1. Properties of Liquids: Surface Tension oSeveral properties of liquids can be explained by looking at intermolecular forces. For example, we know that small samples of liquid tend to be round (e.g. water droplets). Why? oMolecules within a liquid are attracted to all of the molecules around them via intermolecular forces. Molecules on the surface of a liquid can only interact with the molecules immediately below them and beside them. As such, the surface molecules feel a net attraction toward the interior of the liquid and act as a “skin” for the liquid. The energy required to break through this surface “skin” is referred to as surface tension. Pin trick, insects… 1 1

2. Properties of Liquids: Surface Tension oA sphere is the shape with the smallest surface area-to-volume ratio – giving the smallest ratio of surface molecules to bulk molecules (i.e. non-surface molecules). This maximizes the intermolecular forces: oThis effect can also be seen when looking at the convex (“inverted”) meniscus of mercury (Hg) in a glass test tube: 2 Water behaves differently because water molecules… 2 2

3. Properties of Liquids: Surface Tension oWhat happens if we add a solute to the liquid (now a solvent)?  If the intermolecular forces between the solute and the solvent are stronger than the intermolecular forces between solvent molecules, the solute will be pulled into the solution away from the surface.  If the intermolecular forces between the solute and the solvent are weaker than the intermolecular forces between solvent molecules, the solute will tend to stay at the surface and is referred to as a surfactant (“surface active agent”). Surfactants reduce surface tension.  Detergents are important surfactants (in water). They consist of a long nonpolar “tail” and a small polar “head” (often ionic). e.g. dodecylsulfate ion 3 3

4. Properties of Liquids: Capillary Action oWhen a liquid is in contact with a solid surface, we must also consider intermolecular forces between the liquid molecules and the molecules of the solid.  If the liquid molecules are more strongly attracted to the surface than to each other, wetting will be observed as the liquid sample spreads over the surface to maximize those attractions. e.g. water in a glass test tube  If the liquid molecules are more strongly attracted to each other than to the surface, non-wetting will be observed as the liquid sample appears to ‘bead’ on the surface. e.g. mercury in a glass test tube, liquid nitrogen 4 4

5. Properties of Liquids: Capillary Action oThe familiar concave meniscus of water on glass is an example of wetting leading to capillary action – specifically, capillary rise.  Glass consists of polar Si-O bonds so, if a narrow glass tube is placed in water, the water molecules are attracted to the glass. Other water molecules are attracted to the initially “stuck” molecules, and are pulled up by surface tension. This continues until the force of gravity pulling water molecules down is equal to the force of surface tension pulling water molecules up.  Because the force of attraction between the water and the glass has to support the weight of the column of water (i.e. counteract the force of gravity), narrow capillaries allow the liquid to rise higher (compared to wide capillaries). oA non-wetting liquid-surface combination will give capillary depression. How do you think that works? 5 5

6. Properties of Liquids: Viscosity oViscosity is a liquid’s resistance to fluid flow. Liquids with high viscosities tend to be thick and difficult to pour. oViscosity increases as intermolecular forces increase. As a result, viscous liquids tend to be either large or polar (or both). e.g. gasoline vs. mineral oil (nonpolar, ~8 carbons) (nonpolar, ~15-40 carbons) 6 6

7. Kinetic Molecular Theory of Gases/Ideal Gases oIn an ‘ideal gas’:  The distance between gas particles (atoms or molecules) is much larger than the size of the particles. The gas particles therefore occupy a negligible fraction of the volume.  Gas particles are in constant motion.  Gas particles do not interact except when they collide.  When gas particles collide with each other (or the walls of their container), collisions are elastic (no energy is lost).  Gas particles in a sample move at different speeds, but the average speed is proportional to temperature. All gases have the same average kinetic energy at a given temperature. Law of Large Numbers (as applied here) The behaviour of a system containing many molecules is unlikely to deviate significantly from the behaviour predicted from the statistical average of the properties of the individual molecules. 7 7

8. Kinetic Molecular Theory of Gases/Ideal Gases oThe kinetic energy of a particle depends on its mass and speed: where K is kinetic energy, m is mass and v is speed. oSpeeds of molecules are distributed statistically in a Maxwell-Boltzmann distribution: oWhen the temperature increases, the average speed of the gas particles increases and the distribution of speeds spreads out. 8 8

