Transcript Gas Mixtures Dalton’s Law

Gas Mixtures
Dalton’s Law
• So far: pure gases
• Many gases are actually mixtures of two or
more gases:
– air: O2, N2 , H2O, etc
• How do mixtures of gases behave?
Gas Mixtures--Partial Pressure
Gas Mixtures--Partial Pressure
P= 6 psi
O2 (g)
P= 8 psi
N2 (g)
P= 9 psi
CO2 (g)
Gas Mixtures--Partial Pressure
What happens when you put all three samples of gas
together into one container (the same size container as each
was in alone)?
P
•The gases form a homogeneous mixture.
•The pressure in the container increases, V and T stay the
same
– How do you know what the new pressure will be?
Gas Mixtures--Partial Pressure
• Each gas in a mixture behaves independently of the
other gases present.
– Each gas exerts its own pressure on the container.
• PO = pressure exerted by O2
• PN = pressure exerted by N2
2
• PCO2 = pressure exerted by CO2
2
Gas Mixtures--Partial Pressure
• Partial pressure: the pressure exerted by a particular
gas present in a mixture
• Dalton's Law of Partial Pressure: 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 + ………
Gas Mixtures--Partial Pressure
• Ptotal = PO + PN + PCO
2
2
• So for this example:
Ptotal = 6 psi + 8 psi + 9 psi
= 23 psi
2
Partial Pressure
• In other words, at constant T and V,
– Ptotal depends only on the total number of moles
of gas present
– Ptotal is independent of the type (or types) of gases
present.
Partial Pressure-Mole Fraction
• When describing a mixture of gases, it is useful to
know the relative amount of each type of gas.
• Mole fraction (X): a dimensionless number that
expresses the ratio of the number of moles of one
component compared to the total number of moles
in a mixture.
Mole Fraction
• If a gas mixture contains 5.0 mol O2 (g), 3.0 mol H2O
(g), and 12.0 mol N2 (g),
XO=
nO2
nt
=
5.0 mol
20.0 mol
= 0.25
• On the exam, you must be able to calculate the mole
fraction of each component of a gas mixture.
Partial Pressure
• The partial pressure of a gas in a mixture can be
found:
PA = XA Ptotal
where PA = partial pressure of gas A
XA = mole fraction of gas A
Ptotal = total pressure of mixture
Partial Pressure Calculation
A mixture of gases contains 0.51 mol N2, 0.28 mol H2, and 0.52
mol NH3. If the total pressure of the mixture is 2.35 atm, what is
the partial pressure of H2?
PH2 = XH2 Ptotal
0.28 mol
XH2=
0.28 mol + 0.51 mol + 0.52 mol
PH2 = 0.21 x 2.35 = 0.50 atm
= 0.21
Dalton’s law of Partial Pressure
The simple gas laws and idea gas law apply to individual gases as well as to a mixture of
nonreactive gases.
What is responsible for the pressure in a gas mixture?
Since the pressure of pure gas at constant V and T is proportional to its amount
(P=nRT/V), the pressure contribute from each individual gas in a mixture is also its amount
in the mixture.
In other words, the total pressure exerted by a mixture of gases in a container at constant
V and T is equal to the sum of the partial pressure of each individual gas in the container,
a statement known as Dalton’s law of partial pressure
Ptot = PA + PB+ PC….at constant V and T
Where PA, PB, PC …. refer to the pressure each individual
were alone.
gas would have if it
Dalton’s law of partial pressures
The pressure exerted by a particular gas in a mixture, PA, PB, PC is called partial pressure
and refer to the pressure each individual gas would exert if it were alone in the container.
That is,
PA = nA RT
Vtot
PB = nB RT
Vtot
PC = nC RT
Vtot
......and so forth.
Since all the gases in the mixture have the same T and V
Ptot = (nA +nB + nC +....) RT
Vtot
Here V = VA =VB = V tot
The Concentration of any individual component in a gas mixture is usually expressed as
mole fraction (X). The mole fraction of a component in a mixture is the fraction of moles
of that component in the total moles of gas mixture.
Mole fraction (X) =
Moles of component
Total moles in mixture
The mole fraction of component A , for example, is
nA
XA =
nA+ nB + nC + .....
=
nA
ntotal
But since n= PV/RT, we can also write
XA =
PA Vtot
RT
Vtot
Ptot
RT
=
PA
Ptot
Which can be rearrange to solve PA, the partial pressure of component A:
PA = XA ·Ptot
At constant P and T, where P = PA =PB = PC = Ptot, the volume of each gas would
individually occupy at a pressure equal to Ptot is
VA = nART/Ptot ; VB =nBRT/Ptot … and so on.
Then since V = nRT/P, we can write
XA =
nA RT
Ptot
RT
ntot
Ptot
=
VA
Vtot
The mole fraction of component A is
XA =
nA
ntot
=
PA
Ptot
=
VA
Vtot