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Kinetic Molecular Theory

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Title: Kinetic Molecular Theory


1
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.

2
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)
  • 1 atm 760 mmHg 760 torr

3
TEMPERATURE
  • A physical property of matter that determines the
    direction of heat flow.
  • Measured on three scales.
  • Fahrenheit oF Celsius
    oC
  • Kelvin K
  • oF (1.8 oC) 32 oC (oF - 32)/1.8
  • K oC 273.15

4
  • GAS LAWS
  • Boyles Law P1V1 P2V2
  • Charles Law V1 / T1 V2 / T2
  • Guy-Lussacs Law P1 / T1 P2 / T2
  • Avogadros Law V1 / n1 V2 / n2
  • Combined Gas Law P1V1 / T1 P2 V2 / T2
  • Ideal Gas Law PV nRT
  • P pressure (atm) V volume (L)
  • n chemical amount (mol) T Temperature (K)
  • R ideal gas constant 0.08206 L-atm / mol-K

5
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
  • P1689 mmHg V1 124 mL
  • P2 ? V2 75 V1
  • From the variables, choose the appropriate
    equation, in this case Boyles Law P1V1P2V2
  • (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

6
Empirical Gas Laws
  • 2. The gases in a rigid Helium filled ball at
    25oC exerts a pressure of 4.2 atm. If the ball
    is placed in a freezer and the pressure decreases
    to 1/8 of its original value, what is the
    temperature inside the ball?
  • First make a list of the measurements made
  • P14.2 atm T1 25 oCc 273.15 298.15
  • P2 1/8 P1 T2 ?
  • From the variables, choose the appropriate
    equation, in this case Guy Lussacs Law
    P1/T1P2/T2
  • (P1) / (298 K) (1/8 P1) / T2
  • Solve for T2
  • T2 (298 K) (1/8 P1) / (P1) 298 / 8
    37.3 K or -235 oC
  • 3. A balloon containing 6.50 moles of NH3 has a
    volume of 550L at a certain temperature and
    pressure. How many grams of NH3 would have to
    be removed from the balloon in order for the
    volume to decrease to 250 L under the same
    conditions?

Mass of NH3 removed 60.3 g of NH3.
7
Avogadros Hypothesis
  • Avogadro pictured the moving molecule as
    occupying a small portion of the larger space
    apparently occupied by the gas. Thus the
    volume of the gas is related to the spacing
    between particles and not to the particle size
    itself.
  • Imagine 3 balloons each filled with a different
    gas (He, Ar, Xe). These gases are listed in
    increasing particle size, with Xe being the
    largest atom. According to Avogadros
    Hypothesis, the balloon filled with one mole of
    He will occupy that same volume as a balloon
    filled with one mole of Xe.
  • So for a gas, the volume and the moles are
    directly related. V a n

8
Avogadros Hypothesis
  • A sample of N2 gas at 3.0 atm and 20.0oC is known
    to occupy a volume of 1.43 L. What volume would
    a 0.179 mole sample of NH3 gas occupy at the same
    pressure and temperature?

First calculate the number of moles of nitrogen
gas PV nRT where P 3.0 atm, V 1.43
L, R 0.082 L-atm/mol-K, and T 20.0 oC 273
293K n PV / RT (3.0 atm x
1.43L) / (0.082 L-atm/mol-K x 293K)
0.179 moles of N2 So since the moles of N2 is
0.179 mol and the moles of ammonia is 0.179 mol
according to Avogadros hypothesis the volume of
NH3 at that pressure and that temperature is 1.43
L, the same!!!
9
At STP, gas molecules are so far apart that for 1
mole of gas, the overall volume does not
change.STP P 1 atm T 273 K
10
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 STP.
  • 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

11
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.
  • Calculate the temperature if the pressure is
    decreased to 10 torr the volume is reduced to
    500 mL.

P2 2.1 x 103 mmHg
T2 3.4 K or -270 oC
12
IDEAL GAS LAW
  • . What is the pressure inside a gas balloon if it
    filled with 852 g of Xe gas at 25.0oC and
    occupies a volume of 7.00 L?
  • P ? 852 g Xe ( 1 mol / 131 g) 6.50 mol
  • V 7.00 L T 25oC 273 298 K
  • P nRT
  • V
  • P (6.50 mol) (0.082 L-atm / mol-K) (298 K)
  • 7.00 L
  • P 22.7 atm

13
IDEAL GAS LAW
  • What would be the temperature of 100 g of Ar gas
    contained in a 500 L sealed container at 0.8976
    atm.
  • How much would a balloon weigh if it contained
    40.0 L of O2 gas at 987 mmHg and 45.3 oC?

