Transcript Chapter 10: Gases - Bergen County Technical Schools

Chapter 10
Gases
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Characteristics of Gases
• Unlike liquids and solids, gases:
– Expand to fill their containers.
– Are highly compressible.
– Have extremely low densities.
Gases
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A. Small molecular weights
B. Large molecular weights
Gases
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Pressure
• Pressure is the
amount of force
applied to an area:
F
P=
A
• Atmospheric
pressure is the
weight of air per
unit of area.
Gases
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A.
B.
C.
D.
100 kPa/ 100 in.2
1x 105 N x 100 in.2
14.7 psi x 100 in.2
14.7 psi/ 100 in.2
Gases
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Units of Pressure
• Pascals
– 1 Pa = 1 N/m2
• Bar
– 1 bar = 105 Pa = 100 kPa
Gases
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Units of Pressure
• mmHg 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
Gases
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A. Increases
B. Decreases
Gases
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Manometer
The manometer is used
to measure the
difference in pressure
between atmospheric
pressure and that of a
gas in a vessel.
Gases
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Standard Pressure
• Normal atmospheric pressure at sea level
is referred to as standard pressure.
• It is equal to
– 1.00 atm
– 760 torr (760 mmHg)
– 101.325 kPa
Gases
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Sample Exercise 10.1 Converting Pressure Units
(a) Convert 0.357 atm to torr.
(b) Convert 6.6  102 torr to atmospheres.
(c) Convert 147.2 kPa to torr.
Practice Exercise
(a) In countries that use the metric system, atmospheric pressure in weather reports is given in kilopascals.
Convert a pressure of 745 torr to kilopascals. (b) The pressure at the center of Hurricane Katrina was
902 mbar (millibars). There are 1000 mbar in 1 bar; convert this pressure to atmospheres.
Gases
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Sample Exercise 10.2 Using a Manometer to Measure Gas
Pressure
On a certain day a laboratory barometer indicates that the atmospheric
pressure is 764.7 torr. A sample of gas is placed in a flask attached to an
open-end mercury manometer ( FIGURE 10.3), and a meter stick is used
to measure the height of the mercury in the two arms of the U tube. The
height of the mercury in the open-end arm is 136.4 mm, and the height in
the arm in contact with the gas in the flask is 103.8 mm. What is the
pressure of the gas in the flask (a) in atmospheres, (b) in kilopascals?
Practice Exercise
Convert a pressure of 0.975 atm into Pa and kPa.
Gases
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A. Increases
B. Decreases
Gases
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Boyle’s Law
The volume of a fixed quantity of gas at
constant temperature is inversely proportional
to the pressure.
Gases
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A.
B.
C.
D.
0 torr
760 torr
1140 torr
1520 torr
Gases
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P and V are Inversely Proportional
Since
PV = k
A plot of V versus P results in a curve.
V = k (1/P)
This means a plot of V versus 1/P will be a
straight line.
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Gases
A. Polynomial curve of third order
B. Quadratic
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C. Exponential
D. Linear
Gases
A.
B.
C.
D.
Increases by doubling its original value.
Increases by tripling its original value.
Decreases to half of its original value.
Decreases to a fourth of its original value.
Gases
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Charles’s Law
• The volume of a fixed
amount of gas at
constant pressure is
directly proportional to its
absolute temperature.
Gases
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Charles’s Law
• So,
V
=k
T
• A plot of V versus T
will be a straight line.
Gases
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A. Yes, because the temperature decreases
by half.
B. No, because the temperature in kelvin (K) does
not decrease by half.
Gases
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Avogadro’s Law
• The volume of a gas at constant temperature
and pressure is directly proportional to the
number of moles of the gas.
• Mathematically, this means
V = kn
Gases
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A.
B.
C.
D.
