Ideal Gases

1
Ideal Gases

• Move Randomly
• No attractive forces between molecules
• Average kinetic energy (KE) (motion) is
  proportional to temperature (T)
• ie. increase T, KE will increase
• Collisions of gas particles are elastic
• ie. total KE of particle is constant

2
Pressure

• Force per unit area pushing against a surface
• Units
• 1 atm 760 mm Hg 760 torr 101.325 kPa

Atmospheric Pressure

• Results from mass of air being pulled to earth
  by gravity
• Atmospheric pressure differs with weather
• Atmospheric pressure differs with altitude
• Higher altitude, lower pressure

3
Measuring Pressure
Barometer
Manometer
4
Blood Pressure
5
Gas Laws
V Volume P Pressure T Temperature
n moles

• Boyles Law
• V ? 1/P (at same T and n)

6
Gas Laws
V Volume P Pressure T Temperature
n moles

• Boyles Law
• V ? 1/P (at same T and n)
• Charles Law
• V ? T (at same P and n)

7
Charles Law
8
Gas Laws
V Volume P Pressure T Temperature
n moles

• Boyles Law
• V ? 1/P (at same T and n)
• Charles Law
• V ? T (at same P and n)
• Avagadros Law
• V ? n (at same P and T)

9
Gas Laws

• Combined Gas Law
• V ? 1/P T n

• Ideal Gas Law
• V (nRT)/P or PV nRT
• R is the universal gas constant
• R 0.08206 L atm/(mol K)
• P is in atmospheres
• V is in liters
• n is in moles
• T is in Kelvin
• Kelvin C 273.15

10
PV nRT
You can find any one of the four measurements (P,
V, n, T) if you know the other three
R 0.08206 L atm mol-1 K-1 V Volume (L) P
Pressure (atm) n moles T Temperature
(K) Kelvin C 273.15
11
Ideal Gas Law Example

• Dry ice was placed in a test tube and allowed to
  sublime. The gaseous CO2 was collected as shown
  below. After all of the dry ice sublimed, the
  level of the container was adjusted so that the
  level of the water inside and outside was equal.
  At this point, the pressure of the gases (CO2 and
  H2O) inside the container equals the atmospheric
  pressure (1.022 atm). The pressure of CO2 equals
  the atmospheric pressure minus the vapor pressure
  of water at 24.0 C which is 22.4 torr. The
  temperature of the water and therefore the gas
  was equal to room temperature (24.0 C) How many
  grams of dry ice was in the test tube if the
  volume of gas produced was 253.0 mL.

12
R is a Constant
PV nT
R
P1V1 n1T1
P2V2 n2T2
R
13
Changing Condition examples
A sealed glass bottle at 24 C and 0.990 atm is
heated to 100 C . What is the new pressure in
this sealed glass bottle?
T1 24 273 297 K T2 100 273 373 K P1
0.990 atm P2 ??? n1 n2 (sealed bottle
so constant moles) V1 V2 (glass bottle so not
flexible)
P1V1 n1T1
P2V2 n2T2
R
P1 T1
P2 T2

P1T2 T1

P2
14
STP (Standard Temperature and Pressure)
Temperature 0 C or 273.15 K Pressure 1
atm
Molar Volumes (1 mol) at STP
Molar Volumes at STP
15
Partial Pressures

• Total pressure of a sample equals the sum of the
  pressures of each gas
• Pt P1 P2 P3 ........
• Total moles of gas equals the sum of the moles of
  each gas
• nt n1 n2 n3 ........

RT V
RT V
Pt nt
or P1 P2 P3 ..... n1 n2 n3 ....
16
Pressure and Mole Ratios
n1 nt
P1 Pt
n1RT/V ntRT/V


n1 nt
Pt ?1 Pt
P1

• ?1 equals the mole fraction of the gas
• The mole percent is ?1 times 100

17
Partial Pressure Example

• At an underwater depth of 250 ft, the pressure is
  8.38 atm. What should the mole percent of oxygen
  be in the diving gas for the partial pressure of
  oxygen in the mixture to be 0.21 atm, the same as
  in air at 1 atm.