Ch. 10
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Transcript of Ch. 10
The Gas Laws Boyle’s: P and V
P1V1 = P2V2
Inversely proportional
Weather balloons expand as they rise through the atmosphere
Breathing
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)
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.
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)
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
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