas is collected at 276 K and then cooled by 14 K. The pressure is held constant at 1.20 atm. Calculate the new volume of the gas. 2. A gas has a volume of L at 35.0 oC and 1.00 atm pressure. What is the temperature inside a container where this gas has a volume of L at 1.00 atm?

Volume and Moles relationships: Avogadro’s Law At constant temperature and pressure, volume is directly proportional to the number of moles of gas present. This makes sense. As more molecules of a gas are placed into a container, number of collisions increase and volume increases. Working Formula: V1 and n1 are the original conditions and V2 and n2 are the new conditions.

Practice Problems: 1. A 13.1 L sample of moles of O 2 is held under conditions of 1.00 atm and 25.0 o C. If all of the O 2 is then converted to ozone (O 3 ) what will be the volume of ozone? 2. If 2.11 g of neon gas occupies a volume of 12.0 L at 28.0 o C. What volume will 6.58 g of neon occupy under the same conditions?

General and Combined Gas equations Combining the equations above, gives If the number of moles of gas in an experiment is constant (frequently the case) the expression becomes

The ideal gas law The combination of laws above leads to the formulation of the ideal gas law. Most gases obey this law at temperatures above 273 K and at pressures of 1.00 atm or lower. An ideal gas has particles that are assumed to have negligible volume when compared to the total volume (the volume of the container), and particles that do not attract one another (they act independently).

PV = nRT R = the universal gas constant which = L atm K -1 mol -1 P is measured in atm V is measured in L. T must always be in K n will be in mols This equation is useful because it can be manipulated to include other variables. For example, n can be replaced by with mass/molar mass to give and manipulated further to include density, since density = mass/volume.

Practice Problems: 1. Assuming ideal behavior, how many moles of helium gas are in a sample that has a volume of 8.12 L at a temperature of 0.00 o C and a pressure of 1.20 atm? 2. A sample of aluminum chloride weighing g was vaporized at 350. o C and 1.00 atm pressure to produce 19.2 mL of vapor. Calculate a value for the molar mass of aluminum chloride.

Dalton’s law of partial pressures Dalton’s Law states that in a mixture of ideal gases the total pressure exerted by the mixture is equal to the sum of the individual partial pressures of each gas. P Total = P 1 + P 2 + P 3 … Assuming ideal behavior the equation can be simplified to;

Practice Problems: 1. Calculate the number of moles of hydrogen present, in a L mixture of hydrogen and water vapor, at 21.0 o C, that has a total pressure of 750. torr, given that the vapor pressure of water at this temperature is 20.0 torr L of Carbon monoxide gas at a pressure of 199. kPa, and 1.00 L of carbon dioxide gas at a pressure of 300. kPa are injected into a 1.25 L container. Assuming no reaction between the two gases, what is the total pressure in the container?

Deviations from ideal behavior At high pressures and low temperatures gas particles come close enough to one another to make two postulates of the kinetic molecular theory invalid. The assumption that gases are composed of tiny particles whose size is negligible compared to the average distance between them begins to fail. When the gas is pressurized into a small space the gas particles size becomes more significant compared to the total volume. The assumption that the forces of attraction or repulsion between two particles in a gas are very weak or negligible begins to fail. – Low temperature means less energy, so the particles are attracted to one another more.

Under these conditions (high P and low T), gases are said to behave non-ideally or like ‘real’ gases. This has two consequences. (i) the observed total volume occupied by the gas under high pressures is artificially large since the gas particles are now occupying a significant amount of that total volume. The real gas situation necessitates the need to correct the volume by subtracting a factor. (ii) The actual pressure of a gas is lower than one would expect when assuming there were no attractive forces between the particles. Because, in a real gas, the particles are attracted to one another, they collide with the walls with less force, and the observed pressure is less than in an ideal gas. This necessitates the need to correct the pressure by adding a factor.

These corrections lead to the van der Waals equation below, where the terms a and b are constants for a particular gas

Root mean square speed The root-mean-square-speed of the velocities of gas particles is the square root of the averages of the squares of the speeds of all the particles a sample at a particular temperature. The root-mean-square-speed (urms) and can be calculated using Where R = universal gas constant = J mol -1 K -1 (where J = kg m 2 s -2 ) T = temperature in Kelvin, M = molar mass of the gas in kg mol -1.

Practice Problems: Note: Questions 1 and 2 represent calculations that you will not be asked to do on the AP exam, BUT they are extremely helpful in understanding question 3, that COULD be asked on the AP exam. 1. Determine the urms of the following gases at 25.0 o C. Include units. (a) Helium (b) Oxygen (c) Radon 2. Determine the urms of the following gases at 50.0 o C. Include units. (a) Helium (b) Oxygen (c) Radon 3. What can be said about the urms of a gas in relation to its molar mass and in relation to its temperature?

