Transcript Avogadro’s Hypothesis

Properties of Gases
• Gases may be compressed.
• Gases expand to fill their
containers uniformly.
• All gases have low density.
• Gases may be mixed.
• A confined gas exerts constant
pressure on the walls of its
container uniformly in all
directions.
Fig. 4-2, p. 97
Kinetic Molecular Theory
• Matter is composed of tiny particles (atoms, molecules or ions) with
definite and characteristic sizes that never change.
• The particles are in constant random motion, that is they possess
kinetic energy. Ek = 1/2 mv2
• The particles interact with each other through attractive and repulsive
forces (electrostatic interactions), that is the possess potential energy.
U = mgh
• The velocity of the particles increases as the temperature is increased
therefore the average kinetic energy of all the particles in a system
depends on the temperature.
• The particles in a system transfer energy form one to another during
collisions yet no net energy is lost from the system. The energy of the
system is conserved but the energy of the individual particles is
continually changing.
Fig. 4-3, p. 98
Fig. 4-4, p. 98
PRESSURE
• A physical property of matter that describes
the force particles have on a surface.
Pressure is the force per unit area, P = F/A
• Pressure can be measured in:
• atmosphere (atm)
• millimeters of mercury (mmHg)
• (torr) after Torricelli, the inventor of the mercury
barometer (1643)
• pounds per square inch (psi)
1 atm = 760 mmHg = 760 torr = 14.69 psi
Fig. 4-13, p. 109
Fig. 4-6, p. 100
TEMPERATURE
• A physical property of matter that
determines the direction of heat flow.
• Measured on three scales.
oF
• Fahrenheit
Celsius
• Kelvin
K
• oF = (1.8 oC) + 32
• K = oC + 273.15
oC
oC
= (oF - 32)/1.8
Fig. 4-1, p. 96
EMPIRICAL GAS LAWS
Boyle’s Law
Charles’ Law
Combined Gas Law
P1V1 = P2V2
V1 / T1 = V2 / T2
P1V1 / T1 = P2 V2 / T2
Boyle’s Law: For a fixed quantity of gas at
constant temperature, pressure is inversely
proportional to volume.
Fig. 4-12, p. 108
Fig. 4-11a, p. 107
Fig. 4-10, p. 106
Charles’s Law: The volume of a fixed
quantity of gas at constant pressure is
directly proportional to absolute
temperature.
Fig. 4-9, p. 105
Empirical Gas Laws
1. At 25oC, a sample of N2 gas under a pressure of 689 mmHg occupies
124 mL in a piston-cylinder arrangement before compression. If the
gas is compressed to 75% of its original volume, what must be the new
pressure (in atm) at 25oC?
First make a list of the measurements made:
P1=689 mmHg
V1 = 124 mL
P2 = ?
V2 = 75% V1
From the variables, choose the appropriate equation, in this
case Boyle’s Law: P1V1=P2V2
(689 mmHg) (124 mL) = P2 (0.75 x 124 mL)
Solve for P2:
P2 = (689mmHg) (124 mL) / (93 mL) = 919 mmHg
Now convert to atm:
919 mmHg (1 atm / 760 mmHg) = 1.21 atm
Empirical Gas Laws
2. The gas in a Helium filled ball at 25oC exerts a volume of
4.2 L. If the ball is placed in a freezer and the volume
decreases to 1/8 of its original value, what is the
temperature inside the ball?
First make a list of the measurements made:
V1=4.2 atm
T1 = 25 oC + 273.15 = 298.15
V2 = 1/8 P1
T2 = ?
From the variables, choose the appropriate equation, in this
case Charles’ Law: V1/T1=V2/T2
(V1) / (298 K) = (1/8 V1) / T2
Solve for T2:
T2 = [(298 K) (1/8 V1)] / (V1) = 298 / 8 = 37.3 K or -235 oC
Empirical Gas Laws
3. A balloon containing 6.50 grams of NH3
has a volume of 10.30 L at a temperature of
20.0oC and a pressure of 689.2 torr. What
would be the pressure of NH3 if the volume
decreased to 2.50 L without a change in
temperature?
