2. 2
No one is credited for the Combined Gas
Law. Putting together Boyle’s, Charles’ and
Gay- Lussac’s together will result to this
statement:
The pressure and volume of a gas are
inversely proportional to each other but are
both directly proportional to the
temperature of the gas.
3. 3
Translating it to mathematical equation will give us the
following:
T= VP/k or V= kT/P or P= kT/ V or k= PV/T
The constant k in the equation above is known as the universal
gas constant. It is the result of the combination of the
proportionality constants in the three gas laws.
Note that the formula is equal to a constant, thus, it is possible
to compute for the change in volume, temperature or pressure
using the following proportion:
P1V1/T1 = P2V2/T2
4. 4
If P2 is unknown then P2 = P1V1T2/ V2T1
If V2 is unknown then V2 = P1V1T2/ P2T1
If T2 is the unknown then T2 = P2V2T1/P1V1
Let’s use the Combined Gas law in
determining change in the final volume,
temperature or pressure of gases
5. 5
Sample problem:
The oxygen tank manufacturer used to
produce 5.00 L oxygen tank at 2000. psi
and 25 oC. Statistics suggests that the 3.00 L
oxygen tank at 1500. psi is more
marketable. What temperature
requirement is needed to produce a 3.00 L
oxygen tank at 1500. psi?
7. 7
Solving for T2
T2= P2V2T1/P1V1
T2= (298K)(1500.psi)(3.00L)
(2000.psi)95.00L)
T2= 134 K
8. 8
Try it!
The volume of a gas at 27 oC and
700.0 mmHg is 600.0 mL. What is the
volume of the gas at -20.0 oC and
500.0 mmHg?
9. 9
Avogadro’s Law
Do you still remember the mole
concept? Can you still recall what
a mole is?
The number of moles quantifies
the amount of a substance.
10. 10
What could be the possible
relationship of the amount of gas in
a mole to its volume?
In 1811, Amedeo Avogadro wrote in
a paper that, “ Equal volumes of all
gases , kept at the same
temperature and pressure, contain
the same number of molecules.
11. 11
Using the proportionality symbol,
we can express the proportionality
between the volume and the number
of moles of a gas as:
V ∞ n at constant T and P
Mathematically, it can be expressed
as:
V/n = k
12. 12
Where V= volume of the gas
n= amount of gas in moles
k=proportionalityconstant
This can also be expressed as
V1/n1= V2/n2 or V1n2= V2n1
13. 13
Sample Problems:
1. A balloon containing 2.00 moles
of He has a volume of 880. mL.
What is the new volume
after 4.00 moles of He are added to
the balloon at the same
temperature and pressure?
16. 16
Ideal Gas Law
Let’s recall the three gas laws:
Boyle’s Law
Charles’Law
Avogadro’s Law
Combining the three laws, you will
get:
17. 17
V ∞ nT/ P
Using the sign of equality will result to this
equation:
V= RnT/P or PV= nRT
Where:
V= volume in liters
P= pressure in atmosphere
n= mole
T= temperature in Kelvin
R=universal gas constant = 0.0821 L .atm/ mol.k
18. 18
Sample Problem:
1. What is the volume of the container that can
hold 0.50 mole of gas at 25.0 oC and 1.25 atm?
Try this:
A 2.0g sample of dry ice (solid Carbon dioxide) is
placed in an evacuated 3.5L vessel at 30oC.
Compute for the pressure inside the vessel after all
the dry ice has been converted to carbon dioxide
gas. (2 significant figures)
19. 19
PERFORMANCE TASK #1
Solve the following problems
1. A chemist collected 56.1cm3 of gas in an open
manometer. The next day, the chemist noted that the
volume had changed to 57.9 cm3 and the barometer
reading was 99.4 kPa. The temp. had not changed. What
had been the barometer reading on the previous day
when the gas was collected?
2. A 1.00 L balloon is filled with He at 1.20 atm. If the
balloon is squeezed into a 0.500 L beaker and doesn’t
burst, what is the pressure of the Helium?
20. 20
3. A balloon has a volume of 2500.0 mL on a day
when the temperature is 30.0 OC. If the
temperature at night falls to 10.0 OC, what will be
the volume of the balloon if the pressure remains
constant?
4. An 800.0 mL sample of nitrogen is warmed from
77OF to 86OF. What is its new volume if the
pressure remains constant?
21. 21
5. A sample of helium gas has a pressure of
1.20 atm. At 22.0oC. At what Celsius
temperature will the helium reach a pressure
of 2.00 atm., assuming constant volume?
6. A gas balloon has a volume of 96.0 L when
the temperature is 35oC and the pressure is
0.974 atm. What will be its volume at 21oC and
1.08 atmospheres? (3 significant figures)
22. 22
7. A sample of 0.500 moles NH3 gas had a volume of 235
mL. The temperature and pressure were held constant,
and some NH3 was removed from the sample; its new
volume was 175 mL. How many grams of NH3 were
removed? (3 significant figures)
8. How many Ammonia (NH3) molecules are in 2.00 kg of
NH3 gas at STP? (3 significant figures)
23. 23
9. The density of an unknown gas is
1.429 g/L at STP. Calculate its molecular
mass.(2 Significant Figure)
10. Calculate the density of air at 22.0oC
and 745 mmHg if its molecular mass is
29.0 g/mole. (2 Significant Figure)
