Transcript Warm-Up Problem!

Warm-Up Problem!
What volume of 0.175 M solution of KOH is needed
to titrate 30.0 mL of 0.200 M H2SO4?
Chapter 10 : Gases
Units of Pressure
• mm Hg or torr
These units are literally
the difference in the
heights measured in mm
(h) of two connected
columns of mercury.
• Atmosphere
1.00 atm = 760 torr
Manometer
Used to measure the
difference in pressure
between atmospheric
pressure and that of a gas
in a vessel.
Boyle’s Law
The volume of a fixed quantity of gas at constant
temperature is inversely proportional to the
pressure.
P1V1 = P2V2
Charles’s Law
• The volume of a fixed
amount of gas at constant
pressure is directly
proportional to its absolute
temperature.
V1 = V2
T1 T2
A plot of V versus T will be a straight line.
Avogadro’s Law
• The volume of a gas at constant temperature and
pressure is directly proportional to the number of
moles of the gas.
Relates V and moles
1 mol gas = 22.4 L gas, D ∝ MW
Ideal Gas Equation
V  1/P (Boyle’s law)
V  T (Charles’s law)
V  n (Avogadro’s law)
nT
V
P
PV = nRT
Warm-Up!
A sample of gas occupies a volume of 1248 ft3 at
0.988 atm and 28 °C.
Calculate the pressure of the gas if its volume is
decreased to 978 ft3 while its temperature is
held constant.
Calculating Density and Molecular
Weight!
dRT
n
P

=
=
P
V
RT
rearrange
to solve for MW
(x M=)
m P
=
V RT
(m/v=d)
P
d=
RT
Cumulative Problem!
An organic compound had the following
analysis: C, 55.8% by mass; H, 7.03%; O, 37.2%.
A 1.500 g sample was vaporized and was found
to occupy 530 cm3 at 100oC and 740 torr. What
is the molecular formula of the compound?
AP Question 1972
A 5.00 gram sample of a dry mixture of potassium
hydroxide, potassium carbonate, and potassium chloride
is reacted with 0.100 liter of 2.0 molar HCl solution.
(a)
A 249 milliliter sample of dry CO2 gas, measured at
22°C and 740 torr, is obtained from the reaction. What is
the percentage of potassium carbonate in the mixture?
(b)
The excess HCl is found by titration to be
chemically equivalent to 86.6 milliliters of 1.50 molar
NaOH. Calculate the percentages of potassium hydroxide
and of potassium chloride in the original mixture.
Warm –Up!
A Scuba divers tank contains 0.29 kg of oxygen
compressed into a volume of 2.3 L.
Calculate the pressure inside the tank at 9 °C.
What volume would this oxygen occupy at 26 °C
and 0.95 atm.
Agenda for Today
• Go back to 1972…
• Partial Pressure discussion
• Partial Pressure Practice Problems!
KOH + HCl  KCl + H2O
K2CO3 + 2HCl  2KCl + H2O + CO2
KCl + HCl  no reaction
1. Find % K2CO3 in original 5 g total solid
Use PV=nRT to find moles of CO2
.249 L * .974 atm = 0.01 moles CO2
.0821Latm/molK(295K)
0.01 moles CO2 x 1molK2CO3 = 0.01 mol K2CO3
1 mol CO2
0.01 mol K2CO3x 138g/mol = 1.38 g
Find percent mass = 1.38g K2CO3/5 g total solid = 27.6%
2. Find moles of original HCl  0.1L x 2 mol/L = 0.2 mols HCl total
3. Find moles of HCl  0.1 moles K2CO3 x 2 mol HCl = 0.02 moles HCl
reacted with K2CO3
1 mol K2CO3
4. Use NaOH titration to find unreacted HCl:
0.0866L NaOH x 1.5 mol = 0.13 moles NaOH = 0.13 moles HCl (b/c 1:1)
L
5. Find moles of HCl that reacted with KOH from steps 2, 3, and 4:
0.2 moles total – 0.02 moles reacted with K2CO3 - 0.13 moles excess = 0.05 moles HCl
6. Find grams of KOH: 0.05moles HCl x 1 mol KOH x 56.1 g KOH = 2.81g KOH
1 mol HCl 1 mol KOH
7. Find mass % KOH  2.81g KOH = 56.2 %
5g total
8. Find % KCl  100 - 56.2 - 27.6 = 16.1 % KCl
Dalton’s Law of Partial Pressures
• The total pressure of a mixture of gases
equals the sum of the pressures that each
would exert if it were present alone.
