Transcript Let’s Learn the Gas Laws

Let’s Learn the
Gas Laws
Some definitions first…
Temperature
 Measure of the average kinetic energy of the particles
in a substance
 Kinetic energy – energy of motion
Volume
 The amount of space occupied by a sample or
substance
Pressure
 Force divided by area
 A “push”  what we will use
What is a gas?
 Gas – no definite shape or volume
 It will take shape of container it is contained in
 Gases have 3 properties we can measure:
 Temperature (T)
 Volume (V)
 Pressure (P)
If there is one constant, there is a relationship between the
other 2!
Now to Gas Laws…
Jacques Charles
1746 – 1823
Volume and Temperature
Charles Law
 The relationship between volume and
temperature
 Pressure is constant
Temperature vs. Volume Graph
30
25
15
10
5
0
– 273
Temperature (C)
100
Volume (mL)
20
Absolute Zero
 If a volume vs. temperature graph is plotted for gases,
most lines can be extrapolated downward so that
when volume is 0 the temperature is -273 C.
 Obviously naturally, gases don’t really reach a 0
volume, but the spaces between molecules approach 0.
 At this point all molecular movement stops.
 –273C is known as “absolute zero” (0 K)
 no KE- energy of motion
 Therefore we get the Kelvin scale…
Kelvin Scale
 Lord Kelvin suggested that a reasonable temperature
scale should start at a true zero value.
 He kept the convenient units of C, but started at absolute
zero.
 Therefore since at 0 volume, temperature is -273 C:
K = C + 273
 Practice: 62C = ? K
 From now on, we will be using Kelvin!!
Back to Charles's Law…
 Your data shows that…
• As T increases, V increases (↑T = ↑V )
• As T decreases, V decreases (↓T = ↓V)
 Therefore this is a direct relationship
But why is this
important??
My experience with a hot air balloon
 The balloon and basket were placed in a field.
 The burner was ignited and a huge fan blew the
heated air into the balloon on the ground.
 The balloon started to fill up and lift off of the
ground.
 When the balloon was
completely filled with hot
air where would it be??????
A balloon and liquid nitrogen
 http://www.youtube.com/watch?v=al5f9q845q0
 What is happening to the balloon?
 What is happening to the temperature? Volume?
Joseph Louis Gay-Lussac.
1778-1850
Pressure and Temperature
Pressure
Lets look at our data…
Temp
Gay-Lussac’s work
 Determined the relationship between temperature and
pressure of a gas.
 Measured the temperature of air at different pressures,
and observed a pattern of behavior which led to his
mathematical law.
 During his experiments volume of the system and amount of gas
were held constant.
 He found: ↑T = ↑P
↓T = ↓P
 Therefore this is a direct relationship.
What is pressure?
 The pressure of a gas is the push exerted on the wall
of the container a gas is trapped in.
 There are several units for pressure depending on
the instrument used to measure it including:




Atmosphere (atm)
Millimeters of mercury (mmHg)
Kilopascals (kPa)
Torr (torr)
 We will only be using atm and torr
Why is this important?
 Car tires… what happens to the pressure
inside the tire during the winter (when
it is cold)?
 As temperature decreases, pressure
decreases
 This is why we have to add air to the
tires during winter
Some practice problems…
 What is the relationship between T and P?
 Whose law is this?
 What is the relationship between T and V?
 Whose law is this?
Lets try some calculations
 Always set up:
P1 =
P2 =
T1 =
T2 =
** Remember temperature has to be in K and pressure in atm **
 You will have one unknown
 Write down the starting temperature or pressure…
 What is the relationship?
 If you want a bigger number
 If you want a smaller number
Lets try some calculations
 Always set up:
V1 =
V2 =
T1 =
T2 =
 You will have one unknown
 Write down the starting temperature or volume…
 What is the relationship?
 If you want a bigger number
 If you want a smaller number
Robert Boyle
1627 – 1631
Volume and Pressure
Lets look at our data…
Boyle’s Law
 Boyle’s law states that pressure and the volume of a
gas are inversely proportional.
