Elemental analysis of b@carotene, a dietary source of vitamin A, ...

Question

Elemental analysis of b@carotene, a dietary source of vitamin A, shows that it contains 10.51% H and 89.49% C. Dissolving 0.0250 g of b@carotene in 1.50 g of camphor gives a freezing- point depression of 1.17 °C. What are the molecular weight and formula of b@carotene? [Kf for camphor is 37.7 1°C kg2>mol.]

Accepted Answer

Hello. In this problem, we are told that alpha took off for all is most commonly found, naturally occurring form of vitamin E. Its elemental composition is 80.85% carbon, 11.72% hydrogen and 7.43% oxygen. A solution of 9.85 g of talks overall and g of cyclo hexane freezes at 215 degrees Celsius below the freezing point of cyclo hexane. Were asked to calculate the molecular weight and the molecular formula of alpha hall. And we are given the freezing point depression constant of cyclo hexane, which is 20.2 degrees Celsius kilograms per mole. So we're gonna carry out this problem in two steps. The first step is to determine the empirical formula from percent composition and then we will determine the molar mass from the freezing point depression. Beginning with step one, we will assume we have 100 g of alpha to call for all, which then means that if it is 80.85% carbon, we have 80.85 g of carbon With 11.2% hydrogen means we have 11.2 g of hydrogen and it is 7.43% oxygen. So we have 7.43 g of oxygen. And so all of those with some 200. Um which is why we make the assumption that we have 100 g. That makes the calculation easier. So now we're gonna convert these all two moles. So we can come up with an empirical formula. So one mole Of carbon has a mass of 12.01, 1 g of carbon or grams of carbon cancels and this works out to 6.731 moles of carbon. Using the molar mass of hydrogen, we have one mole hydrogen has a mass of 1.008g of hydrogen g of hydrogen cancels. This works out to 11.6 - seven moles of hydrogen. And then using the molar mass of oxygen, one mole Of oxygen has a mass of 15.9994 g of oxygen, or roughly 16 g of oxygen cancels. And this works out to 0.4644 moles of oxygen. So now we're gonna divide through by the smallest number of moles, which is the moles of oxygen. We have 7.31 moles of carbon divided by 0.4644 moles of oxygen. This works out to 14. moles of carbon for every mole of oxygen, we have 11.6-7 moles of hydrogen Divided by 0. moles of oxygen. This works out to 25 moles of hydrogen for every mole of oxygen and taking moles of oxygen by itself, they get one. So we can't round up the 14 around down the 14. So we think about the fact that's close to 14.5. And so to make it a whole number. If we multiply by two, if we multiply this by two, we have to multiply all of them by two. So this works out to 28.98 rolls of carbon for every role of oxygen. And this works out to 50 moles of hydrogen for every mole of oxygen. And this works out to two moles of oxygen, every all of oxygen. So the 28.98 moles of carbon for every mole of oxygen. We're gonna round that up to 29. So our empirical formula Is C H 50 02. So we'll calculate the mass solar mass um of our, based on our empirical formula, we call it the empirical mass. Then we have 29 carbons carbon. That's a massive 12.011 g for every mole We have 50 hydrogen, so 50 times the more mass of hydrogen, which is 1.008 grams per mole. And we have two oxygen's. So two times 15. g per mole, roughly 16. and this works out to 437, sorry, 430.7 g. So that's the Mass based on mass based on the empirical formula step # two. Then now we're going to determine. And uh well, the mass from freezing point depression. So the formula then that describes the depression in the freezing point for the solution is the change in freezing point is equal to the van Hoff factor times a freezing point depression, constant times the morality in this problem, then I, Vantaa factory is equal to one because alpha takeoff roll is a non electrolyte, so it's not gonna disassociate in cyclo hexane. Um and cyclo hexane As a freezing point depression, constant value of 20.2 degrees Celsius per morale. And we're told that the change in freezing point Is, it freezes at 2.15°C below that of the actual freezing point of cyclo hexane. So the change in freezing point is 2.15°C. So solving for morality, we have the change in the freezing point. Provided by the van Hoff factor divided by K. F. Change of freezing point is 2.15 degrees Celsius divided by one Divided by 20.2°C Permal al this works out to 0.1064 Morale. Writing that out further, Morality is equal to 0.1064 moles of our salute, which is the alpha to corporal per kilogram of our Sullivan, which is the cyclo hexane. And so based on the problem statement, we were told that we had A solution that had 9. g of alpha toko for all. In 215 g of cyclo hexane and we set it up this way because we're trying to find the molar mass of alpha. Natural. So we know the mass needs to be in the numerator and then I can make use of my morality is a conversion factor. To get my massive cyclo hexane to cancel the kilogram is 1000 g. So we have 1000 g of cyclo hexane. And for every 1000 g of cyclo hexane, we have 0.1064 moles of alpha. So our massive cyclo hexane cancels. We're left with grams of toku to call for all for every mole of took off for all. This works out to be grams per mole. This is our molar mass. So we can come up with what's called the multiplication factor and it's equal to then our Molar mass of our compound divided by the empirical mass. Based on the empirical formula. So this is 431 g per mole. The empirical formula we found is 430.7 g per mole. And this works out to one. So our multiplication factor is one which says then that the molecular formula is the same as the empirical formula. So in this problem we were asked to calculate the molar mass molar mass of alpha took off for all, then is 431 g per mole. And uh like the formula is the same as the empirical formula which is C29 age 02. So this is again both the molecular and the empirical formula for alpha. Thanks for watching Hope This help.

Watch next