KINETIC MOLECULAR THEORY

Physical Properties of Gases: Gases have mass Gases are easily compressed Gases completely fill their containers (expandability) Gases diffuse rapidly Gases exert pressure

Kinetic Molecular Theory A theory that explains the physical properties of gases by describing the behavior of the particles

KMT has 5 postulates:

#1 A gas consists of very small particles that have mass. (molecules or atoms)

#2 Gas particles are very far apart from each other. (therefore gases are easily compressed)

#3 Gas particles are in continuous, rapid, random motion.

#4 Collisions of gas particles (with each other and with container) are perfectly elastic (no energy lost)

#5 The average energy of the gas particles depends on the temperature of the gas.

Measuring gases Experimental work in chemistry requires measurements of quantities. Like volume, temperature, pressure and amount. This quantities are variables.

We can measure gases in 4 ways: MeasurementUnit Amount of gasMoles Volume (V)Liters (L) Temperature (T)°C, °F, or K Pressure (P)atm, kPa, Torr, mm Hg, or lb/in 2

Temperature (T) A measurement of the average kinetic energy of a substance, the temperature is related with speed of the molecules of the gas.

Higher temperatures cause gas particles to move faster

K =  C  C = ? K 14  C = 287K To solve gas problems, the temp must always be in Kelvin (K) !!!

Pressure (P) The force per unit area on a surface

Pressure is caused by gas particles slamming into the container’s walls.

When pressure increases, the number of collisions in a determine time increases also

VOLUME (V) The volume of the gas is the same as the volume of the container. The unit is the Liter (L) = 1000cm3

Units of Pressure: 1) atmosphere (atm) 2) Pascal (Pa) 3) millimeters of Mercury (mm Hg) 4) Torr 5) Pounds per square inch (lb/in 2 ) 1 atm = 101,325 Pa 1 atm= 760 mm Hg = 760 torr 1 atm = lb/in 2 Bar = 100,000 Pa =

Amount of gas The mole is the unit for specifying the amount of a sample of matter. You can relate the number of moles and the mass to the number of gas particles.

The pressure exerted by air in the atmosphere is called atmospheric pressure. VIDEO 1 Weather and air pressure VIDEO 1 Weather and air pressure VIDEO 2 What is weather?

Learning Check A. What is 475 mm Hg expressed in atm? 1) 475 atm 2) atm 3) 3.61 x 10 5 atm B. The pressure of a tire is measured as 29.4 psi. What is this pressure in mm Hg? 1) 2.00 mm Hg 2) 1520 mm Hg 3)22,300 mm Hg

Solution A. What is 475 mm Hg expressed in atm? 485 mm Hg x 1 atm = atm (B) 760 mm Hg B. The pressure of a tire is measured as 29.4 psi. What is this pressure in mm Hg? 29.4 psi x 1.00 atm x 760 mmHg = 1.52 x 10 3 mmHg 14.7 psi 1.00 atm (B)

Enclosed Gases If the container is closed, the pressure inside the container may be different from the atmospheric pressure. Manometer: Instrument to measure the pressure in a closed container.

Determining the pressure in the container will depend on the levels of the Hg on the two sides. Pressure of the gas in the container is the same as the atmosphere WHEN THE TWO LEVELS ARE EQUALY HIGH If the level of mercury is LOWER on the container side, the pressure in the container is higher than atmosphere.

The difference between pressures in mmHg is simply the difference between the heights of the two columns. To find the pressure of the gas in the container you must add or subtract the difference in pressures to the atmospheric pressure, witch you have separately determined by using a barometer.

If the mercury level in the container is HIGHER that atmospheric side, the pressure in the container is less than the atmospheric pressure.

WHEN THE GAS PRESSURE IS HIGHER THAN ATMOSPHERE PRESSURE, THE LEVEL OF MERCURY ON THE SIDE OF THE GAS WILL BE LOWER THAN OPEN ENDED SIDE. Add differences WHEN GAS PRESSURE IS LOWER THAN ATMOSPHERIC PRESSURE, THE LEVEL ON THE SIDE OF THE GAS WILL BE HIGHER THAN OPEN ENDED SIDE.. Subtract differences

P container = Height difference – Atmospheric pressure P container = Height difference + Atmospheric pressure

STOP… collaborate and listen

THE GAS LAWS Mathematical representation of the observed relationships among the 4 variables BOYLE’S LAW : The pressure- volume Famous experiment involved trapping air, changing its pressure, and measuring its volume. If the temperature remains unchanged the product of the pressure times the volume have a constant value K.

