Effusion Rate Ratio Calculator (Ar vs. Kr)
Understanding Effusion Rates and Graham's Law
Effusion is the process by which a gas escapes from a container through a small hole. Graham's Law of Effusion states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass, assuming constant temperature and pressure.
Mathematically, this is expressed as:
$$ \frac{Rate_1}{Rate_2} = \sqrt{\frac{Molar\ Mass_2}{Molar\ Mass_1}} $$
In this calculator, we are comparing the effusion rates of Argon (Ar) and Krypton (Kr). Argon is a lighter noble gas than Krypton. Therefore, according to Graham's Law, Argon should effuse at a faster rate than Krypton.
You can input the molar masses of Argon and Krypton to calculate the exact ratio of their effusion rates. The result will tell you how many times faster one gas effuses compared to the other.
Example Calculation:
Let's use the standard molar masses: Argon (Ar) = 39.95 g/mol and Krypton (Kr) = 83.80 g/mol.
$$ \frac{Rate_{Ar}}{Rate_{Kr}} = \sqrt{\frac{83.80 \ g/mol}{39.95 \ g/mol}} $$
$$ \frac{Rate_{Ar}}{Rate_{Kr}} \approx \sqrt{2.0976} \approx 1.448 $$
This means that Argon effuses approximately 1.448 times faster than Krypton under the same conditions.