Transcript The Gas Laws - Dallas School District

```The Gas Laws
Chapter 9
Kinetic Molecular Theory
1.
A gas is composed of small particles
(molecules) that are spaced widely apart.


2.
Compressible
Low density - about a 1000 times less dense
than a liquid
The molecules of a gas are in rapid, constant
motion


Pressure – the force of the molecules hitting
the side of a container
Fill a container (like a balloon) evenly.
Kinetic Molecular Theory
3.
All collisions are elastic

4.
Molecules don’t lose any energy when they
collide.
Gas molecules have little/no attractive force
on one another.


Too far apart
Mix thoroughly – unlike oil and water (too far
apart for polar/non-polar forces to matter)
Kinetic Molecular Theory
5.
The temperature of a gas is a measure of
average kinetic energy



Kinetic energy – energy in motion
KE = ½ mv2
Graham’s Law of Diffusion – the higher the
molar mass, the slower it moves
v1 =
v2
m2
m1
Graham’s Law Example
At the same temperature, how much faster does
an He atom move than an N2 molecule?
(Ans: 2.65 times faster)
Graham’s Law Example
Which is faster (and by how much): Cl2 or O2?
(Ans: O2 is about 1.5 times faster)
Which is faster and by how much: HCl or NH3?
Our Atmosphere
99% N2 and O2



78% N2
21% O2
1% CO2 and the Noble
Gases
80
Nitrogen
70
60
50
Oxygen
40
30
20
10
0
Gas
Carbon
dioxide
and
Noble
Gases
Pressure
Force
Area
 (Needles, High Heels, Snow shoes)
 Caused by the collisions of gases against a
container
 We live at about 1 atmosphere of pressure

Pressure =
Barometer




Torricelli (1643)
Height of column stayed
The higher the
elevation, the lower the
mercury
Weather


Rising pressure – calm
weather
Dropping pressure –
storm (fast moving air)
Units of Pressure
All of the following are equal:
760 mm Hg (760 torr)
 29.9 inches Hg (weather reporting)
 1 atmosphere (chemistry)
 101.3 kPa (kiloPascals, physics)

760 mm = 29.9 in = 1 atmosphere = 101.3 kPa
Converting Pressures
Examples:
1. Express 485 torr in atmospheres.
2. Convert 2.4 atmospheres to mm Hg
3. Convert 95.0 kPa to atmospheres and mm
Hg.
4. Convert 31.4 inches of mm to atmospheres.
The Ideal Gas Law
Combination of earlier work on gases.
 Works very well in situations close to Earth’s
pressures and temperatures
 Does not work for “extreme” situations
(Jupiter’s atmosphere is too cold and too
dense)

The Ideal Gas Law
PV = nRT
P = pressure in atmosphere
 V = volume in Liters
 n = number of moles
 T = Temperature in Kelvin
 R = gas constant

• R = 0.0821 L-atm / mol-K
The Ideal Gas Law
Examples:
1. What is the pressure of a 1.45 mol sample of
a gas in a 20.0 L container at 25oC?
2. What volume will 5.00 grams of H2 occupy at
10.0oC and 1 atmosphere of pressure?
3. How many grams of O2 are needed to
occupy a 500.0 mL aerosol can at 20.0oC
and 0.900 atmospheres?
STP
Standard Temperature & Pressure
Standard Temperature = 0oC (273 K)
 Standard Pressure = 1 atm
 1 mole of a gas occupies 22.4 L at STP

1 mole
22.4 L
or
22.4 L
1 mole
STP
Examples:
1. What volume will 0.180 moles of nitrogen
gas occupy at STP?
2. How many grams of chlorine (Cl2) gas are
present in 50.0 L at STP?
Comparing Two Situations
Sometimes we want to know what happens
when a gas is under different conditions
 Example: What happens to a basketball if you
pump it indoors, then take it out on a cold
day?

Comparing Two Situations
P1V1 = n1RT1
P2V2 = n2RT2
Solve both equations for R
R = P 1V 1
n1T1
R = P 2V 2
n2T2
P 1V 1 = P 2 V 2
n1T1
n2T2
Comparing Two Situations
See what you can cross out (what you are not
told)
 Remember to convert to Kelvin and moles if
needed.