T2 1914 oC
mass O2 63.7 g
14
DENSITY OF A GAS
  • The density of a gas at STP can be calculated by
  • dSTP molar mass/molar volume
  • Calculate the density of hydrogen sulfite gas at
    STP.
  • Identify an unknown homonuclear diatomic gas that
    was found to have a density of 3.165 g/L at STP.

d (STP) (82 g/mol) / 22.4 L/mol) 3.66 g/L
Cl2
15
Properties of Gases
  • DIFFUSION
  • Diffusion is the ability of two or more gases to
    mix spontaneously until a uniform mixture is
    formed.
  • Example A person wearing a lot of perfume walks
    into an enclosed room, eventually in time, the
    entire room will smell like the perfume.
  • EFFUSION
  • Effusion is the ability of gas particles to pass
    through a small opening or membrane from a
    container of higher pressure to a container of
    lower pressure.
  • The General Rule is The lighter the gas, the
    faster it moves.
  • Grahams Law of Effusion
  • Rate of effusion of gas A v(molar mass B /
    molar mass A)
  • Rate of effusion of gas B
  • The rate of effusion of a gas is inversely
    proportional to the square root of the molar mass
    of that gas.

16
DALTONS LAW OF PARTIAL PRESSURES
  • If there is more than one gas present in a
    container, each gas contributes to the total
    pressure of the mixture.
  • Ptotal Pgas A P gas B Pgas C
  • If the total pressure of a system was 2.5 atm,
    what is the partial pressure of carbon monoxide
    if the gas mixture also contained 0.4 atm O2 and
    1.48 atm of N2?

PT - PO2 - PN2 PCO 2.5 atm - 0.4 atm - 1.48
atm 0.62 atm
17
STOICHIOMETRY THE GAS LAWS
  • 1. Write a balanced chemical equation
  • 2. Convert to moles (if gas, use PVnRT or Molar
    Volume)
  • 3. Use the mole ratio to convert from moles of
    A to moles of B.
  • 4. Convert moles of B to desired measurement,
    if a gas use PVnRT.

1. What volume of O2 is needed to combust 348.0 L
of C3H8? C3H8 5 O2 ? 3 CO2 4 H2O Due to
Avogadros Hypothesis, the moles of a gas are
directly related to the volume of a gas therefore
it is possible to use the mole ratio on volumes
of gas. 348.0 L C3H8 (5 mol O2 / 1 mol C3H8)
1740 L O2
18
STOICHIOMETRY THE GAS LAWS
2. How many grams of CO2 is produced from 348.0 L
of C3H8 if the temperature is 40.0oC and the
pressure is 654 torr? C3H8 5 O2 ? 3 CO2 4
H2O P 654 torr (1 atm / 760 torr) 0.861
atm T 40oC 273 313 K PV / RT n
(0.861 atm) (348.0 L)
/(0.082 L-atm/mol-K) (313 K)
11.67 mol of C3H8 11.67 mol C3H8 (3 mol CO2
/ 1 mol C3H8) 35.02 mol CO2 35.02 mol CO2
(44 g / 1 mol) 1541 g of CO2
19
STOICHIOMETRY THE GAS LAWS
3. In lab, you decomposed potassium chlorate
into oxygen and potassium chloride. What volume
of O2 at STP can be formed from 3.65 g of
potassium chlorate? 2 KClO3 ? 3 O2 2 KCl 3.65
g (1 mol / 122.6g) 0.02977 mol KClO3 0.02977
mol KClO3 (3 mol O2 / 2 mol KClO3) 0.04466 mol
O2 0.04466 mol O2 ( 22.4 L / 1 mol) 1.00 L
20
PRACTICE PROBLEMS 20
1. Both hydrogen and helium have been used as
buoyant gas in blimps. If a small leak were to
occur, which gas would effuse more rapidly and by
what factor? 2. At STP, 560 mL of a gas has a
mass of 1.08 g. What is the molecular weight of
the gas? 3. 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? 4. A 50.0 L cylinder of
nitrogen has a pressure of 17.1 atm at 23oC.
What is the mass of nitrogen in the cylinder? 5.
When a 2.0 L bottle of concentrated HCl was
spilled, 3.0 kg of CaCO3 was required to
neutralize the spill. CaCO3 (s) 2HCl (aq)
? CaCl2 (aq) H2O (l) CO2 (g) What
volume of CO2 gas was released by the
neutralization at 735 mmHg and 20 oC?
Hydrogen effuses first by a factor of 1.41
43.2 g/mol
87.3 mL
986 g
745 L
21
Group Study Problem 20
1. Measured at 65 oC and 500.0 torr, the mass
of 3.21 L of a gas is 3.5 g. What is the molar
mass of this gas 2. A 100.0 mL sample of air is
analyzed and found to contain 0.835 g N2, 0.0640
g CO2 and 0.197 g O2 at 35 oC. What is the
total pressure of the sample and the partial
pressure of each component? 3. What volume
would 5.30 L of H2 gas at STP occupy if the
temperature was increased to 70oF and the
pressure to 830 torr? 4. 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? 5. Hydrogen gas is
produced by the complete reaction of 8.34 g of
aluminum metal with an excess of gaseous hydrogen
sulfate. How many liters of hydrogen will be
produced if the temperature is 50.0 oC and the
pressure is 0.950 atm?
22
Group Study Problem
Answers 1. 45.9 g/mol 2. PN27.53 atm,
PO21.55 atm, PCO20.380 atm PT 9.46
atm 3. 5.23 L 4. 256 L 5. 12.9 L
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