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Graham’s Law of Effusion was formulated by Scottish physical chemist Thomas Graham in 1848. Graham found that the rate of effusion of a gas is inversely proportional to the square root of the molar mass of its particles. Here is the formula:
rate1rate 2 = M2M1 or r ∝ 1M (this is the general formula where r is rate and M is molar mass)
Where, rate 1 is the rate of effusion of the first gas
rate 2 is the rate of effusion of the second gas
M1 is the molar mass of gas1
M2 is the molar mass of gas 2
Graham’s Law states that the rate of diffusion or effusion of a gas is inversely proportional to the square root of its molecular weight. Thus, if the molecular weight of one gas is four times that of another, it would diffuse through a porous plug or escape through a small pinhole in a vessel at half the rate of the other.
Compressing gas and pressure volume
Compressing gas is a gas or mixture of gases in a container having an absolute pressure exceeding 40psi (pound per square inch) at 70 degrees.
When we compress any gas, there are changes initiated in its characteristics: the volume of gas decreases, temperature changes, and the pressure of gas changes, too. But these changes depend on the situation. These can be easily understood by the ‘Ideal Gas Law’ which states that the product of pressure and volume of one gram of molecule is equal to the product of absolute temperature and the universal gas constant, i.e. PV=nRT.
To know more about Graham’s Law, let us first understand diffusion and effusion. Diffusion is the ability of gas to spread and occupy the whole available volume irrespective of the other gases present in the container. Effusion is the process by which a gas escapes from one chamber of a vessel through a small opening.
Graham’s law of diffusion holds good for effusion, too.
Effect of pressure on the state of diffusion
The rate of diffusion of gas at constant temperature is directly proportional to its pressure:
r∝P at constant temperature, where r is rate of diffusion and P is pressure.
But we know that: r ∝ 1M
Therefore, r1r2=P1P2=M2M1 (for two gases)
The kinetic molecular theory and Graham’s Law
This law is based on the postulate that all gases have the same average kinetic energy at the same temperature.
So, we can write expressions for average kinetic energy of two gases with different molar mass as:
KE = 12MbMa (v2)a= 12MbMa(v2)b
Where, a and b are two gases
On rearranging the equation, we get,
(v2)a(v2)b = MbMa
Taking the square root of both sides leads to,
VaVb = MbMa
Thus, the rate at which molecules diffuse or effuse is directly related to the speed at which they move. This equation shows that Graham’s Law is a direct consequence of the fact that gaseous molecules at the same temperature have the same average kinetic energy.
Therefore,rarb = MbMa
Applications of Graham’s Law
- This law is used to detect unknown molar mass of gas.
- This law is used to separate isotopes. For example: 92U235 92U238
- This law is used in Ansil alarms.
Merits and demerits of Graham’s Law
The main demerit of Graham’s Law is that it breaks down when the concentration of the gases becomes considerably high, which means that Graham’s Law stands for ideal gases that are present at a low temperature and pressure.
The main merit of Graham’s Law is that this law is used to calculate the effusion or diffusion rate of a particular gas, and also helps to compare the effusion or diffusion of two different gases. So, this helps the scientist know about the time required by a particular gas to escape the container. This estimation helps to form safety measures in case of gas leakages.
Conclusion
We studied that Graham’s Law states that the rate of diffusion or effusion of a gas is inversely proportional to the square root of molar mass of its particles. Then we also studied in brief how kinetic molecular theory is related to Graham’s Law. We also learnt about compressing gas and pressure volume and explored the merits and demerits of Graham’s Law.
