Gas Laws
Gases-Review
Remember:
- according to the kinetic theory, all matter is composed of particles in
constant motion, and pressure is caused by the force of gas particles
striking the walls of their container.
- the more often gas particles collide with the walls of their container,
the greater the pressure.
- the pressure is directly proportional to the number of particles.
- at higher temperatures, the particles in a gas have greater kinetic
energy, causing them to collide with the walls of the container more
often and with greater force, so the pressure rises.
- standard atmosphere (atm) is defined as the pressure that supports a
760-mm column of mercury.
- the SI unit for measuring pressure is the pascal (Pa), named after the
French physicist Blaise Pascal (1623-1662).
Kinetic-Molecular Theory Review
The gas laws apply to ideal gases, which are described by the
kinetic theory in the following five statements.
-Gas particles do not attract or repel each other.
-Gas particles are much smaller than the spaces between them.
-Gas particles are in constant, random motion.
-No kinetic energy is lost when gas particles collide with each
other or with the walls of their container.
-All gases have the same kinetic energy at a given temperature.
Boyle’s Law-Pressure & Volume
Robert Boyle (1627-1691), an English scientist,
used a simple apparatus to compress gases at
constant temperatures, he had four findings:
1. If the pressure of a gas increases, its
volume decreases proportionately.
2. If the pressure of a gas decreases, its
volume increases proportionately.
3. If the volume of a gas increases, its pressure decreases
proportionately.
4. If the volume of a gas decreases, its pressure increases
proportionately.
Boyle’s Law
By using inverse proportions, all four findings can be
included in one statement called Boyle’s law.
-At constant temperature, the pressure exerted by a gas
depends on the frequency of collisions between gas
particles and the container.
-If the same number of particles is squeezed into a smaller
space, the frequency of collisions increases, thereby
increasing the pressure.
-Thus, Boyle’s law states that at constant temperature, the
pressure and volume of a gas are inversely related.
Applying Boyle’s Law
A sample of compressed methane has a volume of 648 mL at
a pressure of 503 kPa. To what pressure would the
methane have to be compressed in order to have a volume
of 216 mL?
Step 1: Examine the Boyle’s law equation.
-You need to find P2, the new pressure, so solve the
equation for P2.
Step 2: Substitute known values and solve.
Boyle’s Law Practice (p 422 #1-4)
1. The volume of a gas at 99.0kPa is 300.0mL. If the pressure is
increased to 188kPa, what will the new volume be?
2. The pressure of a sample of helium in an 1.00L container is
0.988atm. What is the new pressure of the sample is placed in
a 2.00L container?
3. Air trapped in a cylinder fitted with a piston occupies 145.7mL
at 1.08atm pressure. What is the new volume of air when the
pressure is increased to 1.43atm by applying force to the
piston?
4. If it takes 0.0500L of oxygen gas kept in a cylinder under
pressure to fill an evacuated 4.00L reaction vessel in which the
pressure is 0.980atm, what was the initial pressure of the gas?
Charles’s Law
• When the temperature of a sample of gas is
increased and the volume is free to change, the
pressure of the gas does not increase. Instead, the
volume of the gas increases in proportion to the
increase in Kelvin temperature. This observation is
Charles’s law, which can be stated mathematically
as follows.
Applying Charles’s Law
A weather balloon contains 5.30 kL of helium gas when the
temperature is 12°C. At what temperature will the balloon’s
volume have increased to 6.00 kL?
Step 1: convert the given temperature to Kelvin.
Step 2: solve the Charles’s law equation
for the new temperature, T2.
Applying Charles’s Law
A weather balloon contains 5.30 kL of helium gas when the
temperature is 12°C. At what temperature will the balloon’s
volume have increased to 6.00 kL?
Step 3: substitute the known values and compute the result
Step 4: convert the Kelvin temperature back to Celsius.
New Temperature = 323 – 273 = 50oC
Charles’s Law Practice (p 425 #6-8)
6. A gas at 89⁰C occupies a volume of 0.67L. At what Celsius
temperature will the volume increase to 1.12L?
