What is the molecular formula of a compound that contains 39.0% carbon, 16.0% hydrogen, and 45.0% nitrogen, if 0.1576 g of the compound occupies 125 mL with a pressure of 0.9820 atm at 295.15 K?

Here the practice question states, what is the molecular formula of a compound that contains 39% carbon, 16% hydrogen, and 45% nitrogen if point 1576 grams of the compound occupies a 125 ml with a pressure of 0.9820 atmospheres at 295.15 Kelvin. Alright. So they need us to calculate the molecular formula, and they're giving us percentages of each element. Remember this is kind of reminiscent of empirical formula and molecular formula. If you haven't looked at those videos, I highly suggest you go back and take a look at those before trying to attempt this particular question. Alright. So remember to find the molecular formula, we first need to determine the empirical formula. So what we're gonna do first is we're gonna convert all the percentages automatically into grams. And that's because we're assuming we're dealing with a 100 gram sample. Here, we're dealing with the mono atomic forms of each of these elements. So hydrogen here would not be h 2, it would just be h. Nitrogen here wouldn't be n 2, it would just be n. So we place each of these grams. Next what we do next what we do is we're gonna convert each one of these grams into moles by dividing by their atomic masses from the periodic table. So one mole of carbon according to the periodic table is 12 point 0 1 grams, 1 mole h is 1.008 grams, 1 mole n is 14.01 grams. So here each of the grams cancel out and we'll have the moles of each one of these elements. Here that would come out to be 3.2473 moles of c, 3.2120 moles of oops. H would be actually 15.8730 moles of h and then we'd have 3.2120 moles of n. Now that we have the moles of each, our next step will be divide all of the moles by our smallest mole answer. Our smallest mole answer is the nitrogen's 3.2120 moles. So all of these get divided by that. 21203.2120. So that'll give us the ratio of each one of these elements in relation to one another. So here that would give me 1 carbon, 5 hydrogens, 1 nitrogen. So my empirical formula would be c h five n. But remember, we're not done because we don't want the empirical formula. We want the molecular formula. To figure out the empirical on the molecular formula, recall that molecular formula equals the variable n here times your empirical formula. Remember here, this is not n as in moles, this is n as in your n factor. So we have the empirical formula as c h five n, and now we need to determine our n factor. Remember your n factor is the molar mass divided by your empirical mass. Your empirical mass comes from the empirical formula. So in our empirical formula, what do we have? We have here 1 carbon, 5 hydrogens, and 1 nitrogen. There are masses on the periodic table we plug in, So that gives me 12.01 grams, 5.040 grams, and 14.01 grams. So it's gonna be, point oh, so that's gonna be here, 31.06 grams per mole. So that is my empirical mass. How do I find my molecular mass? Well we just use the ideal gas law molecular formula formula molar mass formula, which would be molar mass equals m r t over p v. We plug in the 0.1576 grams, we plug in our gas constant, after that we plug in our temperature, then we plug in our pressure and our volume. So our pressure is 0.9820 atmospheres and our volume is 0.125 liters. When we do that we get 31.10 grams per mole. So we plug that in here. So we'll see that we have 31.10 divided by 31 point 6 which equals 1. So my n factor here is just 1. So one times my empirical formula gives me back the same formula. Recall sometimes the empirical formula and the molecular formula are the same. So in this particular question, our molecular formula will be c h 5 n for unknown gas.