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Problem 60

Epsom salts, a strong laxative used in veterinary medicine, is a hydrate, which means that a certain number of water molecules are included in the solid structure. The formula for Epsom salts can be written as $\mathrm{MgSO}_{4} \cdot x \mathrm{H}_{2} \mathrm{O},$ where $x$ indicates the number of moles of $\mathrm{H}_{2} \mathrm{O}$ per mole of $\mathrm{MgSO}_{4}$ When 5.061 $\mathrm{g}$ of this hydrate is heated to $250^{\circ} \mathrm{C},$ all the water of hydration is lost, leaving 2.472 g of MgSO $_{4} .$ What is the value of $x ?$

7 water molecules

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## Video Transcript

Okay, So in this problem, we are given with a sample off. Ah, sorry. Named Epsom Salt and which is written as M. Joseph. Forward exit tool or ex indicates the number of months of water our mole of munitions self at. So here we're given a man's off this mgs of water excess. Sure, some solid is five point six one gram. And what is he did all the water of tradition is lost, and this mass of magnesium sulphate is lived. That means this is the massive munitions self it in this formula and where this is the mass of the whole formula. So we have to find a veil off extract mints. We have to find the number off balls off each toe present. Ah, Barmal off. Manage himself says, you know that to find out the number of malls we have toe, um, what we have to do is we have to just to fight the mass by the molar mass. So here we know the massive McNish himself at we know the mass of the ah, formal, um So from this tomb as we confined them mass of water and we know them as a mannish himself it from this too. We can find out on the number of mall surface to and Magnus himself it. And from there we can find out the value ofthe eggs. So here are the steps written down here which will follow in this problem. First, we'Ll calculate the mass of water in the salt and the royal. We will find out the number of malls off water and McNish himself. And then we'LL divide each of this number of malls by the smallest number of moles off this between the smallest witches divide bought off them by the smallest one. Get the simplest all number issue of the malls. And from that reassure, we can identify or deter mined the valor fix. So let's start by finding all the mass off its tour. So massive fish too, will be equal to massive the sample or massive hydrate. Mina's massive MGs of four king. So a massive hydrant here is Ah, this one which is five point or six one and our massive McNish himself it is two point four seven two. So we, um all right. Five point all six one, which is a massive fight. Dread minus the massive munitions self it which is to plant four seven, two gram. And this will give us value off two point five eight nine Graham, which is the massive fish tour here. So now we have found a massive age tool and this is our maximum missions Self it. So from these two, we will find out the number of most of its two and Magnus himself in so number of most of its tool, it would be the massive fish to over is to a smaller man to the masses to burned five, eight, nine and the Moler Massive esto is eighteen point one. As you know, um, Grandpa Ramon segments it will give us a value off zero point one four four more. So this is the number of matloff. It's sure now we'LL find the number of moles off Manish himself. It it's a number of most of Magnus himself. It will be the massive ignition self it which is two point four seven program over the molar mass of my missions self it which, if you calculate, we'LL find one twenty four four Gramp Armel and this will give us a value off zero plant zero to one more. So this is the number of more imagination cellphone. And this is an admirable off h u. So from here we can see that this is the smallest fellow. That mess will divide each number of malls by the zero point zero two one to get simplest the whole number issue. So they're issue off its tools will be the number of most selfish two of which is your open one for three eight mall over The smallest knowledge is zero their plant. Okay, we consider that has zero point one for four. We'LL write it too. Here also And we deliver this by zero point zero two One more Give us so it'LL give us approximate bell of seven and then in goes off Mag nations Self since we're dividing the same number Is there a pond zero toe One more over zero point zero One more city She'LL give us a bell of one So from here you can see that the issue off its tour and m j So four is seven is two one that men's for one mole off my ignitions self at we will have seven more fish tool and This is the value ofthe X, as you know, that the ex is the number of most of its toe present primal of my nation cell phone. That means since we have seven more office, two apart warm, all of English himself and that means the value ofthe exists seven.