Lecture 18

```Final Grade for CHE 103
Calculated as stated in syllabus:
EXAM1 + EXAM2 + EXAM 3 + QUIZZES
350
Outline
I. Gases &amp; Gas Laws
- Kinetic Molecular Theory
- Simple variable relationships
- Ideal/Combined Gas Law
States of Matter - solid, liquid, gas
Gaseous State

Characterized by dominance of kinetic
energy over potential energy


Gas particles have enough kinetic energy to move
far apart from each other.
There is very little attraction between particles
Four Important Gas Variables




1. n = number of moles
2. T = temperature; must be in Kelvin!
 K = oC + 273.15
3. V = Volume
4. P = Pressure = force/area
 1 atm = 760 mm Hg
Relationship Between Pressure and
Volume (Boyle’s Law)

When the pressure is increased on a gas, its volume goes down.
PV = constant (T fixed)
useful form: P1V1 = P2V2
Volume/Pressure Calculation

A balloon is inflated to a volume of 12.6L on a day when the
atmospheric pressure is 675 mm Hg. The next day, a storm drops the
pressure to 651 mm Hg. Assuming constant temperature, what is the
new volume of the balloon?
Relationship Between Temperature and
Volume (Charles’ Law)

When the temperature (K) is increased on a gas, its volume
goes up by a constant: V/T = constant (P fixed)
useful form:
V1/T1 = V2/T2
Volume/Temperature Calculation

The volume of a sample of air at 30. oC is 3.50 L. Assume that
the pressure is held constant. What would be the volume of air
at 300. oC?
Relationship between Temperature and
Pressure (Gay-Lussac’s Law)

When the temperature (K) is increased on a gas, its pressure
goes up as a constant: P/T = constant (V fixed)

Useful form: P1/T1 = P2/T2
When the Temperature
increases, gas molecules
are moving faster and
hitting the sides of their
container more….creating
more pressure….according
to KMT!
Pressure/Temperature Calculations

Consider a container with a volume of 22.4 L filled with a gas at
1.00 atm at 273 K. What will be the new pressure if the
temperature increases to 298 K?
P1/T1 = P2/T2
P1 = 1.00atm,
P2 = ?
T1 = 273K
T2 = 298K
P2 = (1.00atm)(298K)
(273K)
= 1.09atm
 The volume of a gas is
directly related to the
number of moles of gas
 T and P are constant
V1 = V2
n1
n2
Learning Check
If 0.75 mol of helium gas
occupies a volume of 1.5 L,
what volume will 1.2 mol of
helium occupy at the same
temperature and pressure?
1) 0.94 L
2) 1.8 L
3) 2.4 L
V2 = (1.5L)(1.2mol)
(0.75mol)
STP

The volumes of gases can be compared when they have the
same conditions of temperature and pressure (STP, Standard
Temperature and Pressure).
Standard temperature (T)
0&deg;C or 273 K
Standard pressure (P)
1 atm (760 mm Hg)
Molar Volume
At standard temperature and pressure
(STP), 1 mol of a gas occupies a volume
of 22.4 L, which is called its molar
volume.
Molar Volume as a Conversion Factor

The molar volume at STP can be used
to form conversion factors.
22.4 L
1 mol
and
1 mol
22.4 L
Learning Check
A. What is the volume at STP of 4.00 g of CH4?
B. How many grams of He are present in 8.00 L of gas
at STP?
Important Simple Gas Relationships




Boyles Law
Charles Law
Gay-Lussacs
P1V1 = P2V2 (T fixed)
V1/T1 = V2/T2 (P fixed)
P1/T1 = P2/T2 (V fixed)
V1/n1 = V2/n2 (T&amp;P fixed)
STP - Standard Temperature and Pressure (Gases)
T = 273 K (0 oC) and P = 1 atm (760 mmHg)
1 mole of a gas at STP = 22.4L
Combined Gas Laws

Relates the changes in pressure, volume and
temperature, and quantity change of a gas
PV =
nT
constant
Useful form of the expression:
P1V1
n1T1
=
P2V2
n2T2
Combined Gas Law Practice

A fixed quantity of nitrogen gas in a 275 mL
container at a pressure of 625 mm Hg is
transferred to a container with a volume of
750. mL. What is the new pressure if the
temperature changes from 25 oC to 17 oC?
Ideal Gas Law

Let’s now solve for the constant:

PV/nT = constant = R

One set of conditions we know - 1 mole of a
gas at STP. (atm L/mol K)
The Ideal Gas Law

Describes the relationships among the four
variables for gaseous substances: P, T, V, n


PV = nRT
R is called the ideal gas constant


0.0821 atm&middot;L/mol&middot;K
Always make sure you have all your units correct!
Gas Law Calculations

What is the temperature (in oC) of a sample of 3.00 moles of He
at 27.5 atm of pressure and in a 6.00 L container?
A. 670.
B. 397
C. 273
Gas Law Calculations

Methane, CH4, can be used as fuel for an automobile; however, it is a
gas at normal temperatures and pressures, which causes some
problems with storage. One gallon of gasoline could be replaced by
655 g of CH4. What is the volume of this much methane at 25 oC and
745 mm Hg.
A. 30.9
B. 510.
C. 1020
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