Effusion/Diffusion Chemistry Help!!!
If 4.83mL of an unknown gas effuses through a hole in a plate in the same time it takes 9.23mL of Argon, Ar, to effuse through the same hole under the same conditions, what is the molecular mass of the unknown gas? (146amu)
Responses:
* chemistry - DrBob222, Wednesday, June 17, 2009 at 10:19pm
Isn't this just standard use of
rate1/rate2 = sqrt(M2/M1)?
I get 146 also.
I am trying to do this again and cannot figure out what I am doing wrong??
4.83/9.23=.524 when I square that I get .723 not 146.
Any suggestion?
You are squaring incorrectly. Try multiplying 0.524 x 0.524 and I get something like 0.28 or so. You need to do it exactly (and I would divide 4.83/9.23 to get a number and square it without taking it out of the calculator. That way, all of the digits remain in the calculator. Doing that I get 0.27384.)
Thank You, you are absolutely correct!
It seems that you are calculating the square root incorrectly. Let's go through the steps again:
Given:
Rate of unknown gas (U) = 4.83 mL
Rate of Argon gas (Ar) = 9.23 mL
Molecular mass of Argon gas (M1) = 40 amu
We need to find the molecular mass of the unknown gas (M2).
Using the formula:
Rate1 / Rate2 = sqrt(M2 / M1)
Plugging in the values:
4.83 / 9.23 = sqrt(M2 / 40)
Now, let's solve for M2.
Squaring both sides of the equation:
(4.83 / 9.23) ^ 2 = (sqrt(M2 / 40)) ^ 2
0.524 ^ 2 = M2 / 40
0.274 = M2 / 40
Multiply both sides by 40:
0.274 * 40 = M2
10.96 = M2
So, the molecular mass of the unknown gas is approximately 10.96 amu, not 146 amu. It seems there was an error in the initial response.
To solve this problem, we can use Graham's Law of effusion, which states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass.
The formula to use is:
rate1/rate2 = sqrt(M2/M1)
In this case, we are comparing the rate of effusion of the unknown gas (rate1) to the rate of effusion of argon (rate2). Let's set up the equation:
4.83mL unknown gas / 9.23mL argon = sqrt(M2 / M1)
Now, we need to solve for the molar mass of the unknown gas (M2). Rearranging the equation, we get:
sqrt(M2 / M1) = 4.83 / 9.23
Next, we square both sides of the equation to eliminate the square root:
M2 / M1 = (4.83 / 9.23)^2
Now, we can solve for M2, which is the molar mass of the unknown gas:
M2 = (4.83 / 9.23)^2 * M1
Plugging in the given values, we get:
M2 = (0.524)^2 * M1
M2 ≈ 0.274 * M1
Since M2 represents the molar mass of the unknown gas, and M1 is the molar mass of argon (approximately 40 amu), we get:
M2 ≈ 0.274 * 40 amu
M2 ≈ 10.96 amu
Therefore, the approximate molecular mass of the unknown gas is 10.96 amu, not 146 amu as stated in the earlier response.
It appears that there was an error in the calculation or transcription of the previous response.