<< Chapter < Page Chapter >> Page >

If the temperature of a gas increases, its KE avg increases, more molecules have higher speeds and fewer molecules have lower speeds, and the distribution shifts toward higher speeds overall, that is, to the right. If temperature decreases, KE avg decreases, more molecules have lower speeds and fewer molecules have higher speeds, and the distribution shifts toward lower speeds overall, that is, to the left. This behavior is illustrated for nitrogen gas in [link] .

A graph with four positively or right-skewed curves of varying heights is shown. The horizontal axis is labeled, “Velocity v ( m divided by s ).” This axis is marked by increments of 500 beginning at 0 and extending up to 1500. The vertical axis is labeled, “Fraction of molecules.” The label, “N subscript 2,” appears in the open space in the upper right area of the graph. The tallest and narrowest of these curves is labeled, “100 K.” Its right end appears to touch the horizontal axis around 700 m per s. It is followed by a slightly wider curve which is labeled, “200 K,” that is about three quarters of the height of the initial curve. Its right end appears to touch the horizontal axis around 850 m per s. The third curve is significantly wider and only about half the height of the initial curve. It is labeled, “500 K.” Its right end appears to touch the horizontal axis around 1450 m per s. The final curve is only about one third the height of the initial curve. It is much wider than the others, so much so that its right end has not yet reached the horizontal axis. This curve is labeled, “1000 K.”
The molecular speed distribution for nitrogen gas (N 2 ) shifts to the right and flattens as the temperature increases; it shifts to the left and heightens as the temperature decreases.

At a given temperature, all gases have the same KE avg for their molecules. Gases composed of lighter molecules have more high-speed particles and a higher u rms , with a speed distribution that peaks at relatively higher velocities. Gases consisting of heavier molecules have more low-speed particles, a lower u rms , and a speed distribution that peaks at relatively lower velocities. This trend is demonstrated by the data for a series of noble gases shown in [link] .

A graph is shown with four positively or right-skewed curves of varying heights. The horizontal axis is labeled, “Velocity v ( m divided by s ).” This axis is marked by increments of 500 beginning at 0 and extending up to 3000. The vertical axis is labeled, “Fraction of molecules.” The tallest and narrowest of these curves is labeled, “X e.” Its right end appears to touch the horizontal axis around 600 m per s. It is followed by a slightly wider curve which is labeled, “A r,” that is about half the height of the initial curve. Its right end appears to touch the horizontal axis around 900 m per s. The third curve is significantly wider and just over a third of the height of the initial curve. It is labeled, “N e.” Its right end appears to touch the horizontal axis around 1200 m per s. The final curve is only about one fourth the height of the initial curve. It is much wider than the others, so much so that its right reaches the horizontal axis around 2500 m per s. This curve is labeled, “H e.”
Molecular velocity is directly related to molecular mass. At a given temperature, lighter molecules move faster on average than heavier molecules.

The kinetic-molecular theory explains the behavior of gases, part ii

According to Graham’s law, the molecules of a gas are in rapid motion and the molecules themselves are small. The average distance between the molecules of a gas is large compared to the size of the molecules. As a consequence, gas molecules can move past each other easily and diffuse at relatively fast rates.

The rate of effusion of a gas depends directly on the (average) speed of its molecules:

effusion rate u rms

Using this relation, and the equation relating molecular speed to mass, Graham’s law may be easily derived as shown here:

u rms = 3 R T m
m = 3 R T u r m s 2 = 3 R T u ¯ 2
effusion rate A effusion rate B = u r m s A u r m s B = 3 R T m A 3 R T m B = m B m A

The ratio of the rates of effusion is thus derived to be inversely proportional to the ratio of the square roots of their masses. This is the same relation observed experimentally and expressed as Graham’s law.

Key concepts and summary

The kinetic molecular theory is a simple but very effective model that effectively explains ideal gas behavior. The theory assumes that gases consist of widely separated molecules of negligible volume that are in constant motion, colliding elastically with one another and the walls of their container with average velocities determined by their absolute temperatures. The individual molecules of a gas exhibit a range of velocities, the distribution of these velocities being dependent on the temperature of the gas and the mass of its molecules.

Key equations

  • u r m s = u 2 ¯ = u 1 2 + u 2 2 + u 3 2 + u 4 2 + n
  • KE avg = 3 2 R T
  • u rms = 3 R T m

Questions & Answers

Types of electrolytes
Treasure Reply
list 6 subatomic particles and their mass, speed and charges
Dubem Reply
combination of acid and base
Ayibiro Reply
that salt
Talhatu
calculate the mass in gram of NaOH present in 250cm3 of 0.1mol/dm3 of its solution
Omego Reply
The mass is 1.0grams. First you multiply the molecular weight and molarity which is 39.997g/mol x 0.1mol/dm3= 3.9997g/dm3. Then you convert dm3 to cm3. 1dm3 =1000cm3. In this case you would divide 3.9997 by 1000 which would give you 3.9997*10^-3 g/cm3. To get the mass you multiply 3.9997*10^-3 and
Kokana
250cm3 and get the mass as .999925, with significant figures the answer is 1.0 grams
Kokana
nitrogen, phosphorus, arsenic, antimony and Bismuth
faith Reply
What is d electronic configuration of for group 5
Miracle Reply
Can I know d electronic configuration of for group 5 elements
Miracle
2:5, 2:8:5, 2:8:8:5,...
Maxime
Thanks
Miracle
Pls what are d names of elements found in group 5
Miracle
define define. define
Muh Reply
what is enthalpy
Ayilaran Reply
total heat contents of the system is called enthalpy, it is state function.
Sajid
background of chemistry
Banji Reply
what is the hybridisation of carbon in formic acid?
Maham Reply
sp2 hybridization
Johnson
what is the first element
Josh Reply
HYDROGEN
Liklai
Element that has positive charge and its non metal Name the element
Liklai
helium
oga
sulphur
oga
hydrogen
Banji
account for the properties of organic compounds
mercy Reply
properties of organic compounds
mercy
what's the difference between molecules and compounds
Amha Reply
A compound can be a molecule however compounds must contain more than one element. For example ozone, O3 is a molecule but not a compound.
Justin
what is che? nd what is mistry?
Mukhtar
What's elixir?
EMEKA Reply
An Elixir is a substance held capable of changing base metals into Gold.
Nwafor
Give an example for each of the six groups of element
Francis Reply
Practice Key Terms 2

Get the best Chemistry course in your pocket!





Source:  OpenStax, Chemistry. OpenStax CNX. May 20, 2015 Download for free at http://legacy.cnx.org/content/col11760/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Chemistry' conversation and receive update notifications?

Ask