# 9.5 The kinetic-molecular theory  (Page 3/6)

 Page 3 / 6

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] .

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] .

## 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:

$\text{effusion rate}\phantom{\rule{0.2em}{0ex}}\propto \phantom{\rule{0.2em}{0ex}}{u}_{\text{rms}}$

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

${u}_{\text{rms}}=\sqrt{\frac{3RT}{m}}$
$m=\phantom{\rule{0.2em}{0ex}}\frac{3RT}{{u}_{\text{r}\text{m}\text{s}}^{2}}\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}\frac{3RT}{{\overline{u}}^{2}}$
$\frac{\text{effusion rate A}}{\text{effusion rate B}}\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}\frac{{u}_{\text{r}\text{m}\text{s}\phantom{\rule{0.2em}{0ex}}\text{A}}}{{u}_{\text{r}\text{m}\text{s}\phantom{\rule{0.2em}{0ex}}\text{B}}}\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}\frac{\sqrt{\frac{3RT}{{m}_{\text{A}}}}}{\sqrt{\frac{3RT}{{m}_{\text{B}}}}}\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}\sqrt{\frac{{m}_{\text{B}}}{{m}_{\text{A}}}}$

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

• ${u}_{\text{r}\text{m}\text{s}}=\sqrt{\overline{{u}^{2}}}=\sqrt{\frac{{u}_{1}^{2}+{u}_{2}^{2}+{u}_{3}^{2}+{u}_{4}^{2}+\dots }{n}}$
• ${\text{KE}}_{\text{avg}}=\phantom{\rule{0.2em}{0ex}}\frac{3}{2}RT$
• ${u}_{\text{rms}}=\sqrt{\frac{3RT}{m}}$

hydrogen is a monovalent why aluminum is a divalent
Did you mean trivalent? This is because Aluminium has three electroms orbiting in the valence (furthest shell) which are involved in covalent bonding where each electron becomes a pair with another one in the other non metal and make a single bond. N. B: each single covalent bond contains 2 electr
Abdelkarim
Electrons, one from each atom. Did you know that god said '' And, [O Muhammad], you are not [engaged] in any matter or recite any of the Qur'an and you [people] do not do any deed except that We are witness over you when you are involved in it. And not absent from your Lord is any [part] of an atom
Abdelkarim
... atom's weight within the earth or within the heaven or [anything] smaller than that or greater but that it is in a clear register. ''
Abdelkarim
wat gives perfume it's sweet smell
These are organic compounds, which have plentiful functional groups which react with certain substances through a pathway in the cells lining nostrils which sends impulses that make you sense its sweet. Did you prophet Muhammad (peace upon him) encourages the use of perfume.
Abdelkarim
what is it use for
amagai
Prophet Muhammad (peace be upon him) used to love cleanliness and good scent. ... It was highlighted, in many hadiths, his love for fragrance and good scent like musk, 'ud and ambergris.
Abdelkarim
the types of giant covalent structure
define the following terms. electrovalent bonding
Nobert
 An unknown noble gas was allowed to flow into a 300.0 mL glass bulb until the P = 685 torr. Initially, the glass bulb weighed 32.50 g, but now it weighs 33.94 g. If the temperature is 27.0 °C, what’s the identity of the gas?
* Use PV=nRT with correct units to find n (number of moles) * Use n = mass/ Ar (Ar is relative atomic mass) Ar = 131.15 -> Xenon N. B: P is in pascals, V in m3, n in mol, R in J/ k. Mol, T in kelvin *Thank God
Abdelkarim
N. B: As it is a noble gas it is mono-atomic so the Ar does not need to be divided by two (not diatomic).
Abdelkarim
what is molecule
molecules are produced by double atom from example this is hydrogen atom and this is hydrogen2 are call that hydrogen molecules or gass
Naldo
What is the generic name for the compound
what is the formular for methane
CH4 , it is the simplest alkane
Abdelkarim
what is the formula for alkaline
Olom
hi
Yusuf
I wish to learn to more of chemistry, can someone please teach me.
Yusuf
what is zero gravity
every object is that zero gravity
Rabiu
Probably when an object is in space and there are no nearby masses that pull her, and exert gravity
Abdelkarim
Alright. .good job
Rabiu
And all majesty to God, (وَهُوَ ٱلَّذِی خَلَقَ ٱلَّیۡلَ وَٱلنَّهَارَ وَٱلشَّمۡسَ وَٱلۡقَمَرَۖ كُلࣱّ فِی فَلَكࣲ یَسۡبَحُونَ) [سورة الأنبياء 33 And it is He who created the night and the day and the sun and the moon; all [heavenly bodies] in an orbit are swimming. General theory of relativity in Qur
Abdelkarim
what is molecule?
Olom
what is lattice energy
why is CO a neutral oxide and CO2 an acidic oxide
Because when CO2 dissolves in water forming a weak acid. CO does not dissolve in water as it has strong triple bond.
Abdelkarim
What is acid
which donate H+ or accept lone pair of electron
Kajal
kinetic theory of matter and gas law
hi
Victoria
pls explain
Victoria
what is clay
material containing clay minerals. Clays develop plasticity when wet, due to a molecular film of water surrounding the clay particles, but become hard, brittle and non–plastic upon drying or firing. Most pure clay minerals are white or light-coloured, but natural clays show a variety of colours
Abdelkarim
due iron oxide. The four types of clay are Earthenware clay, Stoneware clay, Ball clay, and Porcelain. All of them can be used to make pottery, but the end result would differ a lot thanks to their different textures, colors, and flexibilities.
Abdelkarim
And do you know that god has created human from clay (وَلَقَدۡ خَلَقۡنَا ٱلۡإِنسَـٰنَ مِن صَلۡصَـٰلࣲ مِّنۡ حَمَإࣲ مَّسۡنُونࣲ) [سورة الحجر 26] And We did certainly create man out of clay from an altered black mud. You can install Quran from paly store for free with translations.
Abdelkarim
darw a periodic table
draw a periodic table
Hazard
You will arrange the elements into row and coloumns according to increasing proton number. You may want to use symbols or their names. Hydrogen, Helium, etc. God has created all these elements from nothing, in Islam we know God is the creator.
Abdelkarim
why are you drawing a periodic table? why not just print one from the internet and use as a reference
Jakhari
Great thought
Bright
how are you?
Marina
am fine
Agbo
Marina
my name is amel
Farid
l use the email of my husband
Farid