# IDEAL GAS LAW

```GASES
Matter and the Environment
Miss Gaby Montemayor
GASES
● One of five states of matter.
● Particles have high kinetic energy
and are loosely packed.
● No definite shape or volumen.
Ideal GASES
● Gases whose particles do not
repel or attract each other
● Gases whose particles have only
elastic collisions
Ideal GASES
● Ideal gases are a concept that
helps us approximate the
behavior of real gases.
● Certain gases are close to ideal,
so this concept is useful.
IDEAL GAS LAW
Ideal GAS LAW
● Describes the relationship
between the pressure, volume,
temperature, and the amount (in
moles) of an ideal gas.
Ideal GAS LAW
Expressed by the formula:
PV= nRT
Ideal GAS LAW
Expressed by the formula:
PV= nRT
P= Pressure
V= Volume
n= moles
R= Ideal Gas constant
T= Temperature (in Kelvin)
PRESSURE
Pressure= Force/Area
Pressure units include
- atm (atmospheres)
- Pascals (N/m2)
- mmHg (mm of Mercury)
volume
Volume indicates the amount of
space taken up by a gas.
Volume units include:
- Liters (L)
- Cubic meters (m3)
MOLES
Describes the amount of gas molecules
1 mol= 6.022x1023 molecules
WHY DOES 1 MOL EQUAL
6.022X 1023 MOLECULES?
proposed that the
number of atoms or
molecules is
proportional to its
physical mass.
a proportion used to
relate the number of
atoms in an element
or molecules in
compound to its
physical mass.
6.022x1023
MOLE
International
System of Units
(SI) that
measures the
amount of
”chemical entity”.
1 mole= 6.022x1023
MOLE
A mole is just a number!
For example:
1 dozen= 12 of something
1 mole= 6.022x1023 of something
TEMPERATURE
ALWAYS expressed in Kelvin.
How to convert from &ordm;C to K:
T= &ordm;C+273.15
Hence: 0&ordm;C= 273.15 K
IDEAL GAS CONSTANT (R)
Its is a number that describes the
behavior of gases under ideal conditions.
STP
Stands for STANDARD TEMPERATURE
AND PRESSURE (STP). The conditions are:
- Temperature= 273.15 K (0&ordm;C)
- Pressure= 1 atm
IDEAL GAS CONSTANT (R)
States that 1 mole of an ideal gas at STP
occupies a volume of 22.414 L.
R = PV
nT
IDEAL GAS CONSTANT (R)
States that 1 mole of an ideal gas at STP
occupies a volume of 22.414 L.
R = PV = (1 atm)(22.414L)
nT
(1 mol) (273.15)
IDEAL GAS CONSTANT (R)
States that 1 mole of an ideal gas at STP
occupies a volume of 22.414 L.
=
0.082 atm*L
mol*K
IDEAL GAS CONSTANT (R)
States that 1 mole of an ideal gas at STP
occupies a volume of 22.414 L.
R=
0.082 atm*L
mol*K
=
8.31
J
mol*K
HOW TO IDENTIFY IDEAL GAS LAW PROBLEMS?
&uuml; Problem gives data on pressure,
volume, temperature, and number of
moles
&uuml; Problem specifies the value of R
SAMPLE PROBLEMS
PROBLEM 1- SOLVING FOR PRESSURE
If a 3.0 L tank of oxygen (O2) contains
0.45 moles of O2 at 24&ordm;C, what is the
pressure (in atm) in the tank?
R= 0.0821 L*atm/mol*K
PROBLEM 1- SOLVING FOR PRESSURE
P= ?
V=3.0 L
n= 0.45 moles
R= 0.0821 L*atm/mol*K
T= 24&ordm;C +273.15= 297.15K
PROBLEM 1- SOLVING FOR PRESSURE
PV= nRT
P= nRT
V
PROBLEM 1- SOLVING FOR PRESSURE
P= (0.45 mol) (0.0821 L*atm/mol*K)(297.15 K)
3.0 L
P= 3.6 atm
PROBLEM 2- SOLVING FOR VOLUME
A ball is filled with 2.1 moles of gas.
The temperature is 25&ordm;C and the
pressure in the ball is 2.5 kPa. Find
the volume of the ball.
R= 8.31 L*kPa/mol*K
PROBLEM 2- SOLVING FOR VOLUME
P= 2.5 kPa
V= ?
n= 2.1 moles
R= 8.31 L*kPa/mol*K
T= 25&ordm;C +273.15= 298.15K
PROBLEM 2- SOLVING FOR VOLUME
PV= nRT
V= nRT
P
PROBLEM 2- SOLVING FOR VOLUME
V= (2.1 mol) (8.31 L*kPa/mol*K)(298.15 K)
2.5 kPa
V= 2,081.21 L
PROBLEM 3- SOLVING FOR MOLES
A gas tank has a volume of 130 L.
How many moles of gas are required
to fill the drum at 110kPa of
pressure and 27&ordm;C?
R= 8.31 L*kPa/mol*K
PROBLEM 3- SOLVING FOR MOLES
P= 110 kPa
V=130 L
n= ?
R= 8.31 L*kPa/mol*K
T= 27&ordm;C +273.15= 300.15K
PROBLEM 3- SOLVING FOR MOLES
PV= nRT
n= PV
RT
PROBLEM 3- SOLVING FOR MOLES
n=
(110 kPa) (130 L)
(8.31 L*kPa/ K*mol) ( 300.15 K)
n= 5.73 moles
PROBLEM 4- SOLVING FOR TEMPERATURE
A 5.0 L tank of carbon dioxide (CO2)
gas contains 7.0 mol of CO2 at 4.8
atm of pressure, what is the
temperature (in K) in the tank?
R= 0.0821 L*atm/mol*K
PROBLEM 4- SOLVING FOR TEMPERATURE
P= 4.8 atm
V= 5.0 L
n= 7.0 moles
R= 0.0821 L*atm/mol*K
T= ?
PROBLEM 4- SOLVING FOR TEMPERATURE
PV= nRT
T= PV
nR
PROBLEM 4- SOLVING FOR TEMPERATURE
T=
(4.8 atm) (5.0 L)
(0.0821 L*atm/ K*mol) (7.0 mol)
T= 41.76 K
```