Tip:
Highlight text to annotate it
X
An exercise to the ideal gas law.
Reminder:
the ideal gas law summarizes the laws of Boyle-Mariotte,
CHARLES, Gay-Lussac
and Avogadro together in
p = n * R * T / V;
It is the state equation
an ideal gas.
For gas mixtures DALTON Partialddruck introduced the so-called p (i),
of themselves as
p (i) = y (i) * p (ges) total pressure p (saturated) by mole fraction y (i)
the respective
Component i
In a container there are nitrogen and oxygen.
It should
- The density of this mixture - the molar volume and
- The average translational energy
The nitrogen molecules
be calculated.
We outline the two-component system
Blue for oxygen
Green for
Nitrogen
Mass of nitrogen: 2.8 g Mass of oxygen: 3.2 g
We expect the masses in quantities by (n = m / M) and obtain
n (O2) = 0.1 mol
N and nitrogen (N2) = 0.1 mol
Oxygen.
In this equimolar mixture
is the mole fraction
(The mole fraction y)
of nitrogen and 50 mol% of oxygen. y (N2) = y (O2) = 0.5
After the
Dalton's
Law
calculate the partial pressure:
(In each case half of the total pressure of nitrogen and oxygen)
p (N2) = 50 000 Pa
for nitrogen and p (O2) = 50 000 Pa for oxygen.
The molar volume (molar volume), we obtain
according to the ideal gas equation V = nRT / p.
We use n to the total molar amount of all gases, or 0.2 mol, a.
The ideal gas constant in SI units is 8.314 J / (mol * K)
the standard temperature of 298.15 K and 100 000 Pa is
the standard pressure. The volume of the mixture
is 0.00496 cubic meters or
4.96 liters.
Approx. 5 liters to 0.2 mol, corresponding to a
Molar volume V / n of 0.0248 m³ / mol or 24.8 L / mol.
(About 25 liters)
(Each and every ideal gas ideal gas mixture has at standard conditions
the molar volume
24.8 L / mol)
Density is defined as the mass of MoluMen rho = m / V
The Gesamtmassse is 6 g,
the volume is 4.96 liters,
so that the density is calculated as 1.2 g / L, or
1.2 kg / m³.
One can
Charge density as a quotient of the molar mass and molar volume.
For gas mixtures, the average molecular weight is needed
the average molecular weight
calculated
with 2 components as
Mole fraction of component 1 * molar mass of component 1
plus mole fraction of component 2 * molar mass of component 2
For our gas mixture which results in an average molecular weight of from 30 g / mol.
We divide by
the molar volume and get back 1.2 g / L.
(Grams per liter)
To the velocity distribution
of the gas after the
Maxwell-Boltzmann theory
to calculate, we need mass and temperature.
(Here the distribution of nitrogen and different temperatures)
To calculate the average energy
is only required temperature. In fact, the temperature of the kinetic theory of gases
a measure of the average translational energy
and
with the relation E (trans) = 3/2 * Boltzmann constant * T
we obtained at room temperature (298 K)
an average translational energy of 0.04 eV
This value applies to the nitrogen and to the particles
Oxygen ponds.
For one mole we obtain (by multiplication by the Avogadro number)
3.72 kilojoules for the
thermal (translational) energy.