A gas diffuses 3.98 times slower than H2 at the same temperature and pressure. What is the molar mass of the gas?
Well, well, well, looks like we have a "diffusing" question here! Let me put on my scientific clown nose and help you out.
So, we know that the gas in question is diffusing 3.98 times slower than hydrogen gas (H2) at the same temperature and pressure. Now, diffusion is all about equalizing the playing field - or in this case, equalizing the molar masses.
The rate of diffusion is inversely proportional to the square root of the molar mass. So, we can set up a little equation to solve this riddle:
(rate of gas / rate of H2) = sqrt(Molar mass of H2 / Molar mass of gas)
Plugging in the values we have:
(1/3.98) = sqrt(2 / Molar mass of gas)
Now we just have to do some good ol' algebra to isolate Molar mass of the gas:
Molar mass of H2 / 2 = (1/3.98)^2
Molar mass of H2 / 2 = 0.0625
Molar mass of H2 = 0.125
And finally, solving for the molar mass of the gas:
0.125 / 2 = Molar mass of gas
Molar mass of gas = 0.0625
So, with a shower of confetti and a honk of the horn, the molar mass of the gas is approximately 0.0625!
To determine the molar mass of the gas, we can use Graham's law of diffusion. According to Graham's law, the rate of diffusion of a gas is inversely proportional to the square root of its molar mass.
Let's assume the molar mass of H2 is MH2 and the molar mass of the gas in question is MG.
According to the given information, the gas diffuses 3.98 times slower than H2. Mathematically, we can write this as:
Rate of diffusion of the gas = Rate of diffusion of H2 / 3.98
Using Graham's law:
Rate of diffusion of the gas = √(MH2 / MG)
Plugging in the values we have:
√(MH2 / MG) = 1 / 3.98
To solve for the molar mass of the gas (MG), we square both sides of the equation:
MH2 / MG = (1 / 3.98)^2
Cross-multiplying:
MG = MH2 / (1 / 3.98)^2
Simplifying further:
MG = MH2 / (1 / 15.84)
MG = 15.84 * MH2
Now, let's substitute the molar mass of hydrogen (H2) with its value. The molar mass of H2 is approximately 2 g/mol:
MG = 15.84 * 2
MG = 31.68 g/mol
Therefore, the molar mass of the gas is approximately 31.68 g/mol.
To determine the molar mass of the gas, we can use Graham's law of effusion. Graham's law states that the rate of effusion or diffusion of a gas is inversely proportional to the square root of its molar mass.
Let's denote the molar mass of the unknown gas as M, and the molar mass of hydrogen gas (H2) as M(H2). The rate of diffusion can be represented by the ratio of the rates of the two gases, which in this case is given as:
Rate of diffusion of the unknown gas / Rate of diffusion of H2 = 1 / 3.98
According to Graham's law, this ratio is equal to the square root of the ratio of the molar masses:
√(M/M(H2)) = 1 / 3.98
To solve for M, we need to square both sides of the equation:
M/M(H2) = (1/3.98)^2 = 1/15.8404
Now, rearranging the equation to solve for M:
M = (1/15.8404) * M(H2)
The molar mass of hydrogen gas (H2) is approximately 2 g/mol. Therefore, substituting this value into the equation, we can calculate the molar mass of the unknown gas:
M = (1/15.8404) * 2 g/mol
M ≈ 0.1261 g/mol
Hence, the molar mass of the unknown gas is approximately 0.1261 g/mol.
mm = molar mass
rate gas = 1 L/min (I just made up that number)
Then rate H2 = 3.98*1 = 3.98L/min.
Substitute into the below equation and solve for mm gas.
(rate H2/rate gas)= sqrt (mmgas/mm H2)