TEMA PARA LA MATERIA DE QUÍMICA...t/t

1. Principles of Chemistry I
GASES
QBA Miguel A. Castro Ramírez

2. CHARACTERISTICS OF GASES
The Distinction of Gases from Liquids and Solids
• Expand to fill their containers
• Are highly compressible
• Have relatively low densities under normal condition- (g/L) :
When a gas is cooled, its density increases because its volume is decreases.
• Gas volume changes greatly with pressure
• Gas volume changes greatly with temperature
• Gases have relatively low viscosity– flow much more freely
• Gases are miscible – Form homogenous mixtures with each other
regardless of the identities or relative proportions of the component
gases.

3. CHARACTERISTICS OF GASES
The Distinction of Gases from Liquids and Solids
The chemical behavior of a gas depends on its
composition, while all gases have very similar physical
behavior. This is because the individual molecules are
relatively far apart. Thus, each molecule behaves largely as
though the others were not present.
For instance, although the particular gases differ, the same
physical behaviors are at work in the operation of a car
and in the baking of bread.

4. PRESSURE
• Pressure conveys the idea of a force, a push that tends to
move something in a given direction. Pressure (P) is in fact, the
force (F) that acts on a given area (A).
F
P=
A
• Atmospheric pressure is the weight of air per unit of area
• The pressure on the outside of the body is equalized by the
pressure on the inside.

5. PRESSURE
Effect of atmospheric pressure on object at Earth surface
• The pressure on the outside of the body is equalized by the
pressure on the inside.

6. PRESSURE
• Standard atmospheric pressure which correspond to the
typical pressure at sea level, is the pressure sufficient to support
a column of mercury 760mm high.
1 atm = 760 mm Hg = 760 torr = 1.01325 x 105 Pa = 101.325 kPa
• Must able to convert between one and another
• Manometer: Devices used to measure the pressure of a gas in
experiment.

7. PRESSURE
closed-end
• A) equal pressure
• B) Insert gas, it pushes the
mercury , so the mercury
level rises.
• The different in height =
the gas pressure
open-end

8. PRESSURE
Converting Units
EXAMPLE:
A geochemist heats a limestone (CaCO3) sample and collects
the CO2 released in an evacuated flask attached to a closed-
end manometer. After the system comes to room
temperature, Dh = 291.4 mm Hg. Calculate the CO2 pressure
in torrs, atmospheres, and kilopascals.

9. THE GAS LAW
The Pressure-Volume Relationship: Boyle’s Law
• Boyle’s law: The volume of a fixed quantity of gas maintained
at constant temperature is inversely proportional to the pressure.
• The total pressure applied to
the trapped air was the pressure
of the atmosphere (measured by
barometer) plus that of height
mercury column.
• By adding mercury, the air
volume decreased (T and amount of
air is constant)

10. THE GAS LAW
• The result as shown in the graph.
• When the pressure gets larger, the
volume of the gas become lower.
• So, it is inversely proportional.
1
• V P
α
• This relationship also, can be
expressed as
PV = constant (k) or
V = k (1/P)
• This means a plot of V versus 1/P
will be a straight line.

11. THE GAS LAW
The Temperature-Volume
Relationship: Charles’s Law
• Charles found that the volume of a
fixed quantity of gas at constant
pressure increases linearly with
temperature.
• V α T
So, V = constant(k) x T
or
V
T =k

12. THE GAS LAW
• Extrapolated of the graph: passes though – 273 °C (0 K).
• Gas predicted to have 0 volume at this temperature.
• However, absolute zero never reached because no matter can
have zero volume.
• Gas will liquefy before reached this temperature.
• Charles Law: The volume of a fixed amount of gas maintained at
constant pressure is directly proportional to its absolute (Kelvin)
temperature.

13. THE GAS LAW
Other Relationship Based on Boyle’s and Charles
Law
Amontons’s V and n are fixed
P α T
Law
P
= constant P = constant x T
T
Combined gas T
law V V = constant x T/P
P
α
PV = constant
T

14. THE GAS LAW
The Quantity – Volume Relationship: Avogadro’s Law
• Different mol of gas will occupy different volume.
• Double up the quantity (mol) of gas will double up the volume
occupied by the particular gas. (refer B)

15. THE GAS LAW

16. THE IDEAL-GAS EQUATION
• So far we’ve seen that
V ∝ 1/P (Boyle’s law)
V ∝ T (Charles’s law)
V ∝ n (Avogadro’s law)
• Combining these, we get
V ∝ nT nRT
P PV = nRT or V = P
R = gas constant
© 2009, Prentice-Hall, Inc.

17. THE IDEAL-GAS EQUATION
PV = nRT or V = nRT
P
fixed n and T fixed n and P fixed P and T
Boyle’s Law Charles’s Law Avogadro’s Law
V = constant V = constant X T V = constant X n
P
Temperature: Absolute Temperature (K)
Quantity of Gas: moles
Pressure: atm
Volume: Liters

18. THE IDEAL-GAS EQUATION
• The value and unit for R are depend on the units of P,V,n and T.
• In working problems with the ideal-gas equation, the units of
P,V,n & T must agree with the units in gas constant.
• We often use: R = 0.08206 L-atm/mol-K or 0.0821 L-atm/mol-K
• Use the value R = 8.314 J/mol-K consistent with the unit Pa for
pressure is also very common.

