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Problem 148 Easy Difficulty

Leaded gasoline contains an additive to prevent engine "knocking." On analysis, the additive compound is found to contain carbon, hydrogen, and lead (Pb) (hence, "leaded gasoline"). When $51.36 \mathrm{g}$ of this compound are burned in an apparatus such as that shown in Figure $3.6,55.90 \mathrm{g}$ of $\mathrm{CO}_{2}$ and $28.61 \mathrm{g}$ of $\mathrm{H}_{2} \mathrm{O}$ are produced. Determine the empirical formula of the gasoline additive.

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Video Transcript

So for this problem, we want to find the empirical formula of some gasoline additive when you know that this gassing attitude that the original massive it with the mass of the total compound with the additive 51 0.36 grams. And we're told that in the by process of this that the mass of carbon dioxide formed it's 55 0.90 grams and that the math of the H 20 formed is 28.61 grips. So the first thing that we want to do is you want to find the masses of all of the elements that are relevant. So you want to find the masses of hydrogen, the mass of carbon and the massive 11 this compound. So the first thing we could do is you can find the master both carbon and hydrogen by taking advantage of the masses of carbon dioxide of underwater. But before we do that, we need to find the molar masses about those substances. So for co two, well, carbon, it's just 12 point no one to Oxygen's or each 16 point a little. That means stream or mass of 44 point no one grams for more, not each 20 well for H 20 we have two hydrogen, each of which are one point rate the oxygen, which is 16 in the wrong. And then we add those two together will get 18.2 grams purple. So now we can use these to find grams of carbon and grams of hydrogen. So let's first you carbon. So we have 55 0.90 grams of co two first and you want to divide by the molar mass. So you get malls of the now the multiple ratio. Well, there's one atom of carbon in every carbon dioxide molecule. The multiple ratio is 1 to 1 and finally we just multiply by the atomic math of carbon which is troll 0.1 to get grams of carbon. And when we do this you get 15 0.26 grams of carbon. I want to do the same thing for hydrogen. We have 28 0.61 grams of h two will and we could divide by the more massive age too, so that we get motivate show enough the conversion well in every molecule beach to their two hydrogen atoms. The multiple ratio must be 2 to 1. So two Mol of H everyone will love each to. And then finally we multiplied by the tonic math of each one point of grams to get the massive hydrogen. It turns out to be 3.2 grams of hydrogen. So now that we found the massive carbon hydrogen, you can then find the mass of the lead. The reason why is because we know the master, the total compound, and we could subtract the massively to other elements to get the mass. The third we have 51 0.36 which is a massively total compound subtracted Matthey Haijun, which is three point you. And then we offer subtract the mass of the carbon just 15 0.26 grams. And when you get that, we'll get that the total mass that we're dealing with this 32 or 33.0 grams have led. So now that we have 33 rooms of lead and be in fact isolated the masses of all of these substances, we could then find their multiple ratios. So you have 33 grams of lead and if we divide by the Atomic Matha would, which is 207 two grams for one mole of lead. We'll get 0.1 five nine Moles of people. Let's do the same thing for hydrogen. Well, we have 3.20 grams of hydrogen. You know that in one mole of age, Tom McManus, one point. Oh, wait. You multiply that through, they will get 3.18 moles of hydrogen and lastly carpet. Well, we have 15.26 grams of carbon. Really divide by its atomic mass of 12 point no. One, you'll get 1.27 moles of carbon. Now we need to divide these all by some number to get some positive information. So naturally, we're gonna divide by the smallest number just 0.15 It's obviously for lead. We're getting one as a ratio for hydrogen. Let me do this. You'll get roughly 20. And when you do this for carbon will get roughly eight. So the ratio off lead to hydrogen carbon is 1 to 28. So now we have our empirical formula. We have one ledge, you have 20 hydrogen and you have eight. So that is the empirical formula for the attitude on both the final answer

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