how would you set this problem up?
An unknown gas effusees at .850 times the effusion rate of nitrogen dioxide, NO2. Estimate the molar mass of the unknown gas.
rate1/rate2 = sqrt[M2/M2]
I would arbitrarily pick a number, say 10 cc/min, for the effusion rate of NO2. Then 850*10 = the rate for the unknown gas. Substitute into the above equation and solve for M2.
To set up this problem, we need to utilize 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.
Let's represent the unknown gas as "X" and nitrogen dioxide as "NO2". We are given that the effusion rate of X is 0.850 times the effusion rate of NO2.
Let's denote the effusion rates as rX and rNO2, and the molar masses as MX and MNO2, respectively.
According to Graham's law, we have the following relationship:
rX / rNO2 = sqrt(MNO2 / MX)
Since we are looking to estimate the molar mass of the unknown gas (MX), we can rearrange the equation to solve for it:
MX = MNO2 * (rNO2 / rX)^2
Now, we need the molar mass of nitrogen dioxide (MNO2) in order to calculate the molar mass of the unknown gas.
The molar mass of nitrogen dioxide (NO2) can be calculated by adding the atomic masses of nitrogen (N) and two oxygen (O) atoms. Consulting the periodic table, we find that the atomic masses of nitrogen and oxygen are approximately 14 and 16 grams/mol, respectively.
MNO2 = 14 g/mol + 2 * 16 g/mol
MNO2 = 14 g/mol + 32 g/mol
MNO2 = 46 g/mol
Now that we have the molar mass of nitrogen dioxide (MNO2) and the ratio of effusion rates (rNO2 / rX = 0.850), we can calculate the molar mass of the unknown gas (MX) using the equation:
MX = MNO2 * (rNO2 / rX)^2
MX = 46 g/mol * (0.850)^2
Using a calculator, we can evaluate the right-hand side of the equation to find the molar mass of the unknown gas.