0.5
1
1.5
2
Gases
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Sample Exercise 10.3 Evaluating the Effects of Changes in P, V, n,
and T on a Gas
Suppose we have a gas confined to a cylinder with a movable piston. (Sections 5.2, 5.3) Consider the following
changes (assuming no leaks): (a) Heat the gas from 298 K to 360 K at constant pressure. (b) Reduce the volume
from 1 L to 0.5 L at constant temperature. (c) Inject additional gas, keeping temperature and volume constant.
Indicate how each change affects the average distance between molecules, the pressure of the gas, and the
number of moles of gas in the cylinder.
Practice Exercise
Recall that density is mass per volume. (Section 1.4) What happens to the density of a gas as (a)
the gas is heated in a constant-volume container; (b) the gas is compressed at constant
temperature; (c) additional gas is added to a constant-volume container?
Gases
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Ideal-Gas Equation
• So far we’ve seen that
V  1/P (Boyle’s law)
V  T (Charles’s law)
V  n (Avogadro’s law)
• Combining these, we get
nT
V
P
Gases
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Ideal-Gas Equation
The relationship
nT
V
P
Can be written as V = R nT
P
or
PV = nRT
Gases
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Ideal-Gas Equation
The constant of
proportionality is
known as R, the
gas constant.
Gases
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Ideal-Gas Equation
• But how is R determined?
• At STP (0°C, 1 atm) the volume of 1
mol of a gas = 22.41L
PV (1.0atm)(22.41L)
Latm
R

 0.08206Kmol
nT (1m ol)(273.15K )
Gases
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A. 6.023 x 1023 molecules
B. 22.4 x 6.023 x 1023 molecules
1
C.
x 6.023 x 1023 molecules
22.4
D. 3.012 x 1023 molecules
Gases
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A.
B.
C.
D.
Helium is an inert gas.
Helium is a member of the first period.
Helium is a very small atom and inert.
Helium possesses two valence electrons.
Gases
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Sample Exercise 10.4 Using the Ideal-Gas Equation
Calcium carbonate, CaCO3(s), the principal compound
in limestone, decomposes upon heating to CaO(s) and
CO2(g). A sample of CaCO3 is decomposed, and the
carbon dioxide is collected in a 250-mL flask.
After decomposition is complete, the gas has a pressure
of 1.3 atm at a temperature of 31 C. How many moles
of CO2 gas were generated?
Practice Exercise
Tennis balls are usually filled with either air or N2 gas to a pressure above atmospheric pressure to increase
their bounce. If a tennis ball has a volume of 144 cm3 and contains 0.33 g of N2 gas, what is the pressure
inside the ball at 24 C?
Gases
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Sample Exercise 10.5 Calculating the Effect of Temperature
Changes on Pressure
The gas pressure in an aerosol can is 1.5 atm at 25 C. Assuming that the gas obeys the ideal-gas equation,
what is the pressure when the can is heated to 450 C?
Practice Exercise
The pressure in a natural-gas tank is maintained at 2.20 atm. On a day when the temperature is –15 C, the
volume of gas in the tank is 3.25  103 m3. What is the volume of the same quantity of gas on a day when
the temperature is 31 C?
Gases
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Sample Exercise 10.6 Calculating the Effect of Changing P and T
on Gas Volume
An inflated balloon has a volume of 6.0 L at sea level (1.0 atm) and is allowed to ascend until the pressure is
0.45 atm. During ascent, the temperature of the gas falls from 22 C to 21 C. Calculate the volume of the
balloon at its final altitude.
Practice Exercise
A 0.50-mol sample of oxygen gas is confined at 0 C and 1.0 atm in a cylinder with a movable piston. The piston
compresses the gas so that the final volume is half the initial volume and the final pressure is 2.2 atm. What is the
final temperature of the gas in degrees Celsius?