Ptotal = P1 + P2 + P3 + …
Partial Pressure Practice (say that 3 times fast)
What is the total pressure exerted by a mixture
of 2.00 g of hydrogen and 8.00 g of nitrogen at
273 K in a 10.0-L vessel?
Partial Pressure = Mole Fraction x Ptot
• What’s a mole fraction?
– The relationship between the moles of each gas to
the total moles of the gas mixture
n1/ntotal = c1
Use the mole fraction and total pressure to find
partial pressures!
P1 = c1 (Ptotal)
What is the mole fraction of oxygen in air?
Air = 78% nitrogen, 21% oxygen, 1% water vapor,
0.9% argon, and .04% carbon dioxide
Partial Pressures
• A mixture of 9.00 g of oxygen, 18 g of argon,
and 25 g of carbon dioxide exert a pressure of
2.45 atm. What is the partial pressure of
Argon in the mixture?
• What is the partial pressure of oxygen in air?
(Atmospheric pressure = 760 torr)
AP Multiple Choice Warm Up!!
•
A student pipetted five 25.00-milliliter samples of hydrochloric acid and
transferred each sample to an Erlenmeyer flask, diluted it with distilled water, and
added a few drops of phenolphthalein to each. Each sample was then titrated with
a sodium hydroxide solution to the appearance of the first permanent faint pink
color. The following results were obtained.
Volumes of NaOH Solution
First Sample..................35.22 mL
Second Sample..............36.14 mL
Third Sample.................36.13 mL
Fourth Sample..............36.15 mL
Fifth Sample..................36.12 mL
Which of the following is the most probable explanation for the variation in the
student's results?
(A) The burette was not rinsed with NaOH solution.
(B) The student misread a 5 for a 6 on the burette when the first sample was titrated.
(C) A different amount of water was added to the first sample.
(D) The pipette was not rinsed with the HCl solution.
(E) The student added too little indicator to the first sample.
Collecting Gases over Water
Ptotal = Pgas + PH2O
2KClO3(s)  2KCl(s) + 3O2(g)
The volume of gas collected is 0.250 L at 26°C and 765 torr total
pressure. (a) How many moles of O2 are collected? (b) How
many grams of KClO3 were decomposed? (The pressure of water
vapor at 26°C = 25 torr .)
Kinetic – Molecular Theory
• Gases consist of large numbers of molecules
that are in continuous, random motion.
• The combined volume of all the molecules of
the gas is negligible relative to the total
volume in which the gas is contained.
• Attractive and repulsive forces between gas
molecules are negligible.
• The collisions between molecules are perfectly
elastic.
• The average kinetic energy of the molecules is
proportional to the absolute temperature.
• Pressure is caused by collisions of
molecules with the walls of the
container!
– Magnitude of pressure is related to how
often and how forcefully the particles
strike the walls.
• Temperature of a gas is a measure of
the average kinetic energy of its
molecules!
– Motion increases with increasing
temperature.
• Why does pressure increase with
increasing temperature?
KE = 1/2mu2
√
M2
M1
√
M1
M2
r1 =
r2
t1 =
t2
Effusion Problem
• At a particular T and P, neon gas effuses at a
rate of 16 mol/s.
• (a.) What is the rate at which Ar effuses under
the same conditions?
• (b.) Under a different set of conditions, 3.0
mol of Ar effuse in 49.0 seconds. How long will
it take an equal amount of helium to effuse?
Deviation from Ideal Behavior
Real gases at high pressure are
like the mall at christmas.
Too many people in a small space,
people are on top of one another!
Compared to the space in the checkout
line, the people in front of you and behind
you have significant volume. Ugh…
If molecules are crowded in a container,
as pressure increases attractive
forces take over. Also the volume of the
gas particles are significant compared to
the volume of the container. NOT IDEAL!
Deviation from Ideal Behavior
At low temperature there is not
enough energy to overcome
attractive forces and the gas is
forced to condense into a liquid.
Ice is NOT an ideal gas…
The van der Waals Equation – corrects for non-ideal behavior
(P +
n2a
V2 ) (V − nb) = nRT
Non-Ideal Practice
Arrange the following gases in order of
increasing deviation from ideality:
H2O, CH4, Ne
WHY???