Grahams Law of Effusion and Diffusion Effusion is the process in which a gas escapes from one vessel to another by passing through a very small opening. Diffusion is the process by which a homogeneous mixture is formed by the random mixing of two different gases. Graham's law of effusion and diffusion states that the rate of effusion or diffusion of two gases is inversely proportional to the square roots of their respective densities and molecular masses. You will not be asked to perform a calculation on this on the AP exam, but you should appreciate that smaller gas particles effuse and diffuse at higher rates than larger gas particles.

Henry’s law, temperature and the solubility of gases (c = kp ) At higher pressures more gas particles strike the surface of the solution and enter the solvent, the concentration of the gas dissolved in the solvent is greater. Gas solubility decreases with increase in temperature of the solution, the gas particles have more energy and can escape from the solvent meaning less gas is dissolved in solution. For soda – when is it most ‘fizzy’? (most carbon dioxide dissolved in the sugar solution) Answer, when it is cold (when the CO 2 does not have sufficient energy to escape), and when it is sealed, under pressure (when the CO2 is forced into the solution). Warm soda = flat soda.

Solutions Solutions are homogeneous mixtures and are composed of a solute and a solvent. They can be gases (air), liquids or solids (brass). For a liquid solution the solute can be a gas, liquid or a solid. In solutions the solvent particles are very tiny (molecular size).

Colloids and Suspensions A colloid is a mixture of two separate phases, where the particles are larger in size than molecules, up to approx nm. A suspension is a mixture of two separate phases, where the particle size exceeds 1000 nm. These particle size distinctions mean that a mixture can appear homogeneous or heterogeneous depending on the scale on which it is observed. For example, with the naked eye, a colloid (like an emulsion paint with a solid dispersed in a liquid) looks homogeneous, but on a hugely magnified scale, it may appear heterogeneous.

Liquid solutions - cannot be separated into their components using a filter paper and have no particles large enough to scatter visible light. Two methods that can be used to separate solutions are chromatography and distillation.

Chromatography All chromatography techniques involve a moving phase and a stationary phase. Paper chromatography - the paper is the stationary phase and the solvent is the moving phase. When the solution mixture is exposed to the two phases, each component of the mixture will have a greater or lesser affinity for the stationary or the moving phase.

If a component of the mixture has a high affinity for the solvent (mobile phase), it will travel a relatively long distance on the chromatogram. A component with less affinity for the solvent (mobile phase), or only an affinity for the paper (stationary phase), will not move as far. The different distances of travel mean the components of the mixture are physically separated.

It is possible to apply a quantitative analysis to the chromatogram by calculating an Rf value. The distance travelled by the solvent is determined by measuring the distance from the baseline (where the original mixture was spotted), and the maximum distance that the solvent has travelled, known as the solvent front.

Distillation Distillation is a simple separation technique based upon differences in boiling points of a mixture two liquids. The boiling point of the individual component of a mixture depends upon the intermolecular attractions between the particles of that component.

Ethanol and Water Compared to water, ethanol molecules: have a relatively low intermolecular attraction for one another are relatively easily separated from one another and have a aelatively low boiling point (78 o C). Water molecules: have relatively high intermolecular attractions are more difficult to separate and have a relatively high boiling point (100 o C). As a result, a solution composed of ethanol and water can be separated by heating the mixture.

ethanol molecules vaporize before the water molecules can be collected as a vapor and then cooled to condense them back into a liquid in separate container. The water molecules do not vaporize as easily are left behind in the original container This process of separation by different boiling points is called distillation.

Composition of solutions The composition of a solution can be expressed as Molarity (moles / liter ) Low molarity solutions have small numbers of solute particles High molarity solutions have large numbers of solute particles (sometimes used as stock solutions for dilution) Dilution Solutions are prepared by adding water to (diluting) more concentrated ones. For example, if 4.0 L of a 2.0 M solution was required, it could be prepared by diluting a 10. M solution.

We know that: # mols before dilution = # mols after dilution and mols = (M)(V) therefore, M 1 V 1 = M 2 V 2 For example, What volume of water that must be added to prepare 2.0 L of 3.0 M KOH from a stock solution that has a concentration of 8.0 mol L-1, follow this method?

Will the solution process be exothermic or endothermic? Consider a substance dissolving in water. Three separate, independent processes must take place, each with its own associated energy change. 1. The solute particles must separate from one another (bond breaking process, endothermic). 2. The solvent particles must separate from one another (bond breaking process, endothermic). 3. The solvent and solute particles must interact (bond making process, exothermic)

The energy change of the overall process is a sum of energy changes 1, 2 and 3, and can be exothermic or endothermic depending on the magnitudes of each part.