A gaseous hydrogen- and carbon-containing compound is decomposed and found to contain 85.63% C and 14.37% H by mass. The mass of 258 mL of the gas, measured at STP, was 0.646 g. What is the molecular formula of the compound?

Video transcript

Hello everyone today. We are being given the following question and asked to solve for it says the mass of a 150 mL of a gaseous hydrocarbon determined at S. T. P, which is standard temperature pressure is 0.174 g. The same hydrocarbon is analyzed and discovered to contain 92.24% carbon and 7. percent of hydrogen by mass. We're being asked to reduce the molecular formula of the compound. Well the first thing you want to do is find the empirical formula. So we're going to find the empirical formula. And by doing this, the first thing I wanna do is we want to get the molar mass of this hydrocarbon. So we're gonna use the ideal gas law or derivative of it. We're gonna see the molar mass is equal to the mass of the hydrocarbon times the gas constant, times the temperature over pressure times volume. Given the values in our question stem, We know that the mass of this hydrocarbon is .174 g. We know the gas constant is .08-1 And at standard temperature pressure temperature is 273° Kelvin. Our pressure at standard temperature pressure is one atmospheres and our volume as given in the question is 150 ml but we must use a conversion factor That says that one ml makes one Leader. So we say one leader is equal to 1000 middle leaders. This gives us .15 L and we can just plug this into our equation Ultimately wind up with the molar mass of 26 g per mole and we will put this number to the side and use it later in the problem. So now that we've found the molar mass, we now need to work towards getting the empirical formula. So we take our percentages and we turned them into grams. For example because we have 92.24%. That would just be 92.24 g. We then multiply by the molar mass. So we say one mole of carbon is equal to 12 g of carbon. And this gives us the number of moles. So this gives us 7.686 moles of carbon. We do the same thing for hydrogen. So 7.76% turns into 7.76 g. Multiplying by the molar mass we get one more is equal to 1. g of hydrogen. This gives us an answer of 7.7 moles of hydrogen. Okay, next we want to divide each of our moles by the least denominator. So for example, that would be our carbon. So we're gonna take our seven 0.68 six smalls And divide that by 7.686. And this gives us one. We do the same for hydrogen. We take 7.7 moles and we divide by the least denominator, giving us a value of approximately one. So our empirical formula in this example is ch. However, we are being asked to solve for the molecular formula, we take this molar mass that we used earlier 26 grams from all, and then we divide by 13.008g from all. We divide by the molar mass of our empirical formula that we wrote out 13.008 grams ramon. And when we solve this we get 1.99 or two. This is what we multiply each of our the number of atoms that we have. So for example, we have one carbon and one hydrogen. Therefore this is going to turn into C2 H two and this will be our molecular formula. I hope this helped and until next time.