A student is working with a sample of nitrogen
gas. The gas is contained in a cylinder with a
volume of 5.0 liters, and is under a pressure of
3.5 atmospheres. The student carefully
transfers the gas sample into a 7.0 liter
container. What will the pressure on the gas
be in its new container? What law governs
this?
2.5 atm
Boyles’ Law
Announcements
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Six-Week’s Assignment List
Date Issued
Date Due
WS - The Kinetic Molecular
Theory and Nature of Gases
2/24
3/3
Quiz – Pressure Unit Conversions
3/3
3/3
WS – The Gas Laws
3/3
3/10
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The Gas Laws
The Gas Laws
• Boyle’s Law
pressure – volume relationships
• Charles’s Law
volume - temperature relationships
• Gay-Lussac’s Law
pressure – temperature relationships
• The Combined Gas Law
volume – temperature – pressure changes
• Dalton’s Law of Partial Pressures
partial pressures and total pressures
Charles’ Law
• Volume - Temperature relationships
• The relationship between volume and
temperature was discovered by the
French scientist Jacques Charles in
1787.
• Charles’s experiments showed that all
gases expand to the same extent when
heated through the same temperature
interval.
Charles’ Law
• Charles found that the volume changes
by 1/273 of the original volume for
each Celsius degree, at constant
pressure and an initial temperature of
0°C.
– Ex) Raising the temperature to 1°C causes the gas volume to
increase by 1/273 of the volume it had at 0°C.
– A 10°C temperature increase causes the volume to expand by
10/273 of the original volume at 0°C.
– If the temperature is increased by 273°C, the volume
increases by 273/273 of the original, that is, the volume
doubles.
Charles’ Law
• The same regularity of volume
change occurs if a gas is cooled
at constant pressure.
– At 0°C, a 1°C decrease in temperature
decreases the original volume by 1/273.
– At this rate of volume decrease, a gas cooled
from 0°C to -273°C would be decreased by
273/273.
– In other words, it would have zero volume,
which is not actually possible.
Charles’ Law
• In fact, real gases cannot be cooled to
273°C - before they reach that
temperature, intermolecular forces exceed
the kinetic energy of the molecules, and
the gases condense to form liquids or
solids.
• The Kelvin temperature scale is a scale that
starts at a temperature corresponding to 273.15°C.
• That temperature is the lowest one
possible.
Charles’ Law
• The temperature -273.15°C is referred to as absolute
zero and is given a value of zero in the Kelvin scale.
• This fact gives the following relationship between the
two temperature scales:
K = °C + 273
For calculations in this book, 273.15 is rounded off to 273.
• The average kinetic energy of gas molecules is more
closely related to the Kelvin temperature.
Charles’ Law
• Gas volume and Kelvin temperature
are directly proportional to each
other.
– Ex) Quadrupling the Kelvin temperature causes the volume of
a gas to quadruple
– Reducing the Kelvin temperature by half causes the volume of
a gas to decrease by half.
• The relationship between Kelvin
temperature and gas volume is known
as Charles’s law.
Charles’ Law
• Charles’s law states that the volume of a
fixed mass of gas at constant pressure
varies directly with the Kelvin temperature.
• Charles’s law may be expressed as follows.
V = kT or V/T = k
– The value of T is the Kelvin temperature
– k is a constant - the value of k depends only
on the quantity of gas and the pressure.
– The ratio V/T for any set of volumetemperature values always equals the same k.
Charles’ Law
• The form of Charles’s law that can
be applied directly to most
volume-temperature problems
involving gases is as follows.
V1/T1 = V2/T2
– V1 and T1 represent initial conditions.
– V2 and T2 represent a new set of conditions.
– When three of the four values V1, T1, V2 , and T2 are known,
this equation can be used to calculate the fourth value.
Charles’ Law
Sample Problem
• A sample of neon gas occupies a volume of 752 mL at 25°C.
What volume will the gas occupy at 50°C if the pressure remains
constant?
• Unknown is V2 of Ne in mL
V1/T1 = V2/T2
V2 = V1T2/T1
V2 = (752 mL Ne)(323K)/298K
V2 = 815 mL Ne
Gay-Lussac’s Law
• Pressure - Temperature relationships
• For a fixed quantity of gas at constant
volume, the pressure is directly
proportional to the Kelvin temperature,
which depends directly on average kinetic
energy.
• For every kelvin of temperature change,
the pressure of a confined gas changes by
1/273 of the pressure at 0°C.
Gay-Lussac’s Law
• Joseph Gay-Lussac is given credit for
recognizing this in 1802.
• Gay-Lussac’s law: The pressure of a fixed
mass of gas at constant volume varies
directly with the Kelvin temperature.
P = kT, or P/T = k
– The value of T is the temperature in kelvins
– k is a constant that depends on the quantity
of gas and the volume.
Gay-Lussac’s Law
• For a given mass of gas at constant
volume, the ratio P/T is the same for any
set of pressure-temperature values.
• Unknown values can be found using this
form of Gay-Lussac’s law:
P1/T1 = P2/T2
• When values are known for three of the
four quantities, the fourth value can be
calculated.
Gay-Lussac’s Law
Sample Problem
• The gas in an aerosol can is at a pressure of 3.00 atm at 25°C.
Directions on the can warn the user not to keep the can in a
place where the temperature exceeds 52°C. What would the gas
pressure in the can be at 52°C?
• Unknown is P2 of gas in atm.
P1/T1 = P2/T2
P2 = P1T2/T1
P2 = (3.00 atm)(325K)/298K
P2 = 3.27 atm