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Peroxyacylnitrate (PAN) is one of the components of smog. It is a compound of $\mathrm{C}, \mathrm{H}, \mathrm{N},$ and O. Determine the percent composition of oxygen and the empirical formula from the following percent composition by mass: 19.8 percent $\mathrm{C}$ 2.50 percent H, 11.6 percent N. What is its molecular formula given that its molar mass is about $120 \mathrm{g} ?$

Molecular formula is C2H3NO5 which is also the empirical formula since there is no simpler ratio of the elements

Chemistry 101

Chapter 3

Mass Relationships in Chemical Reactions

Chemical reactions and Stoichiometry

Carleton College

University of Maryland - University College

University of Toronto

Lectures

04:02

A chemical reaction is a process that leads to the transformation of one set of chemical substances to another. Chemical reactions can be either spontaneous, requiring no input of energy, or non-spontaneous, typically following the input of some type of energy, such as heat, light or electricity. Chemical reactions are usually characterized by a chemical change, and they yield one or more products after the reaction is complete. Chemical reactions are described with chemical equations, which symbolically present the starting materials, end products, and sometimes intermediate products and reaction conditions. Chemical reactions happen at a characteristic reaction rate at a given temperature and chemical concentration. Typically, reaction rates increase with increasing temperature because there is more thermal energy available to reach the activation energy necessary for breaking bonds between atoms.

08:02

In chemistry, a combination reaction is a chemical reaction in which two or more reactants combine to form more than one product. In a decomposition reaction, one reactant splits into two or more products.

05:06

Peroxyacylnitrate (PAN) is…

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so to solve this problem, we have a compound that we know has the elements carbon, hydrogen, nitrogen and oxygen. And we know that the percentage present of these elements in the compound for carbon, hydrogen and nitrogen and we're trying to determine one what is the percent of oxygen in the compound? And then also we're trying to determine what is the molecular formula of the compound. So I'm left your formula. We mean we were to rewrite this, as in the format of see. But however many moles of C H, the number of most of beach and how many moles, same as oxen were trying to determine the number of moles of each of these elements in the compound So we can write its molecular formula like this. And we've also been told in a problem that theme elect the molar mass of the this compound should be 120 grams per mole. So first off to salt, this is we determine what is the percent of oxygen in the So to do this. We know that since these four elements are the only ones present in the compound, that the percentage of all of these should total to 100% so known that information we can determine that oxygen is president 66.1% which is just 100 minus each of these percentages. Now we can go on to the steps, the steps we need to take to determine what is the molecular formula. So the first thing do for that is we need to determine how many moles of each compound they are of each element there are in the compound. Excuse me. So the first thing we can do is we have the percentages, but we don't have any value of the of the present of each element in terms of grams or moles. So we can approximate how many grams of each element are present. By using an easy number like 100 you can say that of our total compound. We have 100 grams of it and use that value to approximate the rest for information. So in as a sample calculation for carbon, we have 19.8% which is equal to 0.19 eight and then you can see that if we multiply that by ah 100 grams, they're trying to rent. How much carbon is in 100 grams off the compound, knowing that 19.8% of the compound this carbon from that we can determine that that would be 19 point eight grams. And so that's pretty much the same as the percentages. Why using 100 grams easy to approximate. So from that we kind of a problem. Not kind of we can. We can look at the percentages and say OK, so for carbon, there's 19.8 grams hydrogen, 2.5 grams nitrogen, 11.6 and just convert all of these two grams knowing that we're working out of the assumption of 100 grams of the compound. So now we need to convert all of these grams into molds again. I'll do a sample calculation with carbon, so we're gonna try and you need to determine the number of moles of carpet. So do that by simple calculation that we have 19.8 grams and then it's Moeller masses 12.1 We're gonna divide that these cancel out and then from that we get, we see that there's 1.65 moles of carbon. So if we do the same type of calculation, using our number grams to the from percentages and the more their way of each of these elements. We get the fallen values for the rest of the elements. 2.48 Moles of hydrogen 0.8 28 Moles of nitrogen, four point 13 Moors of Oxygen. So we have the number of moles of each element determined to what we're trying to do as reminder is to see how many moles of each one there are in our final compound. So the way do that is to compare mole ratios between the beach element. So we'll start with the element that by determining out of these four, rich element has the lowest number of moles because we'll use that to base our ratios off. So for this problem, that's nitrogen. And so what we do is we find out the ratio of how many carbs how many moles of carbon is there tonight, Shin, How many moles of hydrogen, nitrogen and how many moles of oxygen tonight you and we set up our ratios, but this have as so I'll do an example of carbon and then just give the answers for the rest of them. For carbon, you have set up the ratio by saying, as 1.65 moles of carbon, and then you set up the ratios of fraction to the number of moles. Is your point 8 to 8 of nitrogen, and that's going to approximate into two. We don't have to have an exact number because we're just trying to figure out the ratio and then so enjoy the same thing for Heidrun, you divided by the number of moles of nitrogen. For that, when the answer is three and then nitrogen, it's ratio with itself is going to be one and then oxygen the ratio. The number of moles of nitrogen is going to be equal to five. So now, looking at these argues, all circle them work. The that gives us the chemical formula of see to H three and 05 and so this is its most simplified form. So it's also nice the empirical formula and then, But the question is asking for what's the molecular formula and the difference being a molecular formula and the empirical formula is that the molecular formula is not necessarily the most simplified So this is where using the molecular weight of the final compound comes becomes required in our calculations. So what we need to do is digital is to determine what the Moeller molar Mass of this compound of this empirical formula we calculated is so the molecular weight of this ends up being 121.1 grams per mole. And so, similarly, if we set up a ratio to the molar mass, we are looking for riches 1 20 rams Permal, then that ratio is one. So that tells us that the and the formula we're looking at now is at an equal ratio to what we're expecting. So it is our final answer. We don't have to make any other modifications to it. So this is one of those cases where the empirical formula is equal to the molecular formula. But normally, if the problems

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