7. The Celsius temperature of a 3.00L sample of gas is lowered
from 80.0⁰C to 30.0⁰C. What will the resulting volume be?
8. What is the volume of the air in a balloon that occupies 0.620L
at 25.0⁰C if the temperature is lowered to 0.00⁰C?
Gay-Lussac’s Law
Boyle’s Law relates pressure and volume of a gas.
Charles’s Law relates a gas’s temperature and volume.
Gay-Lussac’s Law relates a gas’s temperature and pressure.
Gay-Lussac’s Law states that the pressure of a given mass of gas
varies directly with the Kelvin temperature when the volume
remains constant.
P1 = P2
T1
T2
Applying Gay-Lussac’s Law
The pressure of a gas in a tank is 3.20atm at 22.0⁰C. If the
temperature rises to 60.0⁰C, what will the be gas pressure in the
tank?
Step 1: obtain the temperatures in Kelvin
TK = 273 + TC = 273 + 22.0 = 295K
TK = 273 + TC = 273 + 60.0 = 333K
Step 2: solve the Charles’s law equation for the new pressure, P2.
P1 = P2
T1
T2
P2 = P1 T2
T1
Applying Gay-Lussac’s Law
The pressure of a gas in a tank is 3.20atm at 22.0⁰C. If the
temperature rises to 60.0⁰C, what will the be gas pressure in the
tank?
Step 3: substitute the known values into the equations and solve
P2 = P1 T2 = (3.20atm)(333K)
T1
295K
= 3.61atm
Gay-Lussac’s Law Practice (p 427 #9-12)
9. A gas in a sealed container has a pressure of 125kPa at a
temperature of 30.0⁰C. If the pressure in the container is
increased to 201kPa, what is the new temperature?
10. The pressure in an automobile tire is 1.88atm at 25.0⁰C. What
will be the pressure if the temperature warms up to 37.0⁰C?
11. Helium gas in a 2.00L cylinder is under 1.12atm of pressure. At
36.5⁰C, that same gas sample has a pressure of 2.56atm. What
was the initial temperature of the gas in the cylinder?
12. If a gas sample has a pressure of 30.7kPa at 0.00 ⁰ C, by how
much does the temperature have to decrease to lower the
pressure to 28.4kPa?
Gas Laws Review
1. Explain why gases such as the oxygen found in tanks used at
hospitals are compressed. Why must care be taken to prevent
compressed gases from reaching a high temperature?
2. A weather balloon of known initial volume is released. The air
pressures at its initial and final altitudes are known. Why can’t
you find it’s new volume by using these known variables and
Boyle’s Law?
3. Determine which gas law you would use to calculate the
following problem, then solve it:
A gas at 20.0 ⁰ C occupies 1.00L. Assuming the pressure stays
the same, what volume will it occupy at 30.0⁰C?
4. Why are baking instructions different at high altitudes than at
low altitudes?
The Combined Gas Law
The gas laws may be combined into a single
law, called the combined gas law, that
relates two sets of conditions of pressure,
volume, and temperature by the following
equation:
Applying the Combined Gas Law
A sample of nitrogen monoxide has a volume of 72.6 mL at a
temperature of 16.0°C and a pressure of 104.1 kPa. What
volume will the sample occupy at 24.0°C and 99.3 kPa?
Step 1: convert temperatures to Kelvin
Applying the Combined Gas Law
Step 2: Substitute the known quantities and compute V2.
Combined Gas Laws Practice (p 430 # 19-21)
19. A helium-filled balloon at sea level has a volume of 2.1L at
0.998atm and 36⁰C. If it is released and rises to an elevation
at which the pressure is 0.900atm and the temperature is
28⁰C, what will be the new volume of the balloon?
20. At 0.00⁰C and 1.00atm pressure, a sample of gas occupies
30.0mL. If the temperature is increased to 30.0⁰C and the
entire gas sample is transferred to a 20.0mL container, what
will be the gas pressure inside the container?
