(a) The characteristic odor of pineapple is due to ethyl butyrate, a compound containing carbon, hydrogen, and oxygen. Combustion of 2.78 mg of ethyl butyrate produces 6.32 mg of CO₂ and 2.58 mg of H₂O. What is the empirical formula of the compound?

Video transcript

Welcome back everyone to another video. The characteristic odor of pineapple is due to ethylbutyrate, a compound containing carbon, hydrogen and oxygen combustion of 5.41 mg of ethylbutyrate produces 7.95 mg of CO2 and 3.25 mg of HTO. What is the empirical formula of the compound? And we are given the four answer choices. AC two H 40 BC H 302, DT H2O and DT 4h 502. So this is a classical combustion analysis problem. And in order to solve it, we first will have to define the unknown. We know that our compound consists of carbon, hydrogen and oxygen. We can define the empirical formula as cxhyoz. And our goal is to identify Xy and Z to do that, our first step is to always calculate the number of modes of carbon and hydrogen. So first of all, the number of moles of carbon would actually be equal to the number of moles of carbon dioxide because there is one mole of carbon and one mole of carbon dioxide. And we do that by taking the mass of CO2 and dividing by the molar mass of CO2. And let's not forget that we need to use grams instead of milligrams. So what we're going to do here is just multiply bytes into the negative third. The molar mass of CO2 would be 44.01 grams from all. If we calculate the result here, we will get the number of modes of carbon which is equivalent to 1.8 064, multiplied by 10 to the negative fourth mose. Now we want to calculate the number of moles of hydrogen, which would be twice the number of moles of H2O based on stom Mery. So we take two multiplied by we 0.25 multiplied by 10 to the negative third grams divided by the molar mass of HTO which is 18.015 g per mole. And this is how we get 3.6071 multiplied by 10 of the negative word most. So we're done with our first step. In the second step, we want to convert those moles into masses. And the reason why we're doing this is because we want to get the mass of oxygen, we have the total mass of our compound. We will have masses of carbon and hydrogen, meaning the remaining mass will belong to oxygen. So now we're ticking the number of moles, calculate it in the first step and we are converting them into masses. So first of all, 1.8064 moles actually 1.8064 multiplied by 10 to the negative fourth. Most of carbon must be multiplied by its smaller mass of 12.0 11, which would give us the mass of carbon, which in milligrams would be 2.1695. Then we do the same for hydrogen. We take 3.6071 multiplied by its sense of the negative four moles. The molar mass of hydrogen is 1.008. If we multiply these and multiply by 1000, we get the milligrams of H which is 0.3636 mg. And therefore, in the second step, we can now easily calculate the mass of oxygen. Let's find the difference between the total mass of our compound and the masses of the of the previous two elements which are carbon and hydrogen. So we take 5.41 minus 2.1695. And we also subtract 0.3636. Now, this gives us a result of 2.8769 mg in the third step. Now that we have the mass of oxygen, we can easily get the number of moles of oxygen. Using the previously indicated formula. We take the mass of oxygen in grams and divide by the molar mass of oxygen which is 16. This gives us the number of moles of oxygen which is equivalent to 1.7981 multiplied by tens of the negative four small. And this is where our problem is nearly solved because if we have the number of moles of each substance or actually each element to be more accurate, we can now find the ratio of those moles. So we have a total of three numbers. We want to identify which one of them is the lowest one. Now, what we're going to do here is calculate the ratio of the number of moles of carbon to hydrogen to oxygen. We'll start with carbon. We are going to include 1.8064. There's no necessity to include the exponent because all of the exponents are the same. Then for hygiene, we have 3.6071 for oxygen 1.7981. And we want to divide all of them by the smallest number which is 1.7981. Now, what do we get? Well, essentially, if we divide all of them by the smallest number, we get our final ratio in whole numbers which would be 1 to 2 to 1, meaning the formula would be one carbon, two hydrogens in one oxygen. As a result, we can conclude that the correct answer to this problem would correspond to the answer choice. C C H2O is the empirical formula of the compound. Thank you for watching.