19. THE IDEAL-GAS EQUATION
Applying the Volume-Pressure Relationship
EXAMPLE
Boyle’s apprentice finds that the air trapped in a J tube
occupies 24.8 cm3 at 1.12 atm. By adding mercury to the
tube, he increases the pressure on the trapped air to
2.64 atm. Assuming constant temperature, what is the
new volume of air (in L)?

20. THE IDEAL-GAS EQUATION
Applying the Pressure-Temperature Relationship
EXAMPLE
A steel tank used for fuel delivery is fitted with a safety valve
that opens when the internal pressure exceeds 1.00x103 torr.
It is filled with methane at 230C and 0.991 atm and placed in
boiling water at exactly 1000C. Will the safety valve open?

21. THE IDEAL-GAS EQUATION
Solving for an Unknown Gas Variable at Fixed
Conditions
EXAMPLE
A steel tank has a volume of 438 L and is filled with 0.885 kg of
O2. Calculate the pressure of O2 at 21oC.

22. FURTHER APPLICATION OF THE IDEAL-GAS
EQUATION
Gas Densities and Molar Mass
• The ideal-gas equation allows us to calculate gas density
from molar mass, pressure and temperature of the gas.
• Density = mass/volume (m/V)
• Rearrange the gas equation to obtain similar units: moles per
unit volume, (n/V): n P
= RT n P x M( molar
V V = RT mass)
Mn MP mass MP
V = RT V = RT Density = MP
(d) RT

23. FURTHER APPLICATION OF THE IDEAL-GAS
EQUATION
Density (d) = MP
RT
• The density of the gas depends on its pressure, molar mass and
temperature.
• The higher the molar mass and pressure the more dense the
gas.
• The higher the temperature, the less dense the gas.
• The above equation can be rearrange :
dRT
Μ= P
• Thus, we can use the experimentally measured density of a gas
to determine the molar mass of the gas molecules.

24. FURTHER APPLICATION OF THE IDEAL-GAS
EQUATION
Finding Density
EXAMPLE
Find the density (in g/L) of CO2 and the number of molecules
(a) at STP (0oC and 1 atm) and (b) at room conditions (20.0 °C
and 1.00 atm).

25. FURTHER APPLICATION OF THE IDEAL-GAS
EQUATION
Volumes of Gases in Chemical Reaction
• The ideal gas equation relates the number of moles of
a gas to P, V, and T.
• Thus, the volume of the gases consumed or produced
during the reaction can be calculated.

26. GAS MISTURES AND PARTIAL PRESSURE
Dalton’s Law of Partial Pressure
The total pressure of a mixture of gases equals the sum
of the pressures that each would exert if it were present
alone.
Partial Pressure: The pressure exerted by a particular
component of a mixture of a gas.

27. GAS MISTURES AND PARTIAL PRESSURE

28. GAS MISTURES AND PARTIAL PRESSURE
Partial Pressures and Mole Fractions
• Because each gas in a mixture behave independently, we can
relate the amount of a given gas in a mixture to its partial
pressure.
(P1/Pt) = (n1 RT/V) / (nt RT/V) = n1/nt
• n1/nt is called mole fraction of gas 1. – denoted as X1
• The mole fraction , X is a dimensionless number that express
the ratio of the number of moles
• Rearrange the equation: P = (n1/n2) Pt = X1Pt
• Thus, the partial pressure of a gas in a mixture is its moles
fraction times the total pressure

29. GAS MISTURES AND PARTIAL PRESSURE
Collecting Gases over Water
• When one collects a gas over water, there is water vapor
mixed in with the gas.
• To find only the pressure of the desired gas, one must subtract
the vapor pressure of water from the total pressure.
Ptotal = Pgas + PH20
• Refer appendix b

30. GAS MISTURES AND PARTIAL PRESSURE
EXAMPLE:
Acetylene (C2H2) is produced in the laboratory when calcium
carbide (CaC2) reacts with water:
CaC2(s) + 2H2O(l) C2H2(g) + Ca(OH)2(aq)
A collected sample of acetylene has a total gas pressure of
738 torr and a volume of 523 mL. At the temperature of the
gas (23oC), the vapor pressure of water is 21 torr. How
many grams of acetylene are collected?

31. KINETIC-MOLECULAR THEORY
• This is a model that aids in our
understanding of what happens to
gas particles as environmental
conditions change

32. KINETIC-MOLECULAR THEORY
• The kinetic-molecular theory is summarized by the following
statements:
1. Gases consist of large numbers of molecules that are in
continuous, random motion
2. The combined volume of all the molecules of the gas is
negligible relative to the total volume in which the gas is
contained.
3. Attractive and repulsive forces between gas molecules are
negligible.

