Transcript
Unit 4 - Gases Ch 5
A/ Properties of Gases (5.1)
Volume changes greatly with pressure.
Volume changes greatly with temperature.
Low viscosity (flow freely).
Low density.
Miscible (ie. will mix to form solution).
Why? Consider the molecular level (see Fig 5.1)
Cp’d to liquids and solids, the molecules of a gas are spread far apart; most of the sample is empty space
Later we will consider this more (KMT)
B/ Pressure (5.2)
What is “pressure”?
P= F/A ie “force per unit area”
Units: See Table 5.2
SI units: N/m2 = [kg m/sec2]/m2 = kg/(m sec2) = Pa
Other units: 1 bar = 105 Pa
1 atm = 1.01325 bar
760 torr = 1 atm
1 torr = 1 mm Hg
Why “mm Hg”?
See Fig 5.4 A manometer
Manometer - a U-shaped tube filled with liquid (usually Hg)
it actually measures the difference in pressure between the two ends of the tube, as opposed to absolute pressure; the difference in the height of the Hg represents the difference in pressure (in mm Hg)
for absolute pressure, one can evacuate one end of the tube and seal it off (a barometer) Fig 5.3
now the difference in the height of the Hg represents the absolute pressure at the open end of the tube
C/ Gas Laws
Pressure and Volume
Boyle - varies P while observing V (at const. T)
Finds: as press. increases, the volume decreases
Volume is inversely proportional to P
V ? 1/P
V = k/P (k= proportionality constant)
PV = k
P1V1 = P2V2
Or finally on a graph (Fig 5.5)
i>clicker Question:
Which of the following plots depicts Boyles Law?
a) b) c) d)
2. Temp and Volume
Charles - varies T and observes V (at constant P)
Finds: as Temp. increases, Volume increases
Volume is directly proportional to temp.
V ? T
V = kT
V/T = k
V1/T1 = V2/T2
Or finally on a graph (Fig 5.6)
i>clicker Question:
Which of the following plots depicts Charles Law?
a) b) c) d)
Notice that if one extrapolates down to when V=0, one finds the temperature at that point is -273.15 °C
called absolute zero
can introduce a new temperature scale called the Absolute or Kelvin temperature scale
Kelvin temp. = °C + 273.15
Ex) 25°C = 298.15 K
- always use temperature in K in gas law calculations
0 b
3. Volume and Amount
What if one changes the amount of a gas sample?
Avagadro’s Law - At a fixed T and P, the volume of a gas sample is directly proportional to the amount of the gas, expressed in moles
V ? n
(See Fig 5.7)
Now combine laws together.
First, Boyles and Charles
V ? 1/P V ? T
therefore V ? T/P
V = kT/P
PV/T = k
P1V1/T1 = P2V2/T2 Combined Gas Law
Now, Boyles and Charles and Avagadro
V ? 1/P V ? T V ? n
therefore V ? nT/P
V = knT/P
PV = knT
or PV = nRT Ideal Gas Law
PV = nRT Ideal Gas Law
R = ideal gas constant
= 0.082056 lit atm/ mole K
= 8.314 J/mole K
STP = standard temperature and pressure (0°C, 1 atm)
Ex) 5.33
D/ Applications of the Ideal Gas Law
can use the ideal gas law to determine M, ? (density)
Density
density = ? = m/V
therefore since PV = nRT
i>Clicker Question:
Which of the following is true:
Density is directly ? to P, inversely ? to T
Density is directly ? to T, inversely ? to P
Density is directly ? to P, directly ? to T
Density is inversely ? to P, inversely ? to T
D/ Applications of the Ideal Gas Law
can use the ideal gas law to determine M, ? (density)
Density
density = ? = m/V
therefore since PV = nRT
PV = (m/M)RT
PM = (m/V)RT
? = m/V = PM/RT
Molar mass, M
PV = nRT
PV = (m/M)RT
M = mRT/PV
See Fig 5.11
Ex) 5.43
Cut-off for Midterm #1
3. Gas Mixtures
Recall: gas mix together homogeneously (form sol’n)
In a gas mixture, each gas behaves as if it were the only gas present. It exerts a pressure of it’s own called a partial pressure
That partial pressure obeys the gas laws
Dalton’s Law: The total pressure is the sum of the partial pressures
PT = PA + PB
PA = nART/V and PB = nBRT/V
Therefore
PT = (nART/V) + (nBRT/V) = (nA + nB)RT/V = nTRT/V
Now consider PA/PT
PA/PT = (nART/V)/(nTRT/V) = nA/nT = xA
xA = the “mole fraction of A
PA = xAPT
Ex) 5.45
E/ Gas Reactions and Stoichiometry (5.5)
can do stoichiometry problems now for equations involving gases
Ex) 5.54
But also…
Consider a chem. eq.
