Chapter 5
(Essentials of General Chemistry, 2nd Edition)
(Ebbing and Gammon)
The Gaseous State
Gas Pressure and its Measurement
pressure
- the force exerted per unit area of surface
eg. calculate pressure on table from penney
(9.3 mm radius and 2.5 g mass)
Force = mass x constant acceleration of gravity
= (2.5 x 10-3 kg) x (9.81 m/s2)
= 2.5 x 10-2 kg · m/s2
-cross-sectional area of the coin is
x (radius)2 = 3.14 x (9.3 x 10-3)2
= 2.7 x 10-4 m2
Pressure = force = 2.5 x 10-2 kg · m/s2 = 93 kg/(m·s2)
area
2.7 x 10-4 m2
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pascal
2
SI unit of pressure
- kg/(m·s2)
- extremely small unit, therefore often use kPa
barometer
- a device for measuring the pressure of the
atmosphere
manometer
- a device that measures the pressure of a gas or
liquid in a vessel
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Figure 5.2
Mercury Barometer
Figure 5.3
A Flask Equipped with
a Closed-Tube Manometer
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millimeters of mercury (mmHg) or torr
- unit of pressure equal to that exerted by a column of
mercury 1 mm high at 0.00oC
atmosphere (atm)
- related unit of pressure equal to exactly 760 mmHg
Note: - the general relationship between pressure, P, and
height, h, of a liquid column in a barometer or
manometer is
P = gdh
where: g = constant acceleration of gravity (9.81 m/s2)
d = density of liquid in manometer
- if g, d and h are is SI units pressure is in pascals
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Relationship between Pressure Units
Table 5.1
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Empirical Gas Laws
- four quantities required to describe gaseous state:
a.) quantity of a gas, n (in moles)
b.) temperature of gas, T (in K = oC + 273.15)
c.) volume of gas, V (L)
d.) pressure of gas, P (atm)
- relationships among these four variables are
called the gas laws
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Boyle s Law
- the volume of a sample of gas at a given temperature
varies inversely with the applied pressure
Note: volume
decreases as pressure
increases
V
1
P
PV = constant
for a fixed n and T
** an inverse
proportionality
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- use Boyle s law to calculate volume occupied by gas when
pressure changes
PfVf = PiVi
dividing both sides of the equation gives
Vf = Vi x Pi
Pf
Note: pressure-volume product for gas is not precisely
constant
** in fact, all gases follow Boyle s law at low to
moderate pressures but deviate from this law at
high pressures
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Relating Volume and Temperature
A balloon immersed in
liquid nitrogen shrinks.
Balloon removed from
liquid nitrogen, it
expands to its original
size.
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Charles Law
- sample of gas at fixed pressure increases in volume
linearly with absolute temperature
Note: volume increases
as temperature
increases
V
T
or V = constant
T
for a fixed n and P
** a direct proportionality
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- consider a sample of gas at fixed pressure, suppose
the temperature changes from its initial Ti to a final
temperature of Tf
- since volume divided by absolute temperature is
constant, you can write
Vf = Vi
Tf
Ti
Or rearranging,
Vf = Vi x Tf
Ti
Note: to obtain final volume, multiply the initial volume by
a ratio of absolute temperature
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Combined Gas Law
- relating volume, temperature and pressure
- Boyle s law and Charles law combined and
expressed in a single equation
PfVf = PiVi
Tf
Ti
which arranges to
Vf = Vi x Pi x Tf
Pf
Ti
- the final volume is obtained by multiplying the initial
volume by the ratio of pressures and absolute
temperatures
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Avogadro s Law
- equal volumes of any two gases at the same temperature
and pressure contain the same number of molecules
2 H2 (g) + O2 (g)
2 volumes
2 H2O (g)
1 volume
- therefore, two volumes of hydrogen contain twice as
many molecules as one volume of oxygen, in agreement
with the chemical equation for the reaction
- one mole of every gas contains the same number of
molecules (Avogadro s number = 6.02 x 1023)
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V
n
or V = constant
n
at constant T and P
** a direct
proportionality
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**equal volumes of different gases at
the same temperature and
pressure contain the same molar
amounts
molar gas volume
- volume of one mole of gas
standard temperature and pressure (STP)
- reference conditions for gases chosen by convention to
be 0oC and 1 atm pressure
Standard Molar Volume (Vm = 22.4 L)
- 1 mol of any gas occupies a volume of 22.4 L at 0oC and
1.0000 atm pressure
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The Ideal Gas Law
Ideal Gas Law - combination of the 3 individual gas
laws
PV = nRT
R = a proportionality constant - ideal gas constant
(is independent of P, V, n, T or identity of gas)
- includes all the information contained in Boyle s,
Charles and Avogadro s laws
- starting with the ideal gas law, you can derive any of
the other gas laws
Note: like all of the previous gas laws, ideal gas law is most
accurate for low or moderate pressures and for
temperatures that are not too low
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Calculations Using the Ideal Gas Law
- type of problem to which Boyle s and Charles laws
are applied involves a change in conditions (P, V or T)
of a gas
- Ideal gas law enables us to solve another type of
problem: given any three of the quantities P, V, n and
T, calculate the unknown quantity
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Gas Density; Molecular-Weight Determination
- from the ideal gas law, you can obtain an explicit
relationship between the molecular weight and the
density of a gas
- recall that: Mm = m/n
when expressed in grams per mole is numerically
equal to the molecular weight
- rearranging to give n = m/Mm and substituting into
the ideal gas law, you obtain
PV = m RT
or
PMm = mRT
Mm
V
- but, since d = m/V then
PMm = dRT
Mm in g/mol and R in L·atm/(K·mol) gives density
in g/L
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Stoichiometry Problems: Gas Volumes
Problems will be discussed in class.
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Gas Mixtures; Law of Partial Pressures
John Dalton (1801)
- concluded that each gas in a mixture of unreactive
gases acts, as far as its pressure is concerned, as
though it were the only gas in the mixture
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Partial Pressures and Mole Fractions
partial pressure
- the pressure exerted by a particular gas in a mixture
Dalton s law of partial pressures
- the sum of the partial pressures of all the different
gases in a mixture is equal to the total pressure of the
mixture
mathematically,
P T = PA + P B + PC + . . .
Note: individual partial pressures follow the ideal gas law, so
for component A
PAV = NART
where NA = number of moles of component A
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- composition of a gas mixture is often described in terms
of the mole fraction of the component gas
mole fraction of a component gas
- the fraction of moles of that component in the total
moles of gas mixture
- since the pressure of a gas is proportional to moles,
the mole fraction also equals the partial pressure
divided by the total pressure
mole fraction of A = nA = PA
nT
PT
mole percent
- is equivalent to the percentage of the molecules that
are component molecules
mole % = mole fraction x 100
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