Transcript CHAPTER 5

Chapter 5
GASES
What we’ve had so far!
• Different ways of calculating moles of
substances
• Solids:
• Liquids:
Moles =
grams
molar mass
Molarity =
moles
Liter
Ideal Gas Law
• In Chapter 5, everything comes
down to another way of solving for
moles.
PV
=
nRT
where n = number of moles
Atmospheric Pressure
• Pressure exerted by a gas on its
surroundings
Pressure
• Units of Pressure
– mm Hg
– Atm
– Torr (in honor of Evangelista
Torricelli)
– Pascal
(Pa)
Pressure
• Conversions:
–1 atm = 760 Torr = 760 mm Hg
–1 atm = 101,325 Pa
The Gas Laws
• Boyle’s Law
• PV = k
– the product of pressure (P) and
volume (V) of a trapped gas is
constant
Pressure vs. Volume
• P is inversely proportional to V
• Since
PV = k
• If k = 1,
• then P = 1 or
V
V = 1
P
Boyle’s Law
• only holds true at very low
pressures
• at high pressures, PV is not
constant
Application of Boyle’s Law
• commonly used to predict the new
volume when pressure is changed
• If:
PV =
k
• Then: (PV)1 = (PV)2 for same gas
at same temperature
Sample Problem on Boyle’s
Law
• An aerosol can contains 400 mL of
compressed gas at 5.20 atm pressure.
When all the gas is sprayed into a
large plastic bag, the bag inflates to a
volume of 2.14 L. If the T is
constant, what is the pressure of gas
inside the plastic bag?
Boyle’s Law
• A gas that strictly follows Boyle’s
Law is an IDEAL GAS.
Charles’s Law
•
filled balloon with H2 and made
the first solo balloon flight
• discovered that the volume of a
gas at constant P increases
linearly with the T of the gas
Charles’s Law
• The V of a gas at constant P is
directly proportional to T.
• Charles’s Law Equation:
• V = kT
where k is
the proportionality constant
Units of Temperature
• Celsius
• Kelvin
• Conversion:
• 0 oC =
273 K
Application of Charles’s Law
• To predict new volume of a gas
when T is changed
• Thus if :
V
• Then: (V1/T1) =
=
kT
(V2/T2)
Sample Problem
• If a gas at 15 oC and 1 atm has a
volume of 2.58 L, what volume
will this gas occupy at 38 oC and
1 atm?[Note: Convert all T to K]
Avogadro’s Law
• Avogadro’s Postulate: [Chapter 2]
• Equal volumes of gases at the same
T and P contain the same number of
particles.
Closely obeyed by gases at low P.
Avogadro’s Law
• V = axn
– where n = number of moles
–
a = proportionality constant
• So for a gas at constant T and P, the
volume is directly proportional to
the number of moles of gas.
Application of Avogadro’s Law
• To predict changes in V when
the number of moles changes.
• V1/n1 =
V2/n2
Charles’ Law
• the volume of a gas at constant P
increases linearly with the T of
the gas
Summary of 3 Laws
• Boyle’s Law:
V = K/P
[at constant T and n]
• Charles’s Law:
V = bT
•
[at constant P and n]
• Avogadro’s Law: V = an
[at constant T and P]
Sample Problem
• A 1-L container contains 2.75 moles of H2
at 400 oC. What would be the pressure in
the container at this temperature?
Sample Problem
• 3.5 moles of N2 has a pressure of 3.3 atm
at 375 oC. What would be the pressure of
the 5.3 moles of gas at 900 oC?
Boyle’s Law
• A gas that strictly follows Boyle’s
Law is an IDEAL GAS.
Ideal Gas Law
• expresses behavior that real gases
approach at low P’s and high T’s
• An Ideal Gas is a hypothetical
substance!
Ideal Gas Law
• Since most gases approach close to
ideal behavior anyway, we will
assume that the gases we encounter
in this course are all ideal gases.
Ideal Gas Law
• PV
=
nRT
–where R = universal gas
constant
–
= .08206 L-atm/K
Sample Problem
• A sample of methane gas that
has a volume of 3.8 L at 5 oC is
heated to 86 oC at constant P.
Calculate its new volume.
Another Sample Problem
• A sample of hydrogen gas has a
volume of 10.6 L at a T of 0 oC
and a P of 2.5 atm. Calculate the
moles of hydrogen gas present in
this gas sample.
Molar Mass and Density
• Molar Mass =
• Density =
gmRT
PV
Molar Mass x Pressure
RT
Dalton’s Law of Partial
Pressures
• For a mixture of gases in a
container, the total P exerted is the
sum of the pressures that each gas
would exert if it were alone.
• Ptotal = P1 + P2 + P3 …….
Dalton’s Law
• Ptotal = P1 + P2 + P3 …….
• If P1 = n1RT/V P2 = n2RT/V
P3= n3RT/V
• Then: Ptotal = (n1RT/V) +
(n2RT/V) + (n3RT/V)
Gas Stoichiometry
• PV
= nRT
• For 1 mole of an ideal gas at 0 oC,
the molar volume at STP is 22.42 L.
• STP = standard T and P
•
where T = 0 oC and P = 1 atm
Sample Problem
• A sample of nitrogen gas has a
volume of 1.75 L at STP. How
many moles of N2 are present?
Kinetic Molecular Theory
• Is a model that attempts to
explain the behavior of ideal
gases
• Based on speculations about the
behavior of the gas particles
Postulates of KMT
• The gas particles are assumed to:
•
•
•
•
1] be so small and have V = 0
2] be in constant motion.
3] exert no force on each other
4] have average KE that is a T (in
Kelvin)
KMT on P and V
• Since P a 1 (Boyle’s Law)
V
• As V increases, P decreases.
• As V decreases, P increases.
KMT: As V is decreased, P increases
because particles hit walls of
container more often.
KMT on P and T
• As T is increased, the speed of
the particles increases resulting
in more collisions and stronger
collisions. Thus P increases.
KMT on V and T
• Charles’s Law: V a
T
• KMT: As T is increased, P normally
increases because particles collide
more. To keep P constant, V has to
increase to compensate for the
increased collisions.
KMT on V and n
• Avogadro’s Law:
V a n
• KMT: Normally, an increase in n
(moles of particles) increases P if V
was held constant. To return P back
to normal, V has to be increased.