"The analyzer said that at 20degreesC the unknown gas was 82.8% carbon by weight and 17.2% hydrogen. The analyzer also diffused the gas through a special apparatus and measured the rate of its diffusion compared to how fast oxygen gas diffused under the same conditions. The rates of diffusion were 5.0cm(cubed)/sec for oxygen gas and 3.7cm(cubed)/for unknown gas. With this information figure out the molecular formula for the unknown gas

You go through and redo the math for more accurate numbers but here is how you do with some estimates along the way.

Take a 100 g sample. This will give you
82.8 g C and 17.2 g H. Convert to moles.
grams/atomic mass = moles.
moles C = 82.8/about 12 = 7
moles H = 17.2/about 1 = about 17
Now find the ratio of the two elements to each other. The easy way to do this is to divide the smaller number by itself, which assures you of getting 1.00 for that. Then divide the other number by that same small number. I get
7/7 = 1.00
17/7 = about 2.4
I expect when you do the numbers more accurately you will obtain 1 to 2.5 which obviously is a whole number ratio of 2 to 6 so the empirical formula is C2H5.

From the diffusion data:
(5/3.7) = sqrt(Munk/MO2)
Solve for Munk (molar mass unknown). I think you will get something like 58 (but not exactly). Then
So the formula for the compound must be (C2H5)n and you want to determine n.
The empirical formula mass is about 29 (2*12 + 5*1) = about 29.
n = 58/29 = 2 and the formula will be
(C2H5)2 or C4H10.

To figure out the molecular formula for the unknown gas, we can use the concept of molar mass and mole ratios.

First, let's calculate the molar masses of the elements involved based on their atomic masses:

- The atomic mass of carbon (C) is approximately 12 g/mol.
- The atomic mass of hydrogen (H) is approximately 1 g/mol.
- The atomic mass of oxygen (O) is approximately 16 g/mol.

Next, let's calculate the masses of carbon (C) and hydrogen (H) in the unknown gas:

- Carbon mass = 82.8% of the unknown gas mass
- Hydrogen mass = 17.2% of the unknown gas mass

Now, we need to find the mole ratio between carbon and hydrogen. We can use the fact that the molar ratio of carbon to hydrogen in a compound is always a whole number ratio.

To find this mole ratio, let's assume we have a certain mass of the unknown gas. We can choose any mass we want, but for simplicity, let's assume we have 100 grams of the unknown gas.

Using this assumption, we can calculate the actual masses of carbon (C) and hydrogen (H) in the 100 grams of the unknown gas:

- Carbon mass = 82.8 grams (82.8% of 100 grams)
- Hydrogen mass = 17.2 grams (17.2% of 100 grams)

Next, we need to convert these masses to moles by dividing them by their respective molar masses:

- Moles of carbon (C) = Carbon mass / molar mass of carbon
- Moles of hydrogen (H) = Hydrogen mass / molar mass of hydrogen

Now we have the mole ratios of carbon to hydrogen in the unknown gas:

- Moles of carbon (C) / Moles of hydrogen (H) = Ratio of carbon (C) to hydrogen (H)

To find the molecular formula of the unknown gas, we need to know the ratio of carbon to hydrogen in the compound. This information can be used to determine the empirical formula.

However, the information about the diffusion rates of the unknown gas and oxygen gas is not directly related to finding the molecular formula. This information is likely given to provide additional context, but it is not necessary for calculating the molecular formula based on the given data.

Please note that without additional information about the molecular weight of the unknown gas, we cannot determine its molecular formula with certainty. The molecular weight can be determined experimentally using techniques such as mass spectrometry or other analytical methods.