A sample of neon effuses from a container in 80 seconds. The same amount of an unknown noble gas requires 163 seconds
Identify the gas.
Kr
163/80=sqrt(unknown/20.3)
It is Krypton.
The effusion time is inversely proportional to the molar mass of the gas. Lighter gases require less time to effuse from a container than heavier gases. Graham's law of effusion compares the rates of effusion and molar masses of two gases. Since you are given time, you should first take the inverse of time to represent a rate. The calculation of the molar mass of this gas is summarized as follows:
rateHeratexMxMx===MxMHe−−−√(rateHe)2(ratex)2×MHe(1.25×10−2s−1)2(6.14×10−3s−1)2×20.18 g/mol
Therefore, the unknown gas has a molar mass of 83.7 g/mol , which corresponds to Krypton.
I would assume a volume of 1L.
Then Ne rate = 1/80. mass = 20.3
rate unknown = 1/163. mass = ?
(1/80/1/163) = sqrt(?/20.3)
Solve for ? and identify from the periodic table.
Hmm, well that unknown noble gas sounds like it really takes its sweet time to effuse, doesn't it? It's like the slowest guest at a party, always showing up fashionably late. But fear not, dear inquirer, for I, the magnificent Clown Bot, shall unveil the identity of this tardy gas! Considering its effusion rate compared to neon, I have a hunch that this gas may just be the one and only, the illustrious, the sluggish... krypton! Yes, that's right! Krypton, the noble gas that loves to take its time. So, sit back, relax, and watch as krypton slowly but surely makes its grand entrance into the world!
To identify the gas, you can use Graham's Law of effusion. This law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass.
Let's assume the molar mass of neon is M₁, and the molar mass of the unknown gas is M₂. According to Graham's Law, the ratio of the rates of effusion can be expressed as:
Rate of effusion of neon (R₁) / Rate of effusion of unknown gas (R₂) = √(Molar mass of unknown gas (M₂) / Molar mass of neon (M₁))
Given that the time for neon to effuse is 80 seconds and the time for the unknown gas is 163 seconds, we can write the following equation:
80 / 163 = √(M₂ / M₁)
To solve for the unknown gas, you need to rearrange the equation and square both sides:
(M₂ / M₁) = (80 / 163)²
Now, you can substitute the values and calculate:
(M₂ / M₁) = (80 / 163)² = 0.191
By comparing the molar masses of different noble gases, you can determine which gas has a molar mass ratio closest to 0.191. The gas with that molar mass will be the unknown gas.