9. Kinetic Molecular Theory of Gases/Ideal Gases oThere are three different ways to look at the speed of gas particles in a sample:  v mp = ‘most probable’ speed  v av = ‘average’ speed  v rms = ‘root mean square’ speed (square each particle’s speed then calculate the average then take the square root) oBecause kinetic energy is proportional to v 2, it makes most sense to use v rms in kinetic energy and temperature calculations. where K is the average kinetic energy of gas particles, m is the mass of one particle, R is the ideal gas constant and T is temperature (in K). oNote that, at a constant temperature:  particles with __________ mass will have __________ v rms 9 9

10. Kinetic Molecular Theory of Gases/Ideal Gases oThe Maxwell-Boltzmann equation can be derived from the kinetic-molecular theory of gases: or where P is pressure, V is volume, N is the number of gas particles, m is the mass of one particle, and v rms is the root-mean-square speed. oSince the Maxwell-Boltzmann equation and the ideal gas law both describe ideal gases, they can be related: and Therefore: Recall that pressure is force exerted on an area. (P=F/A) 10

11. Kinetic Molecular Theory of Gases/Ideal Gases oThe mass of one particle (m) multiplied by the number of particles (N) gives the total mass of gas particles. When this total mass is divided by the number of moles of gas particles (n), we get the molar mass for the gas particles (M). oSince can be rewritten as We get: or Note that, in order for the units to cancel out, M must be converted to kg/mol. e.g. Calculate v rms for N 2 at 20 °C. 11

12. Kinetic Molecular Theory of Gases/Ideal Gases oYou have a sample of helium gas at 0.00 ˚C. To what temperature should the gas be heated in order to increase the root-mean-square speed of helium atoms by 10.0%? 12

13. Nonideal Gases oThe ideal gas law and kinetic molecular theory are based on two simplifying assumptions:  The actual gas particles have negligible volume.  There are no forces of attraction between gas particles. These two assumptions are not always valid. oUnder what conditions would you expect these assumptions to no longer apply? 13

14. Nonideal Gases oUnder ideal conditions, the volume of a container of gas is almost 100% empty space – so the volume available for gas particles to move into is the entire volume of the container. oUnder nonideal conditions, there is less “available volume” in the same sized container. We can correct for this “excluded volume” by adding a term to the ideal gas law: where b is an experimentally determined constant specific to the gas. This constant tends to ______________ as the size of the gas particles increases. oThe effect of this “excluded volume” is to _________________ the pressure of the gas. 14

15. Nonideal Gases oUnder ideal conditions, particles in a gas sample don’t experience intermolecular forces. oUnder nonideal conditions, the gas particles are close enough together that they do experience intermolecular forces. We can correct for these attractive forces by adding a term to the ideal gas law: where a is an experimentally determined constant specific to the gas. This constant tends to ______________ as the polarity of the gas particles increases. oThe effect of the intermolecular forces is to ________________ the pressure of the gas. 15

16. Real gases: van der Waals Equation of State oThe Kinetic Molecular theory ignores: (1) the actual volume occupied by the gas molecules (2) intermolecular forces of attraction oThe latter means that molecules can affect each other when they pass closely, not just when they directly collide; this acts like gravitational forces between moving planets, etc. oJohannes van der Waals (1837-1923) developed an empirical correction to the ideal gas law oThe van der Waals equation of state has correction factors for inherent volume (b) and intermolecular forces (a) 16

17. Nonideal Gases oWhen both corrections are applied, we get the van der Waals equation: oThe table below gives some sample values for a and b a (kPa·L 2 ·mol -2 )b (L·mol -1 ) HydrogenH2H2 24.80.02661 MethaneCH 4 2280.04278 AmmoniaNH 3 4230.03707 WaterH2OH2O5540.03049 Sulfur dioxideSO 2 6800.05636 17

18. Nonideal Gases oYou have two 1.00 L containers at 298 K. One contains 1.00 mol of hydrogen gas while the second contains 1.00 mol of ammonia gas. (a)Calculate the pressure in each container according to the ideal gas law. (b)Calculate the actual pressure in each container. a (kPa·L 2 ·mol -2 )b (L·mol -1 ) HydrogenH2H2 24.80.02661 AmmoniaNH 3 4230.03707 18