Gases
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Gas Stoichiometry – ΔP Problems
• When a reaction occurs at constant
volume, the change in the pressure can be
used to number of moles reacted and/or
formed.
n( RT )
P
V
n( RT )
P 
V
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Gases
Gas Stoichiometry – ΔP Problems
A small amount of butane is mixed with air in a
rigid container. The mixture, initially at 1.00 atm., is
ignited:
2C4H10(g) + 13 O2(g) → 8 CO2(g) + 10 H2O(g)
After the sample is completely combusted, and
cooled to the initial temperature, the pressure is
now 1.12 atm. What is the initial pressure of the
butane?
Gases
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Solution
P  Pfinal  Pinitial
 1.12atm  1.00atm  0.12atm
PressureC4 H10 molesC4 H10 used 2


P
 molesgas
3
P ressureC4 H 10  P 
 (0.12 atm) 
2
3
2
 0.080 atm
3
Check your work with an ice chart!
Gases
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Densities of Gases
If we divide both sides of the ideal-gas
equation by V and by RT, we get
n
P
=
V
RT
Gases
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Densities of Gases
• We know that
– Moles  molecular mass = mass
n=m
• So multiplying both sides by the
molecular mass () gives
m P
=
V RT
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Gases
Densities of Gases
• Mass  volume = density
• So,
m P
d=
=
V RT
Note: One needs to know only the
molecular mass, the pressure, and the
temperature to calculate the density of
a gas.
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Gases
Molecular Mass
We can manipulate the density equation
to enable us to find the molecular mass
of a gas:
P
d=
RT
becomes
dRT
= P
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Gases
A. More dense
B. Less dense
Gases
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Sample Exercise 10.7 Calculating Gas Density
What is the density of carbon tetrachloride vapor at 714 torr and 125 C?
Practice Exercise
The mean molar mass of the atmosphere at the surface of Titan, Saturn’s largest moon, is 28.6 g/mo. The surface
temperature is 95 K, and the pressure is 1.6 atm. Assuming ideal behavior, calculate the density of Titan’s
atmosphere.
Gases
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Sample Exercise 10.8 Calculating the Molar Mass of a Gas
A large evacuated flask initially has a mass of
134.567 g. When the flask is filled with a gas of
unknown molar mass to a pressure of 735 torr at 31 C,
its mass is 137.456 g. When the flask is evacuated again
and then filled with water at 31 C, its mass is
1067.9 g. (The density of water at this temperature is
0.997 g/mL.) Assuming the ideal-gas equation
applies, calculate the molar mass of the gas.
Practice Exercise
Calculate the average molar mass of dry air if it has a density of 1.17 g/L at 21 C and 740.0 torr.
Gases
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Sample Exercise 10.9 Relating a Gas Volume to the Amount of
Another Substance in a Reaction
Automobile air bags are inflated by nitrogen gas
generated by the rapid decomposition of sodium azide,
NaN3:
2 NaN3(s)  2 Na(s) + 3 N2(g)
If an air bag has a volume of 36 L and is to be filled
with nitrogen gas at 1.15 atm and 26.0 C, how many
grams of NaN3 must be decomposed?
Practice Exercise
In the first step in the industrial process for making nitric acid, ammonia reacts with oxygen in the presence
of a suitable catalyst to form nitric oxide and water vapor:
4 NH3(g) + 5 O2(g)  4 NO(g) + 6 H2O(g)
How many liters of NH3(g) at 850 C and 5.00 atm are required to react with 1.00 mol of O2(g) in this reaction?
Gases
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A.
B.
C.
D.
The pressure exerted by N2 gas does not change when O2 is
added to the container.
The pressure exerted by N2 gas changes only if an equal or
greater amount of O2 is added to the container.
The pressure exerted by N2 gas decreases when O2 is added
to the container.
The pressure exerted by N2 gas increases when O2 is added
to the container.
Gases
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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.
• In other words,
Ptotal = P1 + P2 + P3 + …
Gases
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Sample Exercise 10.10 Applying Dalton’s Law of Partial Pressures
A mixture of 6.00 g O2(g) and 9.00 g CH4(g) is placed in a 15.0-L vessel at 0 C. What is the partial pressure
of each gas, and what is the total pressure in the vessel?
