Gases Properties of gases – Easily compressed, fills its container; mixes completely with any other gas; varying reactivities; exerts pressure. Ideal gas – High temperature, low pressure – large space in between particles, no interactions except perfectly elastic collision (see Kinetic Molecular Theory) Gas Pressure – pressure is caused by a force acting over a certain area. When gas particles in motion collide with their container, they exert a force on that container. Force/Area = Pressure

Kinetic Molecular Theory This theory (KMT) explains the effects of temp. and pressure on matter through 3 basic assumptions: 1.All matter is composed of small particles. 2.These particles are in constant random motion (particle KE is proportional to temp in K). 3.All collisions are perfectly elastic. there is no change in the total kinetic energy of the 2 particles before and after the collision. assumed that the gas particles attraction for each other is negligible The motion of the particles varies w/ changes in temperature, # of particles, and particle mass.

Measuring Pressure of a Trapped Gas Use a manometer – device used to measure gas pressure Open-armed manometer if gas end lower than open end, P gas = P air + diff. in height of Hg if gas end higher than open end, P gas = P air – diff. in height of Hg Closed-armed manometer P gas = difference in height of mercury Barometer – special closed-armed manometer designed to measure air pressure. Developed by Evangelista Torricelli (1644)

Torricelli Barometer The air pushes down on the mercury in the dish. The space above the mercury is… nothing. So the mercury rises to the point that the forces of air pressure and gravity are equal. Normal atmospheric pressure pushes the mercury column to a height of 76.0 cm (760. mm). So 1.00 atm of pressure = 760. mmHg = 760. Torr = 101,325 Pa = kPa

Fig. E The number of particles at speed v varies with the absolute temperature, as the shape of the curve changes. However, the distribution really has the same profile; the distribution is pushed to the left and upward as temperature decreases, and is pushed to the right and down as the temperature increases. The Maxwell-Boltzmann Distribution (Kinetic Energy)

Simple Gas Laws

Boyle’s Law: P  1/V PV = k P 1 V 1 = P 2 V 2 Charles’ Law: V  T V = kT V 1 = V 2 T 1 T 2 Charles’ Law: P  T P = kT P 1 = P 2 T 1 T 2 Combined ?

Simple Gas Laws - Examples 1.53 dm 3 of sulfur dioxide gas at 5.60 kPa is contracted to dm 3. What is the new pressure (in atm)? Gas at C has a volume of 2.58 dm 3. If the gas is heated to C, what is the new volume? A sample of diborane (B 2 H 6 ) gas has a pressure of 345 torr at C and 3.48 dm 3. If the temperature of the gas is increased to 36 0 C and the pressure is increased to atm, what is the volume of the gas? A gas occupies a volume of 180 mL at 35.0 o C and 740 mm Hg. What is it’s temperature (in Celsius) at 1.3 atm and 250 mL?

IDEAL GASES In the early part of the 19 th Century, Amadeo Avogadro demonstrated the relationship between the number of particles and gas volume. As amount of gas increases volume increases proportionally (at constant P and T) that is, V/n = a. As a result of this, equal volumes of gases at the same temperature and pressure have the same … number of particles. What do we ignore w/ these? At standard temperature and pressure (STP) 1 mol of any gas has a volume equal to … 22.4 L

Boyles Law: V = k/P Charles Law: V = bT Avogadro’s Law: V = an kba = constant, R Therefore,V = R(Tn/P),orP V= nR T THE IDEAL GAS LAW!! Let’s try a problem A sample of hydrogen gas has a volume of 8.56 L at 0 0 C and 1140 mmHg. How many grams of gas are present? If the density of a gas at STP is g/L, what is the M r of the gas?

Gas Density PV = nRT n = mass (g) M r PV = gRT M r P = gRT VM r g = mass = density (ρ) V volume P = ρRT M r ρ = P M r RT M r = ?

If you have 2L of H 2 (g) and 1L of O 2 (g), at the same temperature and pressure, why is there twice as many liters of H 2 ? Because there are 2X as many particles. If you mixed the two gases and the total pressure of the mixture was 99 kPa, what is the partial pressure of each gas? H 2 would be 66kPa,O 2 would be 33kPa. This is Daltons Law of Partial Pressures. An important application of this law is when a gas is collected over water.

Magnesium metal reacts with aqueous HCl to produce hydrogen gas. The gas is collected over water at 25 0 C and 747 mmHg and is found to have a volume of L. How many grams of Mg were used in the reaction? n.b. Assume 100% yield. Partial pressure of water at 298 K = 23.8 mmHg What is the partial pressure of each gas in a mixture (in mmHg) which contains 12.45g of hydrogen, 60.67g of nitrogen and 2.38g NH 3, if the total pressure of the mixture is atm?

Diffusion and Graham’s Law As a result of the constant and rapid motion of gas particles, 2 things can occur: 1. Diffusion – particles move from an area of higher particle concentration to an area of lower particle concentration. Diffusion 2. Effusion – same as diffusion except the gas particles escape through small holes (pores) in a container. Effusion Graham’s Law – the rate of the effusion of a gas is inversely proportional to the square root of its formula mass Rate A Rate B = √ formula mass B √ formula mass A

Think About It 1.Rank the following gases in terms of their velocities, assuming they are at the same temperature (1-highest, 4- lowest). CO 2, O 2, N 2, H 2 2.Rank the following gases based on the appropriateness for inflating a balloon you want to keep inflated (1-best to use, 4-worst to use). CO 2, O 2, N 2, H 2 3. Draw a Maxwell – Boltzmann curve comparing each of the gases at the same temperature.

If 0.10 mol of iodine vapor can effuse from an opening in a heated vessel in 52 s, how long will it take 0.10 mol of hydrogen gas to effuse under the same conditions? A given volume of nitrogen gas requires 68.3 s to effuse from a hole in a container. Under the same conditions, another gas requires 85.6 s for the same volume to effuse. What is the molar mass of this gas?

REAL GASES An ideal gas is a hypothetical concept. No gas exactly follows the Ideal Gas Law, though many do at high temperatures and low pressures, i.e. normal conditions. As long as these conditions exist, the law works well, But at high pressures and/or low temperatures, modifications must be made to the equation. An equation for real gases was developed in 1873 by Johannes van der Waals using experimental values. [P obs + a(n/V i ) 2 ] x (V obs – nb) = nRT a is inatm L 2 /mol 2 b is in L/mol

The values for a and b are determined experimentally and vary for each gas. b tends to increase as molecular size increases and the actual volume available to gas particles is decreased (refer to the equation to verify this). a tends to be larger with an increase in IMF strength. Stronger IMF increases attraction between particles, slowing them and reducing the force with which they strike the container (lower observed pressure).