21. A sample of air in a syringe exerts a pressure of 1.02atm at a
temperature of 22.0⁰C. The syringe is placed in a boiling
water bath at 100.0⁰C. The pressure of the air is increased to
1.23atm by pushing the plunger in, which reduces the volume
to 0.224mL. What was the original volume of air?
Avogadro’s Principle
In the early nineteenth century, Avogadro proposed the idea that
equal volumes of all gases at the same conditions of
temperature and pressure contain the same number of
particles.
An extension of Avogadro’s principle is that one mole (6.02 x 1023
particles) of any gas at standard temperature and pressure (0°C
and 1.00 atm pressure, STP) occupies a volume of 22.4 L.
22.4L/1mol or 1 mol/22.4L
-allows you to interrelate mass, moles, pressure, volume, and
temperature for any sample of gas.
Applying Avogadro’s Principle
What is the volume of 7.17 g of neon gas at 24°C and 1.05
atm?
Step 1: convert mass of neon to moles
If given moles, skip step 1 and go to step 2
Step 2: determine the volume at STP of 0.355 mol Ne.
If you needed volume at STP, you could stop here.
Applying Avogadro’s Principle
What is the volume of 7.17 g of neon gas at 24°C and 1.05
atm?
Step 3: use the combined gas law equation to determine the
volume of the neon at 24°C and 1.05 atm pressure.
Avogadro’s Principle Practice
(p 432 # 24-25;433 # 29-32)
24. Determine the volume of a container that holds 2.4 mol of gas
at STP.
25. What size container do you need to hold 0.0459 mol of
nitrogen gas at STP?
29. How many grams of carbon dioxide gas are in a 1.0L balloon at
STP?
30. What volume in milliliters will 0.00922 g hydrogen gas occupy
at STP?
31. What volume will 0.416 g of krypton gas occupy at STP?
The Ideal Gas Law
The pressure, volume, temperature, and number of moles of gas
can be related in a simpler, more convenient way by using the
ideal gas law.
The following is the law’s mathematical expression,
where n represents the number of moles.
PV = nRT
The ideal gas constant, R, already contains the molar volume of a
gas at STP along with the STP conditions.
-value of R depends on the units in which
the pressure of the gas is measured
-These values are all equivalent. Use
the one that matches the pressure units
you are using.
Applying the Ideal Gas Law
What pressure in atmospheres will 18.6 mol of methane exert
when it is compressed in a 12.00-L tank at a temperature of
45°C?
Step 1: change the temperature to kelvin
Step 2: Substitute the known quantities and calculate P
PV = nRT
Ideal Gas Law Practice
(p 437 #41-44)
41. If the pressure exerted by a gas at 25⁰C in a volume of 0.044L is
3.81atm, how many moles of gas are present?
42. Determine the Celsius temperature of 2.49mol of gas
contained in a 1.00L vessel at a pressure of 143kPa.
43. Calculate the volume that a 0.323 mol sample of a gas will
occupy at 265K and a pressure of 0.900atm.
44. What is the pressure in atmospheres of a 0.108mol sample of
helium gas at a temperature of 20.0⁰C if its volume is 0.505L?
Gas Stoichiometry
Ammonium sulfate can be prepared by a reaction between
ammonia gas and sulfuric acid as follows.
What volume of NH3 gas, measured at 78°C and a pressure of 1.66
atm, will be needed to produce 5.00 x 103 g of (NH4)2SO4?
Step 1: compute number of moles represented by 5.00 x 103 g of
(NH4)2SO4.
-molar mass of (NH4)2SO4 = 132.14 g/mol
Gas Stoichiometry
What volume of NH3 gas, measured at 78°C and a pressure of 1.66
atm, will be needed to produce 5.00 x 103 g of (NH4)2SO4?
Step 2: determine the number of moles of NH3 that must react
to produce 37.84 mol (NH4)2SO4.
Step 3: use the ideal gas law equation to calculate the
volume of 75.68 mol NH3 under the stated conditions.