PV = K The pressure and volume of a sample of gas at constant temperature are inversely proportional to each other. IF PRESSURE INCREASES, VOLUME DECREASES IF VOLUME INCREASES, PRESSURE DECREASES At same temperature the product of the pressure times the volume of a sample is always the same.

Boyle’s Law MUST BE AT CONSTANT TEMPERATURE!! P 1 V 1 = P 2 V 2 1 = trial 1 2 = after (trial 2)

A gas occupies a volume of L at a pressure of 1.01 kPa and temperature of 295 Kelvin. Although the temperature stays the same, the volume is increased to L. What is the new pressure? kPa

Charles’ Law The relationship between volume gas and its temperature while the pressure and the amount of gas were held constant VOLUME INCREASES AS TEMPERATURE INCREASES V= K 2 T At constant pressure the volume of a fixed amount of gas is directly proportional to its absolute temperature.

Charles’ Law MUST BE AT CONSTANT PRESSURE!! V 1 T 2 = V 2 T 1 1 = before 2 = after

What will be the volume of a gas sample at 309 K if its volume at 215 K is 3.42 L? Assume that pressure is constant L

Gay-Lussac’s Law MUST BE AT CONSTANT VOLUME!! 1 = before 2 = after

A balloon with a pressure of atm is heated from 105 K to 155 K. If volume is held constant, what is the new pressure? 1.33 atm

Combined Gas Law 1 = before 2 = after JUST HOLD ONE QUANTITY CONSTANT!! (take it out of the equation)

The gas in a L container has a pressure of 1.39 atmospheres. When the gas is transferred to a L container at the same temperature, what is the pressure of the gas? 0.82 atm

The gas inside a 70.8 mL piston has a temperature of 35.0°C. If the temperature is raised to 100.0°C, what is the new volume of the gas? 85.7 mL

An elastic container is inflated to a volume of 18.0 liters at a pressure of 1.26 atm. The container then expands to a new volume at a pressure of 1.05 atm. What is the new volume? 21.6 liters

Avogadro’s Law The amount- volume relationship Equal volumes of gas (at same P and T) contain the same amount of particles

It states that all gases show the same physical behavior A gas with a larger volume must consist of a greater number of particles. As long as the pressure and temperature do not change If the amount of gas increases the volume increases If the amount of gas decreases the volume decreases

1 mole = 6.02 x particles Only works at same P and T V = K n 1 mole = 22.4 L

Ideal Gas Law The mother of all gas laws. It includes everything! PV = nRT

P = pressure (atm) V = volume (L) n = moles (mol) R = Gas Constant T = Temperature (Kelvin) PV = nRT

MUST USE THESE UNITS!!! PV = nRT

If the pressure exerted by a gas at 0.00°C in a volume of L is 5.00 atm, how many moles of gas are present? 2.2 x moles

Ideal gases don’t really exist… …real gases do!

Ideal Gas A gas that is described by the KMT postulates. Ideal Gas Law works most of the time.

It does NOT work at very low temperatures and very high pressures.

Dalton’s Law of Partial Pressures The sum of the partial pressures of the gases is equal to the total pressure

Dalton’s Law of Partial Pressures P total = P 1 + P 2 + P 3 + …

A balloon contains O 2 and N 2 gas. If the partial pressure of the O 2 is 0.75 atm and the partial pressure of the N 2 is 0.55 atm, what is the total pressure of the balloon? 1.30 atm

The gas inside a 70.8 mL can contains H 2 O (g) and CO 2(g) and has a total pressure of 760 mm Hg. If the partial pressure of the H 2 O is 350 mm Hg, what is the partial pressure of the CO 2 ? 410 mm Hg

STP Standard Temperature and Pressure Behavior of gases depend strongly on temperature and pressure. 0  C or 273 K and 1 atm

How many moles of N 2 gas are in a 4.5 L balloon at STP? 0.20 moles

A gas at STP is heated to 55 ° C. What is the new pressure if volume is held constant? 1.2 atm

A gas tank contains CO 2 and O 2 gas. What is the total pressure in the tank if the partial pressure of CO 2 is 0.45 atm and the partial pressure of O 2 is 0.55? 1.00 atm