Here we're told that a 500 milliliter container at a pressure of 600 milliliters of mercury possesses 29.3 grams of nitrogen gas at 50 degrees Celsius. Here we need to determine the correct units needed for the ideal gas law. So remember, the ideal gas law is PV=nRT. So P stands for pressure. Remember pressure needs to be in units of atmospheres. So here, we're going to do a conversion. We're going to go from 600 millimeters of mercury to atmospheres. Millimeters of mercury go here on the bottom, and then atmosphere goes on top. Remember the relationship is that for every one atmosphere, it's 760 millimeters of mercury. So when we do that, we're going to get a pressure of 0.789 atmospheres. Although 600 has one significant figure, let's just go with three significant figures here, just so we don't have just 0.8 as atmospheres.
Next, volume. Volume needs to be in liters, so we have 500 milliliters. And remember, 1 milli equals \(10^{-3}\). So this would just come out as 0.500 liters.
Next, we need moles, so moles is n. Remember nitrogen gas. Nitrogen in its natural or standard state is N2. It's one of our diatomic molecules. So we're told that we have 29.3 grams of N2. We must convert that into moles, so 1 mole of N2. There are 2 nitrogens. According to the periodic table, each is 14.01 grams. So multiplying that by 2 gives me 28.2 grams for the combined weight in N2. So grams here cancel out and I'll have my moles. Here we'll put it as 1.05 moles of N2.
And then finally, we need our temperature. R is our constant, so we don't have to worry about providing the correct units. It's 0.08206 like we said earlier. So temperature here needs to be in Kelvin. So remember to go from Celsius to Kelvin, you're supposed to add 273.15. Sometimes professors will just say plus 273, but if you want to be as accurate as possible, you want to put 273.15. So when you add that, that's 323.15 Kelvin. So here we have all of the units that we need in the correct forms. So just remember the ideal gas law and what are the correct units that we need to utilize for each one of these variables.
