Ch. 10

Gases

Properties

Expand to fill their container Highly compressible Molecules are far apart

Pressure - conversions

1 atm = 760 mm Hg1 atm = 760 torr1 atm = 1.01325 x 105 Pa1 atm = 101.325 kPa

The Gas Laws Boyle’s: P and V

P1V1 = P2V2

Inversely proportional

Weather balloons expand as they rise through the atmosphere

Breathing

Gas Laws

Charles’s Law: V and T

Directly proportional Temperature in K!

Avogadro

22.4 L of any gas at 0°C and 1 atm contains 6.022 x 1023 gas molecules (or 1 mol)

V = constant x n Volume of a gas is directly

proportional to the number of moles of that gas (if pressure and temp. are constant)

Ideal Gas Law

PV=nRT

STP = standard temperature and pressure (1 atm and 0°C)

Density and Molar Mass Calculations

M = dRT/P

Practice

2NaN3 2Na + 3N2

If an air bag has a volume of 36 L and is to be filled with nitrogen gas at a pressure of 1.15 atm at a temperature of 26.0°C, how many grams of NaN3 must be decomposed?

More than 1 Gas? Dalton’s Law of Partial Pressures Pt = P1 + P2 + P3 + …. nt = n1 + n2 + n3 +…. At constant temperature and

volume, the total pressure is determined by the total number of moles present

Pt = (n1 + n2 + n3 +….) RT/V

Practice

A gaseous mixture made from 6.00 g O2 and 9.00 g CH4 is placed in a 15.0-L vessel at 0°C. What is the partial pressure of each gas, and what is the total pressure in the vessel?

Mole Fractions

Mole fraction – ratio of the number of moles of one component to the total number of moles in the mixture (part/whole)

Partial pressure of a gas in a mixture – mole fraction times the total pressure

Practice

Calculate the partial pressure of O2 in the mixture if the total pressure of the atmosphere is 745 torr. O2 is present at 18.0 mol percent.

Collecting Gases over Water

Practice

A sample of KClO3 is decomposed producing O2 gas that is collected over water. The volume of gas collected is 0.250 L at 26°C and 765 torr total pressure. How many grams of KClO3 were decomposed? Pressure of water vapor at 26°C is 25 torr.

KMT – Kinetic Molecular Theory – The ‘Why’ Behind Gas Behavior

Gases are always in motion (random) Attractive and repulsive forces are

negligible Collisions are elastic – average kinetic

energy of molecules does not change At any given temperature, the

molecules of all gases have the same kinetic energy

So, what……..

If the temperature is doubled, the average kinetic energy is doubled (the individual molecules move at varying speeds)

The distribution ofmolecular speeds for N2

at three temperatures

Applications

Volume increase at constant temperature – longer distance to travel less collisions with the container walls decrease in pressure

(Boyle’s Law)

Increase temperature at constant volume increase kinetic energy increase collisions with container wall increase pressure

(Charles’s Law)

Practice

A sample of O2 gas initially at STP is compressed to a smaller volume at constant temperature. What effect does this change have on

(a) the average kinetic energy of O2 molecules?

(b) the average speed of O2 molecules?

(c) the total number of collisions of O2 molecules with the container walls?

Effusion and Diffusion

Speed of a molecule is inversely proportional to its molar mass

Small = fast Big = slow

Relationship between molar mass andmolecular speed

The Process of Effusion – the escape of a gas molecule through a tiny hole into an evacuated space

Graham’s Law of Effusion

The effusion rate of a gas is inversely proportional to the square root of its molar mass

Lighter gases effuse more rapidly (b/c has more opportunities to get through the hole) – He balloon that deflates too quickly

Diffusion – spreading out of gas molecules

Why does it take a few minutes before you can smell the perfume that has been sprayed from across the room?

Real Gases –don’t always obey the ideal gas law

Do have finite volume (real gases tend to have larger volumes than predicted by the ideal gas law)

they do attract one another (causing a decrease in pressure)

**Deviate from ideal behavior at high pressures and low temperatures**

(Molecules of an ideal gas are assumed to occupy no space and have no attraction for one another)

Van der Waals

Introduced 2 constants, a and b, to account for the attractive forces felt by the “real” gases

nb = measure of volume occupied by gas molecules

n2a/V2 = attractive forces between molecules

Van der Waal’s constants for gas molecules

The values of a and b generally increase with an increase in the mass of the molecule and an increase in the complexity of its structure; larger molecules tend to have greater intermolecular attractive forces