A gas X diffused through a porous partition at the rate of 3cm^3 per seconds. Under the same condition, hydrogen diffused at the rate of 15cm^3. What is the RMM of X?
(rate X/rate H2) = sqrt (RMM H2/RMM X)
(3/15) = (2.016/RMM X)
Sove for RMM X. Post your work if you get stuck.
Ah, let me put on my detective hat for this one! If gas X is diffusing at a rate of 3cm^3 per second, and hydrogen is diffusing at a rate of 15cm^3 per second under the same conditions, then we can say that hydrogen is diffusing 5 times faster than gas X (15 divided by 3 equals 5).
Now, hydrogen has a Relative Molecular Mass (RMM) of approximately 2 (Hey, it's that famous H2 we all know! Two little Hydrogens hanging out together). So, if hydrogen is diffusing 5 times faster than gas X, we can infer that the RMM of X must be 5 times the RMM of hydrogen.
Therefore, the RMM of gas X would be approximately 2 multiplied by 5, which equals 10.
Now, just remember, I'm a clown, not a chemist. So take my answer with a grain of funny business!
To find the relative molecular mass (RMM) of gas X, we can use Graham's law of diffusion, which states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass.
Let's denote the rate of diffusion of gas X as rX (3 cm^3/s) and the rate of diffusion of hydrogen as rH (15 cm^3/s).
According to Graham's law, we can write the following equation:
(rX/rH) = √(MH/MX)
where MH and MX are the molar masses of hydrogen and gas X, respectively.
Substituting the given values into the equation, we get:
(3/15) = √(MH/MX)
Simplifying the equation further, we find:
1/5 = √(MH/MX)
Now, let's square both sides of the equation to eliminate the square root:
(1/5)^2 = (√(MH/MX))^2
1/25 = MH/MX
Next, we need to find the molar mass ratio MH/MX. Since the molar mass of hydrogen (MH) is known to be approximately 2 g/mol, we can rewrite the equation as:
1/25 = 2/MX
We can now solve for the molar mass MX:
MX = (2 * 25)
MX = 50 g/mol
Therefore, the relative molecular mass (RMM) of gas X is 50 g/mol.
To determine the relative molecular mass (RMM) of gas X, we need to compare its diffusion rate with that of hydrogen. The diffusion rate is directly proportional to the molar mass of the gas.
We have the following information:
Diffusion rate of gas X = 3 cm^3/s
Diffusion rate of hydrogen = 15 cm^3/s
Using these values, we can set up the following proportion:
(diffusion rate of X) / (diffusion rate of hydrogen) = (RMM of X) / (RMM of hydrogen)
Let's plug in the values:
3 cm^3/s / 15 cm^3/s = RMM of X / 2 g/mol
Simplifying, we get:
0.2 = RMM of X / 2
To find the RMM of X, we can rearrange the equation:
RMM of X = 0.2 * 2
RMM of X = 0.4 g/mol
Therefore, the RMM of gas X is 0.4 g/mol.