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Problem 87 Hard Difficulty

A binary compound of magnesium and nitrogen is analyzed, and 1.2791 $\mathrm{g}$ of the compound is found to contain 0.9240 $\mathrm{g}$ of magnesium. When a second sample of this compound is treated with water and heated, the nitrogen is driven off as ammonia, leaving a compound that contains 60.31$\%$ magnesium and 39.69$\%$ oxygen by mass. Calculate the empirical formulas of the two magnesium compounds.

Answer

Hence limit will be $-3 / 4$

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Video Transcript

So in this problem, we have an equation. Chemical location. So we have unknown magnesium nitrogen compound that I will just call M g X. And why? And this unknown compound is being heated in water. So it is reacting with the water, and the heat is, you know, hoping the reaction move and to symbolize heat, we usually put a triangle on top of the aero. No, that's not necessary. But just, you know, for accuracy. And then this chemical reaction produces Ammon yellow. We don't know yet how many ammonia compounds it produces. Ammonia and an unknown magnesium oxide. Melo call again. MG X. Why? 00 why? You don't know yet how many addicts of those trump pumps these went this one in that one. So what we've been told was we've been told the mass percent of this magnesium oxide for, um the magnesium it 60.30 60.30%. Mike needs him and 39.69% oxygen. Just useful oxygen. Magnesium. Okay, so let's start all for this magnesium nitrogen compounds. We were told to that this compound he started, like the mass of the magnesium component, is 0.9 to four grams, and the mass of the nitrogen component is 0.351 551 Sorry about that. You can hear the but Okay, so we have the mass of each of these elements. So we are to find you know, how many atoms of each element are in this comp. Oh, so to find, like, the ratio of these number of atoms to each other, we need to, like, work in moles and not in mass. So you can easily turn, um, mass into moles by using this occasion. Over here malls is equivalent to mass over more mass. Okay. And we know that, um, even just look at your periodic table. You know, the molar mass of each of these compounds magnesium and introgen just by looking at its atomic mass. So if we just take these masses and divided by Mullah Mass, be him. Figure out that the mall's then of magnesium and nitrogen are zero point 038 Do with went 38 malls. No, and that of the nitrogen is 0.0 zero 25 15 most Okay, so now what we need to do so basically we figured out what X and y are just X. This is why it's just we need to turn these numbers into integers and not decimals. Yes, Uh, and the way we do this is simply by dividing. You take this X and we divided over what and way we will just take victory. We can always do take the larger moles and divided by the smaller mole. So, you know, it's a number were than one. So if we divide this x value over that y value, we basically get 1.5. Okay, so now Robert needs her. I understand some fraction work to be able to, you know, make this into integer after, so we know that all call numbers or all members are under Junan Meter of one. So x is 1.5. Why is one so here You just also like, play with this number until point with this fraction until it becomes a complete in the whole number overhaul number. So you should be able to recognize that we just need to multiply by two, and then we'll get 3/2 and to multiply, um, fractions. You just go anyways. Excess three wise to. I don't really worry about This. Gets multiplied by two, and that's get multiplied by two lips. Both of them get multiple abated. So this isn't like actual fraction multiplication. But yeah, we're just trying to plant a greater multiple. That's off complete hole number. So what we have is when you re right, that equation, it's m G three and two is the compound that is being treated with water to give off ammonia NH three. You should have that memorized and some magnesium outside. Okay, let's look up here. So what do we know about this being easy? Mark sites. We know the mass percent. So again as we did over here, we have, like, a mass number in mass percent. So we need to turned that mass number into malls he has. That is what will give us X and Y X and y is like a Moeller. I want a team like a mole ratio quantity. So do the same thing again and take mass mass values and divided by more mass values. So just take 60 over more mass of magnesium and 39.69 over the moments of oxygen, which will give us 2.48 and again 2.48 so we can see a lot more clearly. But this Moeller most function is giving us for eight. That's a So Audie is that, um, magnesium and oxygen are no oneto, one mole oration with each other. So X and Y are equivalent and are one. There's no need to do to anything crazier, just one. So then, yeah, it's actually just MGI. Oh, let's make that with a bit clearer. They're them 1 to 1 ratio, so just m g o.

McMaster University
Top Chemistry 101 Educators
TD
Theodore D.

Carleton College

Nadia L.

Rice University

Morgan S.

University of Kentucky

KS
Karli S.

Numerade Educator