Practice Exercise
What is the total pressure exerted by a mixture of 2.00 g of H2(g) and 8.00 g of N2(g) at 273 K
in a 10.0-L vessel?
Gases
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Sample Exercise 10.11 Relating Mole Fractions and Partial
Pressures
A study of the effects of certain gases on plant growth
requires a synthetic atmosphere composed of 1.5 mol
percent CO2, 18.0 mol percent O2, and 80.5 mol
percent Ar. (a) Calculate the partial pressure of O2
in the mixture if the total pressure of the atmosphere is
to be 745 torr. (b) If this atmosphere is to be held in a
121-L space at 295 K, how many moles of O2 are
needed?
Practice Exercise
From data gathered by Voyager 1, scientists have estimated the composition of the atmosphere of Titan,
Saturn’s largest moon. The pressure on the surface of Titan is 1220 torr. The atmosphere consists of 82 mol
percent N2, 12 mol percent Ar, and 6.0 mol percent CH4. Calculate the partial pressure of each gas.
Gases
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Partial Pressures
• When one collects a gas over water, there is
water vapor mixed in with the gas.
• To find only the pressure of the desired gas,
one must subtract the vapor pressure of
water from the total pressure.
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Gases
Sample Exercise 10.12 Calculating the Amount of Gas Collected
over Water
When a sample of KClO3 is partially decomposed in the setup shown in Figure 10.15, 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?
Practice Exercise
Ammonium nitrite, NH4NO2, decomposes on heating to form N2 gas:
NH4NO2(s)  N2(g) + 2 H2O(l)
When a sample of NH4NO2 is decomposed in the apparatus
of Figure 10.15, 511 mL of N2 gas is collected over water
at 26 C and 745 torr total pressure. How many grams of
NH4NO2 were decomposed?
Gases
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Kinetic-Molecular Theory
This is a model that
aids in our
understanding of what
happens to gas
particles as
environmental
conditions change.
Gases
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Main Tenets of 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.
Gases
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Main Tenets of Kinetic-Molecular
Theory
Energy can be
transferred between
molecules during
collisions, but the
average kinetic energy
of the molecules does
not change with time, as
long as the temperature
of the gas remains
constant.
Gases
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Main Tenets of Kinetic-Molecular
Theory
The average kinetic
energy of the
molecules is
proportional to the
absolute
temperature.
Gases
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A.
B.
C.
D.
1/10
1/3
1/2
2/3
Gases
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A. Additional pressure information is needed to
compare average speeds.
B. HCl < O2 < H2
C. HCl < H2 < O2
D. H2 < O2 < HCl
Gases
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Sample Exercise 10.13 Applying the Kinetic-Molecular Theory
A sample of O2 gas initially at STP is compressed to a smaller volume at constant temperature. What effect does this
change have on (a) the average kinetic energy of the molecules, (b) their average speed, (c) the number of collisions
they make with the container walls per unit time, (d) the number of collisions they make with a unit area of container
wall per unit time?
Practice Exercise
How is the rms speed of N2 molecules in a gas sample changed by (a) an increase in temperature,
(b) an increase in volume, (c) mixing with a sample of Ar at the same temperature.
Gases
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The Meaning of Temperature
(KE)avg
3
 RT
2
Kelvin temperature is an index of the random
motions of gas particles (higher T means greater
motion.)
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58
Gases
Kinetic Molecular Theory
• Root mean square speed is an average
molecular speed
• For one mole of a gas KE = 3/2 RT
• For one molecule
KE  1 2 mu 2
• Therefore
N A 1 2 mu 2  3 2 RT
3RT
u 

2
u  urms
2
3RT


where R  8.3145J
K  m ol
Gases
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A. At constant T, root-mean-square speeds increase with increasing
molar masses.
B. At constant T, root-mean-square speeds increase with decreasing
molar masses.