 At constant temperature for a fixed mass.
 Therefore: ↑V = ↓ P
↓V = ↑ P
 Therefore this is a indirect relationship.
Why is this important?
 Let’s try making straw snap…
 Hold both ends and flick it…
 What happened?
 Now reduce the volume and
flick it…
 What happened?
Okay, but what else?
 Making the best water balloons…
 What happens if you keep filling the balloon?
 What is the best water balloon for a water balloon toss?
• Smaller – will not pop as easily
 What is the best water balloon to throw at someone?
• Larger – will pop very easily
Lets try some calculations
 Always set up:
V1 =
V2 =
P1 =
P2 =
** Remember pressure in atm **
 You will have one unknown
 Write down the starting volume or pressure…
 What is the relationship?
 If you want a bigger number
 If you want a smaller number
Gas Laws… Continued
The Combined Gas Law
Lets Review…
 Charles’ Law – volume and temperature
 Boyle’s Law – pressure and volume
Charles’ Law & Boyle’s Law
 Charles’ Law - Temperature and gas have a
direct relationship.
 T↑ V↑ and T↓ V↓
 Boyle’s Law - describes the indirect
relationship between the pressure and
volume of a gas.
 P↑ V↓ and P↓ V ↑
The Combined Gas Law
 The combined gas law is a gas
law which combines Charles‘ law
and Boyle's law.
 In the combined gas law, the
volume of gas is directly
proportional to the absolute
temperature and inversely
proportional to the pressure.
The Combined Gas Law
 Equation:
P1V1 = P2V2
T1
T2
 Where:
 P1 is the initial pressure  P2 is the final pressure
 V1 is the initial volume
 V2 is the final volume
 T1 is the initial
 T2 is the final
temperature (in Kelvin)
temperature (in Kelvin)
Let’s Practice…
 A gas takes up a volume of 17 liters, has a
pressure of 2.3 atm, and a temperature of 299 K. If
I raise the temperature to 350 K and lower the
pressure to 1.5 atm, what is the new volume of the
gas?
P1 =
P2 =
V1 =
V2 =
T1 =
T2 =
Ideal Gas Law
STP
 Standard Temperature and Pressure
 l T = 273K
 l P = 1 atm, 101.3 kPa, 760 mmHg, 760 torr
Ideal Gas
 An Ideal Gas (perfect gas) is one which obeys the
ideal gas law exactly.
Ideal Gas
 An Ideal Gas is modeled on the Kinetic Theory of
Gases which has 4 basic postulates:
 Gases consist of small particles (molecules) which are
in continuous random motion
 The volume of the molecules present is negligible
compared to the total volume occupied by the gas
 Intermolecular forces are negligible
 Pressure is due to the gas molecules colliding with the
walls of the container
Real Gases
 Real Gases deviate from Ideal Gas Behavior
because:
 at low temperatures the gas molecules have less kinetic
energy (move around less) so they do attract each other
 at high pressures the gas molecules are forced closer
together so that the volume of the gas molecules
becomes significant compared to the volume the gas
occupies
 Under ordinary conditions, deviations from Ideal
Gas behavior are so slight that they can be neglected
 A gas which deviates from Ideal Gas behavior is
called a non-ideal gas.
Ideal Gas Laws
 The ideal gas law is a combination of all the gas laws:
Boyle’s, Charles’, Gay-Lussac’s
 The ideal gas law can be expressed as
PV = nRT
 Where:
 P is the pressure in atm
 V is the volume in liters
 n is the number of moles
 R is a constant (0.0821 L atm /mol K)
 T is the temperature in Kelvin
• How do you calculate Kelvin?
Lets Practice…
Number 1 on Homework worksheet
 If I have 4 moles of a gas at a pressure of 5.6 atm
and a volume of 12 liters, what is the temperature?
P=
n=
V=
R=
T=
PV = nRT