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2015/08/20

Gases

Characteristics of Gases
• Unlike liquids and solids, they:
–Expand to fill their containers
–Are highly compressible
–Have extremely low densities
–“have large spaces between the gas molecules”
–Mix easily! (diffuse into one another)
Homogenous mixtures!

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Pressure

• Pressure is the amount of force
applied to an area
...


Example Using

𝑃=

𝐹
𝐴

• A gas exerts a force of 1000 N over an area of 25 m 2, what is the pressure of the gas?
Solution:

𝑃=

𝐹 1000
=
= 40 𝐍𝐦−2
𝐴
25

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Units of Pressure

• Pascals
–

1 Pa = 1 Nm-2

• Bar
–

1 bar = 105 Pa = 100 kPa

• mm Hg or torr
– The difference in the heights in mm (h) of two connected columns of mercury

• Atmosphere
– 1
...


How will gas
pressure
change the
height?

Figure 9
...

Can use the height of Hg directly
Pgas = 760 mmHg + (136
...
8)
Pgas = 760 mmHg + (32
...
6 mmHg

Convert to
kPa, atm, Nm-2

Ans:
1
...
7 kPa,
1
...

• It is equal to:

–1
...
325 kPa

What if?
• What is the height of a column of water that exerts the same pressure as a column
of mercury 76
...

Robert Boyle
British Chemist
1627-1691

As P and V are inversely proportional

A plot of V versus P results in a curve
...


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Charles’s Law

• The volume of a fixed amount of gas at
constant pressure is directly proportional to
its absolute temperature
...


Avogadro’s Law
Joseph Louis Gay-Lussac
(1778-1823)
Law of combining volumes (~1808

• The volume of a gas at constant temperature and pressure is directly
proportional to the number of moles of the gas
...
e
...
314 kPa L/mol K)

Units (1m3 Pa =1J)

P

R = 8
...
3145 J mol-1 K-1

kg m
s2

kg m
2
Pa  s
m2
kgm
1

2
s
m2
 1s  2
Pa  kg m
Pa 

m3 Pa  kg m 2 s  2  1J

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Examples Using PV = nRT
What is the pressure, in kPa, exerted by
1
...
21 mol of a gas occupy at 44 °C and 106 kPa,
• What volume will 5
...
314

kPa L/mol K

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About PV = nRT
• STP
– Defined as 100 kPa and 273
...
00 𝑚𝑜𝑙 × 8
...
15𝐾
=
𝑃
100 𝑘𝑃𝑎
Molar Volume (Vm) = 22
...
2g) was initially at 4
...
The gas was
compressed from 8
...
00 L at a constant temperature
...
0 dm3 at sea level (101
...
6 kPa
...
Calculate the volume of the
balloon at its final altitude
...
𝟑𝟖𝟕𝒅𝒎 𝟑

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Gas Densities and Molar Mass

If we divide both sides of the ideal-gas equation by
V and by RT, we get:

n
V

P
= RT

Gas Densities and Molar Mass

• We know that

–moles  molar mass = mass

n=m
• So multiplying both sides by the molar mass ( ) gives:

m
P
V = RT

i
...
 =

P
RT

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Molecular Mass

We can manipulate the density equation to enable us to find the
molar mass of a gas:

=

P
RT

Becomes

=

RT
P

Molecular Mass Examples

• Propylene is used in the production of plastics
...
1305 g when clean, dry and evacuated; it weighs
138
...
9970 g/mL) and 40
...
3 mmHg and 24
...
What is the molar mass of propylene?

𝟒𝟐
...
g
...
5 g of NaN3
decomposes at 1
...
5 °C??

117
...


• In other words,

Ptotal = P1 + P2 + P3 + …

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Partial Pressures and Mole Fraction
Since P1 = n1RT/V

Then

P1 = n1RT/V
P2 = n2RT/V
n1
=

n2

= X (mole fraction)

𝑃1 = 𝜒1 𝑃 𝑇

Partial Pressures and Mole Fraction

Figure 9
...

• To find only the pressure of the desired gas, one must subtract the
vapour pressure of water from the total pressure
...
5 g He, 9
...
00 g Ar in a 45
...
8 °C?

Gas
He
N2
Ar

Partial
Pressure
(kPa)
169
...
93
17
...
Gases consist of large numbers of molecules that are in continuous,
random motion
...
The combined volume of all the molecules of the gas is negligible
relative to the total volume in which the gas is contained
...
Attractive and repulsive forces between gas molecules are
negligible
...
Energy can be transferred between molecules during
collisions, but the average kinetic energy of the molecules
does not change with time, as long as the temperature of the
gas remains constant
...
The average kinetic energy of the molecules is proportional to
the absolute temperature
...
g
...
E
...

–R = 8
...
𝟏𝟓 × 𝟏𝟎 𝟐 𝐦/𝐬

𝟑𝐑𝐓
𝐌

𝐎 𝟐 = 𝟒
...

Diffusion
The spread of one substance throughout a
space or throughout a second substance
...
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Grahams Law of Effusion

𝐫𝟏
=
𝐫𝟐

𝐌𝟐
𝐌𝟏

r = rate of effusion
M = Molar Mass

Real Gases

In the real world, the behaviour of gases
only conforms to the ideal-gas equation at
relatively high temperature and low
pressure
...
21

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Deviations from Ideal Behaviour

Figure 9
...
23

The assumptions made in the kinetic-molecular
model break down at high pressure and/or low
temperature
...


• The corrected ideal-gas equation is known as the van der Waals equation

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