Gases
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Sample Exercise 10.14 Calculating a Root-Mean-Square Speed
Calculate the rms speed of the molecules in a sample of N2 gas at 25 C.
Practice Exercise
What is the rms speed of an atom in a sample of He gas at 25 C?
Gases
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Kinetic Molecular Theory
• The most probable speed of a gas can also be
determined:
ump
2RT


Gases
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A.
B.
C.
D.
2/3
1
3/2
2
Gases
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Graham's Law
r1  rms 1


r2  rms 2
3RT
M1
3RT
M2

M2
M1
Gases
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Effusion
Effusion is the
escape of gas
molecules
through a tiny
hole into an
evacuated
space.
Gases
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Effusion
The difference in the rates of effusion for
helium and nitrogen, for example, explains
why a helium balloon would deflate faster.
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Gases
A. R
B. n
Gases
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Sample Exercise 10.15 Applying Graham’s Law
An unknown gas composed of homonuclear diatomic molecules effuses at a rate that is 0.355 times the rate at
which O2 gas effuses at the same temperature. Calculate the molar mass of the unknown and identify it.
Practice Exercise
Calculate the ratio of the effusion rates of N2 gas and O2 gas.
Gases
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Diffusion
Diffusion is the
spread of one
substance
throughout a space
or throughout a
second substance.
Gases
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A.
B.
C.
D.
Increasing P
Increase
Decrease
Increase
No change
Increasing T
Increase
No change
Decrease
Decrease
Gases
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Diffusion
When two cottons plugs soaked in ammonia and hydrochloric acid are
simultaneously placed at the ends of a long tube, a white ring forms
where the NH3 and HCl molecules meet.
The calculated ratio is actually greater than the ratio determined from
careful experiments. Why?
Gases
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Real Gases
In the real world, the
behavior of gases
only conforms to the
ideal-gas equation
at relatively high
temperature and low
pressure.
Gases
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A. Always
B. Never
C. Mostly not
Gases
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Real Gases
Even the same gas
will show wildly
different behavior
under high pressure
at different
temperatures.
Gases
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Gases
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A. 100 K and 1 atm
B. 100 K and 5 atm
C. 300 K and 2 atm
Gases
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Deviations from Ideal Behavior
The assumptions made in the kinetic-molecular
model (negligible volume of gas molecules
themselves, no attractive forces between gas
molecules, etc.) break down at high pressure
Gases
and/or low temperature.
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A. Increase
B. Decrease
C. No change
Gases
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A.
B.
C.
D.
Gases deviate from ideal behavior if their molar mass
exceeds that of H2O and temperature is lower than 298 K.
Gases deviate from ideal behavior if the pressure is below 1
am and temperature is lower than 298 K.
Gases deviate from ideal behavior because the molecules
have finite sizes and there are some attractions between the
molecules.
Gases deviate from ideal behavior if their normal boiling
points are below room temperature and greater than the
freezing point of H2O.
Gases
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Corrections for Nonideal Behavior
• The ideal-gas equation can be adjusted
to take these deviations from ideal
behavior into account.
• The corrected ideal-gas equation is
known as the van der Waals equation.
n2a
(P + 2 ) (V − nb) = nRT
V
Gases
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The van der Waals Equation
n2a
(P + 2 ) (V − nb) = nRT
V
Gases
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Sample Exercise 10.16 Using the van der Waals Equation
If 1.000 mol of an ideal gas were confined to 22.41 L at
0.0 C, it would exert a pressure of 1.000 atm. Use the van der
Waals equation and Table 10.3 to estimate the pressure
exerted by 1.000 mol of Cl2(g) in 22.41 L at 0.0 C.
Practice Exercise
A sample of 1.000 mol of CO2(g) is confined to a 3.000-L container at 0.000 C. Calculate the
pressure of the gas using (a) the ideal-gas equation and (b) the van der Waals equation.
Gases
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