2 ZnS(s) + 3 O2(g) --> 2 ZnO(s) + 2 SO2(g)
This implies:
3 molecules of O2(g) produces 2 molecules of SO2(g)
and
3 moles of O2(g) produces 2 moles of SO2(g)
But now recall Avagadro’s law (at const. T,P all gases have the same molar volume)
Therefore, for gaseous species in a chemical reaction, one can view the stoichiometric ratio to be a volume ratio as well as a mole ratio
ie. above
3 L of O2(g) produces 2 L of SO2(g)
Consider likewise the example of the electrolysis of H2O
2 H2O(l) --> 2 H2(g) + O2(g)
2 VO2(g) = VH2(g)
2 ZnS(s) + 3 O2(g) --> 2 ZnO(s) + 2 SO2(g)
Ex) In above rxn, what volume of O2(g) is req’d to produce 7 L of SO2(g)?
F/ Kinetic Molecular Theory of Gases (5.6)
Have seen V ? T, V ? 1/P, V ? n.
But why?
The gas laws “make sense” in light of KMT
KMT is a “model” or picture describing gas samples at the microscopic level.
Postulates (on Unit outline)
Gas samples consist of large numbers of very small particles in random straight line motion.
Molecules are separated by relatively great distances.
3. Molecules collide with each other and the walls.
Collisions are “elastic”.
5. Otherwise no forces exist between molecules.
How does KMT explain the gas laws?
Fig 5.15 - Boyle’s Law
Fig 5.17 - Charles’ Law
Fig 5.18 - Avagadro’s Law
How does KMT explain the gas laws?
Fig 5.15 - Boyle’s Law
As the volume decreases, the frequency of collision of the molecules with the walls increases. Therefore the pressure increases.
Fig 5.17 - Charles’ Law
Fig 5.18 - Avagadro’s Law
How does KMT explain the gas laws?
Fig 5.15 - Boyle’s Law
As the volume decreases, the frequency of collision of the molecules with the walls increases. Therefore the pressure increases.
Fig 5.17 - Charles’ Law
As the temperature increases, the frequency of collision of the molecules with the walls increases. Also the energy of the average collision increases. Therefore the pressure increases. This then pushes the top of the container up and the volume increases.
Fig 5.18 - Avagadro’s Law
How does KMT explain the gas laws?
Fig 5.15 - Boyle’s Law
As the volume decreases, the frequency of collision of the molecules with the walls increases. Therefore the pressure increases.
Fig 5.17 - Charles’ Law
As the temperature increases, the frequency of collision of the molecules with the walls increases. Also the energy of the average collision increases. Therefore the pressure increases. This then pushes the top of the container up and the volume increases.
Fig 5.18 - Avagadro’s Law
As the number of moles of gas increases, the frequency of collision of the molecules with the walls increases. Therefore the pressure increases. This then pushes the top of the container up and the volume increases.
Also an implication of KMT (postulate 4) is that different gas samples at the same temp have the same average kinetic energy.
KE = (1/2)mv2 for a molecule
For a sample:
= (1/2)m
( = avg KE, avg square velocity)
Given two samples at 298K, O2 and CO2
must be greater for O2 because m is smaller.
Can plot a “Boltzmann” Distribution
consider the effect of m on the distribution (previous and Fig 5.19)
consider the effect of T on the distribution (Fig 5.14)
i>Clicker question:
Knowing that average kinetic energy of an ideal gas is directly proportional to absolute temperature, if T1 = 273 °C, which curve represents T = 373 °C?
curve A
curve B
curve T1
G/ Real Gases (5.7)
Recall: PV = nRT
Or for 1 mole of gas PV = RT
PV/RT = 1
Now let’s measure PV/RT for 1 mole of gas sample and repeat at various P (Fig 5.21)
Note: PV/RT doesn’t always equal 1
ie. gases don’t always act “ideally”; instead they are “real gases”.
i>clicker question:
Given that the assumptions of KMT describe an ideal gas, what situation would result in non-ideal behaviour?
a dilute gas
a concentrated gas
i>clicker question:
Therefore which conditions would result in non-ideal behaviour?
High T, High P
High T, Low P
Low T, Low P
Low T, High P
Where (under what conditions) do gases tend to deviate from ideal behavior?
Answer: at higher P (also at lower T)
Why? Again consider KMT
KMT says “There are no forces acting between molecules”
But as P increases, the molecules are forced closer together and the begin to “feel” one another; the intermolecular forces are no longer negligible
Causes PV/RT < 1
Also as the molecules move closer together, the volume of the molecules themselves becomes important ie. the sample no longer consists of “molecules separated by relatively great distances”.
Causes PV/RT > 1
Likewise at low T, the molecules slow down and begin to feel each other’s presence …
