The Gas Laws

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Chapter 13
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• The Gas Laws

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Gases
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• Can diffuse through air
• Some gases are colorless some have color (Cl2,
  NO2)
• Some gases are odorless, some smell

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Gases may be
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• Monatomic Made of one atom, like He
• Diatomic Made of two atoms, like Cl2 or H2
• This is the case for Br, I, N, Cl, H, O,
  F
• Also known as Miss BrINClHOF (Pronounce
  Brinklehoff)
• Polyatomic Made up of more than two atoms, like
  CO2, NO2, or CH4 (methane)

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Observations of Gases
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• 1. Gases have mass
• 2. It is easy to compress a gas
• 3. Gases fill their containers completely
• 4. Different gases can move through each other
  easily (diffusion)
• 5. Gases exert pressure
• 6. The pressure of a gas depends on its
  temperature

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The Kinetic Molecular Theory
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• Used to explain those 6 observations- The
  following are the postulates

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KMT Postulate 1
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• A gas consists of very small particles that have
  mass

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KMT Postulate 2
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• These particles are much much (double much
  intended) smaller than the distance between
  particles. Most of the volume of a gas is
  therefore empty space.
• Compared to the container, the volume of the gas
  is zero. So, we say the volume of the container
  is the volume of the gas

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KMT Postulate 3
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• Gases are composed of a large number of particles
  that behave like hard, spherical objects in a
  state of constant, random motion.
• Basically, gas particles are like billiard
  balls in a 3-D pool table, and they are all
  moving all over the place all the time in
  different directions

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KMT Postulate 4
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• Collisions between gas particles or collisions
  with the walls of the container are perfectly
  elastic. None of the energy of a gas particle is
  lost when it collides with another particle or
  with the walls of the container.
• This is why gases take the shape of their
  container!
• The energy of the system is constant

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(More on postulate 4)
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• These particles move in a straight line until
  they collide with another particle or the walls
  of the container.
• Then they bounce off, and move again- these
  collisions are elastic

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KMT Postulate 5
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• The average kinetic energy of a collection of gas
  particles depends on the temperature of the gas
  and nothing else.
• Think back to the fact that temperature is a
  measure of Kinetic Energy (the motion of
  molecules)
• high energy high temp low energy low temp

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KMT Postulate 6
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• There is no force of attraction between gas
  particles or between the particles and the walls
  of the container.
• Keep in mind- things arent repelled, either.no
  attraction, no repulsion

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Measuring Gases
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• We measure gases in several ways
• Volume V
• Temperature T
• Pressure P
• Number of Moles n

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Volume (V)
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• We usually measure volume in
• Liters (L), but sometimes in other metric units
• 1L 1000mL
• 1L .0001m3
• We will use these conversions- be sure to know
  them!

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Temperature (T)(A Measure of KE!)
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• For most scientists, the Celsius scale is used
• However, we need to use the Kelvin scale for gas
  laws

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The Kelvin Scale
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• Is based in Absolute Zero, which is -273C
• 0K -273C
• 273K0C
• To convert between K and C,
• C 273 K
• or K -273 C
• Its that simple, which is good since no gas laws
  calculations can use C

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Pressure (P)
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• Gas pressure is created by the molecules of gas
  hitting the walls of the container. This concept
  is very important in helping you to understand
  gas behavior. Keep it solidly in mind. This idea
  of gas molecules hitting the wall will be used
  often.
• Pressure is force measured over an area
• PForce/ area

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Units of Pressure
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• atmospheres (atm)
• millimeters of mercury (mm Hg)
• Pascals ( Pa)
• kiloPascals ( kPa)
• Standard pressure is defined as
• 1 atm
• 1atm 760.0 mm Hg
• 1 atm101.325 kPa

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Moles (n)
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• Weve been here VERY recently!

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A few guys and their laws.
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• Dalton
• Boyle
• Charles
• Avogadro
• Gay Lussac
• Graham

P total P1 P2 P3
P1 V1 P2 V2
V1 / T1 V2 / T2
V1 / n 1 V2 / n 2
P1 / T1 P2 / T2
Rate of effusion of gas 1 m2 Rate of
effusion of gas 2 m1
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Daltons Law
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• Air is made up of a mixture of gases. The three
  main gases are oxygen, nitrogen, and carbon
  dioxide. If the pressure of the air is 1 atm,
  and the pressure of the oxygen and carbon dioxide
  gases are 0.200 L and 0.087 L respectively, what
  is the pressure of the nitrogen? In mmHg?