33. KINETIC-MOLECULAR THEORY
4. 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.
5. The average kinetic energy of the molecules is
proportional to the absolute temperature.
• This theory explains both pressure and temperature at
molecular level.
• Pressure: caused by collisions of the molecules with the
wall of the container.
• Absolute Temperature: measure of kinetic energy of its
molecule. If 2 different gases are at the same T, theit
molecules have the same average kinetic energy (stat 5)

34. KINETIC-MOLECULAR THEORY
Distribution of Molecular
Speed
• The curve shows the fraction of molecules moving at each
speed.
• Higher T, a larger fraction of molecules moves at greater
speeds; the distribution curve has shifted to the right toward
higher speed and hence average kinetic energy.

35. KINETIC-MOLECULAR THEORY
Distribution of Molecular Speed
• Root-mean-square (rms) speed- u: The
speed of molecules possessing average
kinetic energy.
• rms speed is important bcoz: The
average kinetic energy of the gas
molecules in a sample, ε, related
directly to u2 : ε = ½ mu2
m = mass of individual molecules
• Mass does not change with T, thus the increase in the average
kinetic energy as the T increases implies that the rms speed (also
the average speed ) of molecules likewise increases with the
increase of T.

36. KINETIC-MOLECULAR THEORY
Application to the Gas Laws
• Effect of a volume increase at constant temperature:
-Constant T: A.K.E unchanged. rms speed,u, unchanged.
- Increased Volume: molecules move a longer distance
between collision. So, fewer collisions per unit time with
container walls & the pressure decreases. – BOYLE’S LAW

37. KINETIC-MOLECULAR THEORY
• Effect of a temperature increase at constant volume:
-Increase T: increased A.K.E thus increase in u.
- If no change in volume, more collision between moleculesand
with the walls.
- Thus, pressure increase.
- CHARLES’S LAW

38. MOLECULAR EFFUSION AND DIFFUSION
Graham’s Law of Effusion
• Effusion (a process by which a gas
escapes from its container) rate of a gas
is inversely proportional to the square
root of its molar mass.
• If we have 2 gases at the same T & P in
containers with identical pinholes.
• If the rates of effusion of the two
substances are r1 and r2 and their
respective molar masses are M1 & M2,
Graham’s Law states:
√
r1 M2
=
r2 M1

39. MOLECULAR EFFUSION AND DIFFUSION
Graham’s Law of Effusion
√
r1 M2
=
r2 M1
• Above equation compares
the rates of effusion of two
different gases under
identical conditions; it
indicates that the lighter gas
effuses more rapidly.
• To escape, molecules have to hit the hall. The faster they move,
the greater they will hit the wall.
• Thus, rate of effusion is directly proportional to the rms speed.

40. MOLECULAR EFFUSION AND DIFFUSION
√
3RT/ M1
√
r1 u1 M2
= =
r2 u2 3RT / M2 = M1
u= √ 3RT /M

41. MOLECULAR EFFUSION AND DIFFUSION
Diffusion and Mean Free Path
• Diffusion is the spread of one substance throughout a
space or throughout a second substance.
• Faster for lower mass molecules.

42. REAL GASES: DEVIATIONS FROM
IDEAL BEHAVIOUR
• In the real world, the
behavior of gases only
conforms to the ideal-gas
equation at relatively high
temperature and low
pressure.
• Real gases do not behave
ideally at high pressure.

43. REAL GASES: DEVIATIONS FROM
IDEAL BEHAVIOUR
• The deviation also depends on T.
• We can see that, as the P
increased, the behavior of the gas
more nearly approaches the ideal
gas
• Thus, the deviations from ideal
behavior increase as T decrease
and becoming significant near the
T at which the gas is converted
into liquid.

44. REAL GASES: DEVIATIONS FROM
IDEAL BEHAVIOUR
Why Real Gases Deviate From Ideal-Gas
• Assumptions: Molecules of ideal gas are assumed to occupy
no space and have no attractions for one another.
• However: Real molecules do have finite volume, and attract
one another.
• Fig: (low P) The free unoccupied space in which molecules
can move is less than the container volume.
• Thus, the free volume of the available to the molecules is
essentially the entire volume of the container.

45. REAL GASES: DEVIATIONS FROM
IDEAL BEHAVIOUR
• Increase P: The free space in which the molecules can move
become smaller fraction of the container volume.
• Thus, the gas volumes tend to be slightly greater than those
predicted by the ideal-gas equation.
• In addition, the attractive forces between molecules also
play at short distance.
• The impact is increased.
• However, the attraction between molecules also increased
due to the short distance.
• As a result, the pressure is less than the ideal gas.

46. REAL GASES: DEVIATIONS FROM
IDEAL BEHAVIOUR
The van der Waals Equation
• The ideal-gas equation can be adjusted to take these
deviations from ideal behavior into account.
• The corrected ideal-gas equation is known as the van der
Waals equation.
•
The van der Waals Equation
n2a ) (V − nb) = nRT
(P + 2
V

47. REAL GASES: DEVIATIONS FROM
IDEAL BEHAVIOUR