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The aluminum sulfate hydrate $\left[\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3} \cdot x \mathrm{H}_{2} \mathrm{O}\right]$contains 8.10 percent Al by mass. Calculate $x,$ that is, the number of water molecules associated with each $\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}$ unit.

The value of $x$ is 18

Chemistry 101

Chapter 3

Mass Relationships in Chemical Reactions

Chemical reactions and Stoichiometry

Rice University

University of Maryland - University College

University of Kentucky

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.

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The aluminum sulfate hydra…

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the aluminum sulfate hydra…

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Aluminum sulfate, $\mathrm…

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A sample of aluminum sulfa…

So for this problem, we have some aluminum sulfate hydrate, and I know that it contains 8.1% aluminum. But us and I want to find how many water molecules are associated with the union to maintain that present mass of aluminum for the first thing that I need to do before I do anything is actually calculate the molar mass of aluminum sulfate. It's like and then use that basic story geometry. So I know that an aluminum sulfate which is ailed to eso 43 I don't have to aluminum, which is going to need two times 26.98 three sulfur just didn't you putting six men 12 Oxygen's, which is 12.16 point of. And then when I multiply all of these things together, we're going to get that. My result is 342 0.15 grams role. That's the molar mass of aluminum sulfate. So now how do I approach this problem as a whole? So my approach is gonna be I'm just going to assume that we have some amount of aluminum sulfate hydrate and then from there, take advantage of the percent aluminum by Mass to find the grams of the aluminum sulfate in that contents. Let's just arbitrarily assume that I have 100 grams of the hydrate compound, so this includes both the aluminum sulfate and all the water in it. So let's just assume I have 100 grams of that. Well, I know that if that's 100 grams, 8.10 grams of that will be aluminum. And the reason why is because it's 8.1% aluminum has given to us in the problem. That's a nice manipulation will use. And now you want to find how many grams of aluminum sulfate there's well, first, I want to divide. I want to find moles of aluminum, so I just divide with the atomic mass of aluminum, which is 26.98 And I know what I want to find the multiple ratio of aluminum aluminum sulfate. I know that there's two moles of aluminum, every one mole of aluminum sulfate because there's two aluminum Adams in every 11 herself, a molecule. And finally, I'm just gonna multiply that by the molar mass of aluminum sulfate metric calculated to be 342.15 So I get grams of aluminum sulfate, which is 51 0.36 grams. So now I want to find grams of water and I can because they know that the grams of water is just going to be the grounds. The total hydrate, which is 100 grams minus the part that is theologians sulfate, which is 51 0.36 grams so that I get that my mass of my water is just going to be 48 point 64 grams of h 20 So now I'm going to find from there the multiple ratio of water to aluminum sulfate. And then from there I can then find number water molecules that money need. So if I have 51 0.36 grams of aluminum selfie well, I need to do is divide by the more mass find moles of aluminum sulfate, and we calculated that to be 300 and 42.15 Multiply this through. I'll get 0.150 Moles of aluminum Sophie. Now I have water 40.64 grams of water. And I know that as we calculated, whereas we can calculate. But the more mass of water means you calculate that Let's just going to be two hydrogen, which is 1.8 plus an oxen, which is 16 point of. So that's going to be the molar mass. And what I multiply all of that through. I get 2.70 moles of water. No, I know that my hydrate is going to have one mole of aluminum sulfate, so I just have to take my given units and find the ratio. And with their ratio, I can then find the number of moles or the emir of units of off water in each unit of aluminum sulfate. So I divide this side by point 150 when they divide that sidelight 1500.15 and I will get one more of aluminum sulfate. And if you divide that by 8.15 I will get 18 more of age to. This means that in my hydrate for every mole of aluminum sulfate is going to the 18 moles of H 20 So I know that my ex or the missing X in the hydrate it's going to be 18 which means 18 water molecules accompany every aluminum selfie molecule in my hydrate, and that is the final answer

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