P total P1 P2 P3
1 atm .200 atm .087 atm PN2
0.713 atm PN2
0.713 atm ( 760.0 mmHg/ 1atm) 542 mmHg
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Boyles Law
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• A sample of gaseous nitrogen in a cars air bag
  has a pressure of 745 mmHg in a 35.0 L bag. If
  the sample is transferred to a 25.0 L bag with
  the same temperature, what is the pressure of the
  gas?
• P1 V1 P2 V2

745 mmHg (35.0 L) P2 (25.0 L)
745 mmHg (35.0 L) P2 (25.0 L)
1040 mmHg P2
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Charless Law
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• A balloon is inflated with helium to a volume of
  45.0 L at room temperature (25.0oC) If the
  balloon is inflated with the same quantity of air
  on a very cold day (-10.0oC), what is the new
  volume?
• V1 / T1 V2 / T2

45.0 L / 298 K V2 / 263 K
263 K (45.0 L / 298 K) V2
39.7 L V2
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Avogadros Law
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• Ammonia can be made by reacting nitrogen and
  hydrogen gases. If you start with 15.0 L of
  hydrogen at a given temperature and pressure,
  what volume of nitrogen would you need to
  complete the reaction (assume temperature and
  pressure remain constant)?
• N2 (g) 3 H2 (g)? 2 NH3 (g)

V1 / n1 V2 / n2
15.0L / 3 mol VN2 / 1 mol
1 mol (15.0 L / 3 mol V2
5.00 L V2
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Gay Lussacs Law
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• You decide that you want to have some pickles
  with lunch (assume room temp is 20.0oC and
  pressure is 760.0 mm Hg). You open a new jar of
  pickles and after eating lunch, you put the jar
  in the fridge (still 760.0 mm Hg but 5.00oC). The
  next time you open the jar, it is difficult to
  open. Why?

P1 / T1 P2 / T2
760.0 mmHg / 293 K P2 / 278 K
278 K (760.0 mm Hg / 293 K) P2
721 mm Hg P2
When you put a pickle jar in the refrigerator,
the drop in pressure from the trapped air
becoming colder makes it hard to open the jar
later!)
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Grahams Law
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• Deals with effusion
• The movement of gas through a tiny opening in a
  container into another container where the
  pressure is low.
• Why latex balloons deflate before Mylar balloons.

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Grahams Law
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• Tetrafluoroethylene, C2F4 , effuses through a
  barrier at the rate of 4.6E-6 mol/h. An unknown
  gas, consisting only of boron and hydrogen,
  effuses at the rate of 5.8E-6 mol/h under the
  same conditions. What is the molar mass of the
  unknown gas?

Rate of effusion of unknown m C2F4 Rate
of effusion of C2F4 munknown
5.8E-6 mol/h 100.0 g/mol 4.6E-6 mol/h
munknown
1.3 100.0 g/mol ? 1.6 100.0 g/mol
63 g/mol munknown munknown
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And a few laws with no guys
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• Combined Gas Laws
• (P1V1)/ T1(P2V2)/T2
• Ideal Gas Law
• PV nRT

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Combined Gas Laws
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• Helium-filled balloons are used to carry
  scientific instruments into the atmosphere.
  Suppose a balloon is launched when the
  temperature is 22.5oC and the pressure is 754 mm
  Hg. If the balloons volume is 4.19E3 L, what
  will it be at a height of 20 miles, where the
  pressure is 76.0 mmHg and the temperature is
  -33.0oC?

(P1V1)/ T1 (P2V2)/T2
(P1V1)/ T1 (T2/P2) V2
(754 mmHg)(4.19E3 L)/ 295.5K (240.0 K / 76.0
mmHg) V2
3.38E4 L V2
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Ideal Gas Law
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• 30.0 kg of He is placed in a balloon. What is
  the volume of the balloon if the final pressure
  is 1.20 atm and the temperature is 22.0 0C?
• R 0.0821 atmL/molK
• 8.31 Pam3/molK
• 62.4 mmHgL/molK

PV nRT
V nRT/P
(7462 atm)(0.0821atmL/molK)(295K)/1.20 atm
1.50E5 L
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Gas Laws and Stoichiometry
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• You are asked to design a cars air bag using
  household items. You know that mixing baking
  soda (sodium bicarbonate) with vinegar (acetic
  acid) creates a gas. You know that the bag
  should be filled with gas with a pressure higher
  than atmospheric pressure, say 828 mmHg at 22.0
  0C. The bag has a volume of 45.5 L. What
  quantity of sodium bicarbonate, should be used to
  generate the required amount of gas?

Need to get grams of sodium bicarbonate. HINT
You will need molar ratios
NaHCO3 CH3COOH ? CH3COONa H2O CO2
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Gas Laws and Stoichiometry (cont.)
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Step 1 use PVnRT to get n nPV/RT
n (1.09atm)(45.5L)/(0.0821Latm/molK)(295.2) n
2.05 mol CO2

• Step 2use mole ratio to get moles of sodium
  bicarbonate

2.05mol CO2 (1 mol NaHCO3 /1 mol CO2 )
2.05 mol NaHCO3
Step 3 convert from moles to grams
2.05 mol NaHCO3 84.01g/mol 172 g