Chapter 10 Gases Second Half
The average kinetic energy of the gas molecules in a sample is equal to...
1/2 m(u_rms)²
Why is the direction of a gas molecule is constantly changing?
Because of molecular collisions.
Why do collisions occur?
Collisions occur because real gas molecules have a finite volume.
Relationship between a given amount of a particular gas to its partial pressure:
P1/Pt =n1/nt
Relating partial pressure to mole fraction
P1=(n1/nt ) Pt=X1 Pt
the mole fraction of N2 in air is 0.78—that is, 78% of the molecules in air are N2. This means that if the barometric pressure is 760 torr, the partial pressure of N2 is...
P_(N_2 )=(0.78)(760 torr)=590 torr
Van der Waals equation:
(P+(n² a)/V² )( V-nb)=nRT
If all the gases are at the same temperature and occupy the same volume, their total pressure equals...
Pt= n_t (RT/V)
If a gas is collected in a bottle that is initially filled with water ad inverted in a water pan, the pressure of the gas collected is measured by...
Ptotal=Pgas+P(H2O)
Partial Pressure
The pressure exerted by a particular component of a mixture of gases.
mole fraction of gas 1
The ratio n_1/n_t, which is denoted X_1.
Root-mean square (rms) speed u_rms:
The square root of the average of the squared speeds of the gas molecules in a gas sample.
Dalton's Law
The total pressure of a mixture of gases equals the sum of the pressure that each would exert if it were present alone.
Why are diffusion rates of gases through a volume of space are much lower than molecular speeds?
This difference is due to molecular collisions, which occur frequently for gas at atmospheric pressure.
True of False? The ideal gas law does not explain why gases behave the way they do.
True
Mole fraction X1 equation
X_1=(Moles of compound 1)/(total moles)=n_1/n_t
rms is the speed of a molecule possessing ...
a kinetic energy identical to the average kinetic energy of the sample.
Kinetic-molecular theory of gases:
a set of assumptions about the nature of gases; these assumptions, when translated into mathematical form, yield the ideal gas equation.
Why do Van der waals constants increase as molecular mass increases?
because molecules with larger molecular masses tend to have larger volumes and greater intermolecular forces.
Why does molecular motion increases with increasing temperature?
because the absolute temperature of a gas is a measure of its average kinetic energy.
Kinetic-molecular theory explains _____ and _______ at a molecular level.
both pressure and temperature
Kinetic-molecular theory of gases tells us that the pressure of a gas is cause by...
collisions of molecules with the walls of the container.
When gas molecules collide, momentum is...
conserved
Kinetic-molecular theory of gases: 1. Gases consist of a large number of molecules that are in ______ motion
continuous, random
An increase in volume at constant temperature causes pressure to...
decrease
As pressure increases, mean free path...
decreases
As volume increases, the number of collisions per unit of time...
decreases
The rate of effusion is ______ to the rms speed of the molecules.
directly proportional
As the temperature of a gas increase from around 200k to 1000k the negative deviation from the ideal value of 1...
disappears
Real gases _____(behavior) at high pressures.
do not behave ideally
A and b are van der waals constants and are quantity that are...
experimentally determined, positive quantities that differ from one gas to another.
For two gases at the same temperature, a gas composed of low-mass particles, such as He, has the same average kinetic energy as one composed of more massive particles, such as Xe. Consequently, the He particles must have _____ rms speed than the Xe particles.
higher
When pressure is sufficiently high, PV/RT is __ compared to the ideal gas prediction.
higher
Kinetic-molecular theory of gases tells us that the magnitude of pressure is determined by...
how often and how forcefully the molecules strike the walls of the container.
A temperature increase at constant volume causes pressure to...
increase
As molecular mass increases, Van der waals constants...
increase
As volume increases, distances between collisions...
increase
As Temperature increases, the number of collisions per unit of time...
increases
As molecular weight decreases, effusion rate...
increases
As pressure decreases, mean free path...
increases
As temperature increase, molecular motion...
increases
As temperature increases, kinetic energy...
increases
As temperature increases, momentum of molecules...
increases
As temperature increases, the range of molecular speeds...
increases
As temperature increases, the rms speeds of molecules, as well as their average speed...
increases
As temperature increases, u_rms...
increases
As the number and force of collisions increase, pressure...
increases
Because the molar mass appears in the denominator of the rms equation, as the mass of the gass decreases, the rms speed...
increases
as temperature decreases, the deviation from ideal behavior...
increases
The effusion rate of a gas is ____ to the square root of it molar mass.
inversely proportional
The mole fraction, AKA X (words)
is a dimensionless number that expresses the ratio of the number of moles of one component in a mixture to the total number of moles in the mixture.
The rms speed is ___to the average (mean) speed, u_av.
is not quite equal
At low pressures (generally below 10 atm) deviation from ideal behavior...
is small.
At high pressures (generally above 10 atm) the deviation from ideal behavior is...
large and different for each gas.
Actual gas pressure is ____than that predicted by the ideal gas law.
less
Because of attractive forces, the impact of a real gas molecule with the container wall is ___ compared to an ideal gas molecule.
less
at normal pressure, actual PV/RT is ___ compared the ideal gas prediction
less
The distributions of molecular speeds are shifted toward higher speeds for gases of...
lower molar masses
As temperature increases, the behavior of a real gas...
more nearly approach that of the ideal gas.
Kinetic-molecular theory of gases: 2. The combined volume of all the molecules of the gas is ______ relative to the total volume in which the gas is contained.
negligible
Kinetic-molecular theory of gases: 3. Attractive and repulsive forces between gases molecules are _______.
negligible
The molecules of an ideal gas are assumed to occupy ____ space and have ____ attraction for one another.
no, no
At high pressure the combined volume of the gas molecules is _____ relative to the container volume.
not negligible
If the rates of two gases are r1 and r2 and their molar masses are M1 and M2, Graham's Law states:
r1/r2 =√(M2/M1 )
Kinetic-molecular theory of gases: 4. If temperature remains constant, average kinetic energy _______.
remains constant
At high pressures, gas volumes tend to be _____ than those predicted by the ideal gas equation.
slightly higher
Kinetic-molecular theory of gases: 5. The average kinetic energy of a molecule is proportional to _________. At any given temperature, the molecules of all gases have the same ________.
the absolute temperature, kinetic energy
The van der waals equation adds pressure because...
the attractive forces between molecules tend to reduce pressure.
in the van der waals equation, (n² a)/V² accounts for...
the attractive forces.
Mean Free Path:
the average distance traveled by a molecule between collisions.
Effusions:
the escape of a gas through an orifice or a hole.
Van der Waals corrections: a
the measure of how strongly the gas molecules attract one another.
Van der Waals corrections: b
the measure of the finite volume occupied by the molecules.
In any graph of the distribution of molecular speeds in a gas sample, the peak of the curve represents...
the most probable speed, u_mp.
in the van der waals equation, the term nb accounts for...
the small but finite volume occupied by the gas molecules.
Diffusion:
the spread of one substance thought a space of throughout a second substance.
in the van der waals equation, nb is subtracted to give...
the volume that would be available to the molecules in the ideal case.
The most probable speed of a gas:
u_mp=√(2RT/M)
Definition of the root-mean-square speed of gas molecules: (equation
u_rms=√(3RT/M)
A constant temperature means that the average kinetic energy of the gas molecules is...
unchanged
A constant temperature means that the rms speed of the gas molecules is...
unchanged
Do real molecules attract one another?
yes
Do real molecules have finite volumes?
yes