CHE 110 Chapter Notes - Chapter 5: Prussian P 8, Mass Spectrum, Number Density
7 May 2018
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Chapter 5: Gases
I. Substances that Exist as Gases
1) Only 11 elements are gases under normal atmospheric conditions
1. Hydrogen
2. Nitrogen
3. Oxygen (O2) and Ozone (O3)
4. Fluorine
5. Chlorine
6. Helium
7. Neon
8. Argon
9. Krypton
10. Xenon
11. Radon
2) Physical Characteristics of Gases
1. Assume volume and shape of their containers
2. Most compressible of the states of matter
3. Mix evenly and completely when confined to the same container
4. Have much lower densities than liquids and solids
II. Pressure of a Gas
1) SI Units of Pressure
1. Velocity: the change in distance with elapsed time; unit (m/s or cm/s)
velocity=distance moved
elapsed time
2. Acceleration: the change in velocity with elapsed time; unit newton (N)
acceleration=change in velocity
elapsed time
3. Pressure: the force applied per unit area; unit (atm)
pressure=force
area
2) Atmospheric Pressure
1. Density of air decreases very rapidly with increasing distance from the earth
2. Atmospheric Pressure: the pressure exerted by Earth’s atmosphere
1) Actual value depends on location, temperature, and weather conditions
3. Barometer: instrument used for measuring atmospheric pressure
4. Standard Atmospheric Pressure: 1 atm; equal to the pressure that supports a
column of mercury at exactly 760 mm high at 0 degrees C.
1) Standard atmosphere = pressure of 760 mmHg
2) mmHg = pressure exerted by a column of mercury 1 mm high
3) mmHg unit is also called the torr
atm= mmHg= torr
atm=, Pa=. x 5 Pa
5. Manometer: device used to measure the pressure of gases other than the
atmosphere
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1) Closed-tube manometer: normally used to measure pressures below
atmospheric pressure
2) Open-tubed manometer: normally used to measure pressures equal to
or greater than atmospheric pressure
III. The Gas Laws
1) Boyle’s Law: The Pressure-Volume Relationship
1. The pressure of a fixed amount of gas maintained at constant temperature is
inversely proportional to the volume of the gas
2. The product of the pressure and volume of a gas at constant temperature and
amount of gas is a constant PV=PV
2) Charles Law: The Temperature-Volume Relationship
1. The volume of a fixed amount of gas maintained at a constant pressure is
directly proportional to the temperature of the gas
2. Absolute Zero: theoretically the lowest attainable temperature
3. Absolute Temperature Scale (Kelvin Temperature Scale): absolute zero is the
starting point; one kelvin (K) is equal in magnitude to 1 degree of Celsius (C).
?K=℃+. ℃ K
℃
V
T=V
T
P
T=P
T
3) Avogadro’s Law: The Volume-Amount Relationship
1. At the same temperature and pressure, equal volumes of different gases contain
the same number of molecules (or atoms)
2. Avogadro’s Law: at constant pressure and temperature, the volume of a gas is
directly proportional to the number of moles of the gas present
IV. The Ideal Gas Equation
1) Summary of Gas Laws
1. Boyle’s Law Volume is proportional to 1/Pressure
2. Charles Law Volume is proportional to temperature
3. Avogadro’s Law Volume is proportional to the number of moles
2) Combining the 3 Gas Laws
1. The three equations can be combined to form a single master equation for the
behavior of gases
1) Volume is proportional to number of moles times temperature divided
by pressure
2) Volume is equal to the product of number of moles and temperature
divided by pressure, all multiplied by the constant R
V=RnT
P
3) The product of pressure and volume is equal to the product of number
of moles, the constant R, and temperature.
PV=nRT
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2. Variables in the Single Master Equation for the Behavior of Gases
1) R = the gas constant
2) V = volume
3) n = number of moles
4) P = pressure
5) T = temperature
3) Ideal Gas Equation: describes the relationships among the four variables pressure,
volume, number of moles, and temperature.
PV=nRT
1. Ideal Gas: hypothetical gas whose pressure-volume-temperature behavior can
be completely accounted for by the ideal gas equation
2. There is no such thing as an “ideal gas” but discrepancies in the behavior of
real gases over reasonable temperature and pressure ranges do not significantly
affect calculations
3. We can safely use the ideal gas equation to solve many gas problems
4) Modified Ideal Gas Equation: allows us to deal with changes in pressure, volume, and
temperature R=PV
nT before changes and R=PV
nT after changes
PV
T=R=PV
T
PV
T=PV
T
5) Standard Temperature Pressure (STP): the conditions at 0℃ and 1 atm.
6) The Constant R is the ideal gas constant.
R=.L ∙ atm
K ∙ mol
1. The dots between L and atm and K and mol remind us that both L and atm are
in the numerator and both K and mol are in the denominator.
2. We use 22.4 L for the molar volume of a gas at STP
7) Density and Molar Mass of a Gaseous Substance
1. The ideal gas equation can be applied to determine the density or molar mass
of a gaseous substance. n
V=P
RT
2. Variables
1) n = number of moles n=m
�
2) m = mass in grams
3) M = molar mass m
MV=P
RT
4) d = mass per unit volume
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Document Summary
Substances that exist as gases: only 11 elements are gases under normal atmospheric conditions. K mol nv= prt: n = number of moles n=m mmv= prt, m = mass in grams, m = molar mass, d = mass per unit volume, variables d= mv=pmrt. Amount of reactant moles of reactant moles of product amount of product. As volume increases, pressure decreases: charles"s law, because the average kinetic energy of gas molecules is proportional to the sample"s absolute temperature: Raising the temperature increases the average kinetic energy. Larger number of molecules are moving at a greater speed: differences in speed distribution curve at the same. Explained by noting that lighter molecules move faster than heavier molecules: root-mean-square speed, answers the question: how fast does a molecule move, on average, at any temperature t, root-mean-square (rms) speed: an average molecular speed. The intermolecular interaction that gives rise to non- ideal behavior depends on how frequently any two molecules approach each other closely.
