Epsom salts is a hydrated ionic compound with the following
formu...

Question

Epsom salts is a hydrated ionic compound with the following
formula: MgSO4 # x H2O. A 4.93-g sample of Epsom salts is heated
to drive off the water of hydration. The mass of the sample
after complete dehydration is 2.41 g. Find the number of waters
of hydration (x) in Epsom salts.

Accepted Answer

hey everyone in this example, we have the following hydrated ionic salt. And we're told that once our hydrated salt is heated, it weighs 7.98 g. However, once it's completely dehydrated, It was then reduced down to 3.52 g. And we need to determine the waters of hydration x in our given salt. So what we should recognize is in order to find the numbers of waters of hydration, we're going to take our moles of our salt and divide that by the smallest number of moles. And we're also going to recall that we're going to take the mold of our water and divided by the smallest number of most. And so this means that we need to find moles of our salt and moles of our water. So what we're going to do is take note of the fact that they tell us that our mass of our salt at the initial moment that it's being dehydrated or sorry, heated Is equal to 7.98 g. So this is the mass of our salt with water. And the second thing we need to take note of is that we have a mass of our salt without the water. So once it's dehydrated. And that according to the problem is this 3.52 g here. So we're going to take the difference of these two different masses to find our mass of water. And so that means we take 7.98 g of our hydrated salt and subtract that from our dehydrated salt. So just our salt alone. And sorry, the mass of that dehydrated salt, which is 3.52 g of just n a two S. 04 sodium sulfate. And so this difference gives us a mass of our water equal to 4.46 g. So now we can use this information to go ahead and find our moles of our salt first. So our moles of our salt according to the problem, can be found from taking our given mass of the salt alone As 3.52 g of sodium sulfate. And in our denominator we don't want to go from grams. We're in our numerator. We want moles so grams tomatoes. So we should recall our molar mass of our salt, sodium sulfate And that's going to equal a value of 142 0. grams per one mole of our sodium sulfate. This allows us to cancel out grams of sodium sulfate, leaving us with moles of sodium sulfate, which is what we want. And we get moles of sodium sulfate are salt equal to 0.02478. So from above, we were able to find our mass of our water and we're going to use it here. Below to find moles of our water. And so Above we found that we have 4.46 g of water. And we're going to do the same thing with the salt. We're going to sorry, we're going to do the same thing as we did with the salt and in our denominator, we're going to plug in our molar mass of water To get two moles of water. And so according to the periodic table, We have a molar mass of water equal to 18. g for one mole of water. And so we can cancel out graham's leaving us with moles of water, which is exactly what we want. And this gives us a value of 0.2476 moles. And so now is the part where we go into calculating our waters of hydration for our salt. And for yeah, for the salt. So what we're going to do is go ahead and take our most of our salt. So again, that was 0.02478. And we're dividing by the smallest number of most. And when we look at our values here, we see we have a zero in front of our molds of our salt. So we can go ahead and sorry, I forgot to write those units of most. We can go ahead and say that this is our smallest number of most. And so we're going to divide by 0. moles of our salt. And so this gives us a ratio of 1-1. So we can just say that we have just one mole of our salt. Our next step is to then go ahead and find our value for X here. So we would say that X. Our waters of hydration is equal to our moles of our water, which above we just found to be 0.24 76 moles of water divided by the smallest number of moles Which came from our salt as 0.02478 most. And this is of our salt and a two s. 04. And so this is going to then cancel out. And we're going to get our X value equal to a value of 9.99. We can go ahead and actually round this to about 10. And so this tells us that our waters of hydration Is going to be 10. So our formula is equal to our salt which we only had one more love in the end, dissolved in 10 moles Of our water or 10 waters of hydration of our water molecule. And so this will complete this example as our final answer here. So I'll just rewrite the X. Term instead of Boxing that in. So we would have our waters of hydration equal to 10. So our final answer Is going to be x equals 10. Our waters of hydration is equal to 10. If you have any questions, please leave them down below. Otherwise I will see everyone in the next practice video

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