4. A sample of CO gas has a volume of 25.0 L
at a pressure of 789 torr and a temperature
of 20oC. What must the temperature be if
the pressure was unchanged but the
volume needed to be increased to 95.0 L?
p. 110
COMBINED GAS LAW
• A gas occupies a volume of 720 mL at 37oC
and 640 mmHg pressure. Calculate the
volume the gas would occupy at 273 K and 1
atm.
P1V1 / T1 = P2V2 / T2
rearranged to solve for V2 is:
V2 = P1 V1 T2 / P2 T1
V2 = (640 mmHg)(720 mL) (273 K) / (760 mmHg) (310 K)
V2 = 534 mL
COMBINED GAS LAW
What would be the volume at STP of 3.62 liters
of nitrogen gas, measured at 649 torr and 16 °C?
P1V1 = P2V2 rearranged to solve for V2 is:
T1
T2
V2 = P1 V1 T2
P2 T1
V2 = (649 torr)(3.62 L) (273 K)
(760 torr) (16 + 273K)
V2 = 2.92 L
COMBINED GAS LAW
• A gas occupies a volume of 720 mL
at 37oC and 640 mmHg pressure.
– Calculate the pressure if the
temperature is increased to 1000oC &
the volume expands to 900 mL.
P2 = 2.1 x 103 mmHg
– Calculate the temperature if the
pressure is decreased to 10 torr & the
volume is reduced to 500 mL.
T2 = 3.4 K or -270 oC
PRACTICE PROBLEM # 20a
1. You prepared carbon dioxide by adding aqueous HCl to marble chips,
calcium carbonate. According to your calculations, you should obtain 79.4
mL of carbon dioxide at 0 oC and 760 mmHg. How many milliliters of gas
would you obtain at 27oC at the same pressure?
87.3 mL
2. Divers working from a North Sea drilling platform experiences pressures of
50 atm at a depth of 5.0 x 102 m. If a balloon is inflated to a volume of 5.0 L
(the volume of a lung) at that depth at a water temperature of 4.0oC, what
would the volume of the balloon be on the surface (1.0 atm) at a temperature of
11 oC?
256 L
3. What volume would 5.30 L of H2 gas at 0 oC and 760 mmHg occupy if the
temperature was increased to 70oF and the pressure to 830 torr? 5.23 L
4. The pressure gauge reads 125 psi on a 0.140-m3 compressed air tank when
the gas is at 33.0 oC. To what volume will the contents of the tank expand if
they are released to an atmospheric pressure of 751 torr and a temperature of
13oC?
1.126 m3
5. A gas has a volume of 397.0 mL at 14.70 atm. What will be its pressure (in
torr) if the volume is changed to 4.100 L?
1082 torr
PRACTICE PROBLEM # 20a
6. Which of the following statements is false?
a) If the Celsius temperature is doubled, the pressure of a fixed volume of gas would
double.
b) All collisions between gas molecules are perfectly elastic (no energy is lost)
according to KMT.
c) The volume of gas is inversely proportional to the temperature of gas present (P
constant)
d) Gases are capable of being greatly compressed.
C
7. Which of the following statements are true?
a) In a large container of O2 gas the pressure exerted by the oxygen will be greater
at the bottom of the container.
b) Of the three states of matter, gases are the most compact and the most mobile.
c) The formula of ozone is 3 O2.
d) Molecules of O2 gas and H2 gas at the same temperature will have the same
average kinetic energies and the same average velocities.
D
GROUP STUDY PROBLEMS
1. A sample of O2 gas initially at 0oC and 1.0 atm is transferred from a 2-L
container to a 1-L container at constant temperature. a) What effect does
this change have on the average kinetic energy of the gas molecules? b)
What effect does the total number of collisions of O2 molecules with the
container walls in a unit time?
2. At constant pressure, a student needed to decrease a
volume of 155 mL of Ne gas by 32.0%. To what temperature,
(in oC), must the gas be cooled if the initial temperature was
21oC?
3. A sample of CO2 gas has a volume of 125.0 L at a pressure
of 789 torr and a temperature of 30oC. What will be the
temperature if the pressure was increased to 900 torr & the
volume decreased to 95.0 L?
4. F2 gas, which is dangerously reactive, is shipped in steel
containers of 30.0 L capacity, at a pressure of 10.0 atm at 26.0
oC. What should be the volume of the tank if the pressure is
increased to 820.0 torr & the temperature is 43.0 oC?