Boyle’s Law
Boyle’s Law Apparatus Demo
 Boyle’s Law – The pressure and volume of a
gas are inversely related
 Bicycle pump example

Piston down – low volume, high pressure
 Piston up – high volume, low pressure

Boyle’s Law
Example:
1. The volume of a car’s cylinder is 475 mL at
1.05 atm. What is the volume when the
cylinder is compressed and the pressure is
5.65 atm?
P1V1 = P2V2
n1T1
n2T2
Boyle’s Law
Collapses to:
P 1V 1 = P 2 V 2
Boyle’s Law
Example:
2. A weather balloon has a volume of 40.0 liters
on the surface of the earth at 1.00 atm.
What will be the volume at 0.400 atm as it
rises?
P1V1 = P2V2
n1T1
n2T2
Charles Law

Charles Law – The temperature and volume of
a gas are directly related
“HOTTER = BIGGER”
 A gas increases in volume 1/273rd per degree
celsius
 Can be used to find absolute zero
 Temperature must be in Kelvin

Charles Law
1.
A basketball has a volume of 12.0 L when
blown up at 25.00 oC. What will be the
volume if it is taken outside on a day when it
is only 5.00 oC?
P 1V 1 = P 2 V 2
n1T1
n2T2
Charles Law
Collapses to:
V1
T1
= V2
T2
Charles Law
2. If a tire contains 30.0 L of air at 10.0 oC, what
volume will it occupy when it is driven and
warms up to 50.0 oC?
Guy-Lussac’s Law

Gay-Lussac’s Law = The temperature and
pressure of a gas are directly related.

1.
Temperature must be in Kelvin
Gas in a spray can has a pressure of 5.00
atm at 25.0 oC. What will be the pressure at
400.0 oC?
P 1V 1 = P 2 V 2
n1T1
n2T2

Avagadro’s Law = The volume of a gas is
directly proportional to the moles present

1.
“MORE = BIGGER”
A balloon has a volume of 1.00 L when 50.0
grams of N2 are in the balloon. What is the
volume if an additional 25.0 grams of N2 are
Putting it all together
Often you change more than one thing at a
time.
 Ex: In a car, volume, temperature, and
pressure may change.

1. The volume of 0.0400 mol of a gas is 500.0
mL at 1.00 atm and 20.0 oC. What is the
volume at 2.00 atm and 30.0oC?
Gases and Reaction
Stoichiometry
1.
What mass of Al is needed to produce 50.0 L
of H2 at STP?
2Al(s) + 6HCl(aq)  2AlCl3(aq) + 3H2(g)
(ANS: 40.2 g Al)
Gases and Reaction
Stoichiometry
2.
What volume of NO gas measured at 0.724
atm and 25oC will be produced from the
reaction of 19.5 g of O2?
4NH3(g) +
(Ans: 16.4 L)
5O2(g)  4NO(g) + 6H2O(l)
Gases and Reaction
Stoichiometry
3.
Car safety bags are inflated through the
decomposition of NaN3. How many grams of
NaN3 are needed to produce 36.0 L of N2 at
1.15 atm and 26.0oC?
2NaN3(s)  2Na(s) + 3N2(g)
(Ans: 72 g)
Gases and Reaction
Stoichiometry
4. How many liters of H2 and N2 at 1.00 atm and
15.0oC are needed to produce 150.0 grams of
NH3?
N2(g) + 3H2(g)  2NH3(g)
Dalton’s Law of Partial
Pressures
John Dalton – Dalton’s Atomic Theory
 Dalton’s Law – the total pressure of a gas is
equal to the sum of the partial pressures
 Ptot = PA + PB + PC + PD +…..
 Patm = PN2 + PO2 + Prest
 1 atm = 0.78atm + 0.21atm + 0.01atm

Dalton’s Law of Partial
Pressures
1. Three gases are mixed in a 5.00 L container.
In the container, there are 255 torr of Ar, 228
torr of N2, and 752 torr of H2. What is the total
pressure?
Dalton’s Law of Partial
Pressures
2.
On a humid day, the partial pressure of water
in the atmosphere is 18 torr.
a)
b)
If the total pressure is 766 torr, what are the
pressures of all of the other gases?
If the atmosphere is 78% N2 and 21% O2,
what are their pressures on this humid day?
Dalton’s Law of Partial
Pressures
3. What is the total pressure (in atm) exerted by
a mixture of 12.0 g of N2 and 12.0 g of O2 in
a 2.50 L container at 25.0oC?
8.
CH4 (16.0) Fastest
Ne (20)
CO (28.0)
Ar (39.9)
Cl2 (71.0)
ClO2 (87.0) Slowest
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