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## Health and medicine

### Course: Health and medicineÂ >Â Unit 4

Lesson 2: Gas exchange

# Graham's law of diffusion

Graham's law of diffusion (also known as Graham's law of effusion) states that the rate of effusion a gas is inversely proportional to the square root of its molar mass. Often, it is used to compare the effusion rates of two gases. This is represented by the formula: $\frac{\text{rate of effusion A}}{\text{rate of effusion B}} = \sqrt{\frac{M_{B}}{M_{A}}}$ where $M$ refers to molar mass. Created by Rishi Desai.

## Want to join the conversation?

• Why are london forces found in all compounds?
• London forces are also called instantaneous dipole attraction, this is because of the polarity resulting from the transient unequal distribution of electrons in a bond or an electron cloud (in the case of single atoms or ions). Electrons are constantly moving and when they are concentrated at a given place of a bond/electron cloud a negative pole is created in that point in time (and a counterpart positive pole due to a local region of electron deficiency at the other end of the bond/atom). Since all chemical species possess electron clouds/bonding electron clouds they can all participate in dispersion/London forces.
• How did Graham, if he was the first to find out, find out how atoms had this weight that could slow or speed them up? I mean, you can't really see an atom unless you use modern technology, right?
• How would you solve for the molecular weight of an unknown gas instead of its rate? For example, if you knew that oxygen's rate of effusion was twice that of an unknown gas, how would you solve Graham's law to obtain the molecular weight (molar mass) of the unknown gas?
• This is how I would do it:

2x / x = sqrt( y / 32 ),
where x = rate of effusion of the unknown gas and y = molecular weight of the unkonwn gas.

2 = sqrt( y / 32)
4 = y / 32
y = 4 * 32
y = 128
• Doesn't that mean whatever you choose for rate 1 will always be faster? Also doesn't that mean what every has a lower Molar Mass is always faster? If so, there is no need for Graham's Law.
• Shouldn't this be Graham's Law of Effusion, as opposed to diffusion?
• No because Effusion is a process that occurs when a gas is permitted to "escape" its container through one or many small holes to another container whitout molecular collisions.
In this case, its diffusion becase there is appening af mixing of molecules by random motion, where molecular collisions occur.
• so, why did the Kinetic energy of the Oxygen molecules and the Kinetic energy of the Carbon dioxide molecules the same to make the equation? (obviously the larger the molecule, the larger the kinetic energy with the same speed; but we don't know the speed of the molecules;)
(1 vote)
• Kinetic Energy of any gas is equal to 3/2RT (and not 3/2nRT), so in this case the temperature of atmosphere is same. Therefore, they have equal kinetic energy.
• At , Rishi says that the energy formulas are the same for O2 and CO2 because they both absorb the same amount of energy. However, you don't have to heat up the pot for the molecules to start diffusing once the top is removed, and in fact the energy absorbed by different molecules is different for the same change of temperature. Can someone please confirm that the two sides of the equation are equal not because they are both absorbing the same amount of energy from the fire, but instead because they are both the same temperature and temperature is basically a measure of molecular kinetic energy?
• You're right on the money.
The internal energy of an O2 molecule is (5/2)kT, while the internal energy of a CO2 molecule is (6/2)kT. The internal energies are different because CO2 can store energy in vibrations in more ways than O2. This difference in internal energies means that CO2 will need to absorb more energy to be at the same temperature as O2. As you noted, the temperature is only related to the translational energy of the molecules, not the vibrational and rotational.
(1 vote)
• Theoretically, how would these molecules have enough energy to move at 1000mph?
(1 vote)
• The nitrogen molecules have enough energy to move at 1000mph simply because of their temperature. If you were to make the nitrogen gas hotter, then the nitrogen molecules would go even faster than 1000mph!