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.

Video transcript

Welcome back. Every once in another video, Epsom salt is a hydrated ionic compound with the following formula, magnesium sulfate, X hydrate. A 14.79 g sample of Epsom salt is heated to drive off the water of hydration. The mass of the sample after complete dehydration is 7.23 g. Find the number of waters of hydration, X and Epsom salt and were given for answer choices. A three B seven C 11 and D 15. So first of all, what we understand is that we're given the total mass of the sample and the mass of the sample. After complete dehydration, let's understand that magnesium sulfate a hydrate will essentially decompose into magnesium sulfate and X moles of water. So according to the law of mass conservation, if we have the total mass of the sample, 14.79 g, we are given the mass of the sample after dehydration, which will correspond to the mass of magnesium sulfate. Why? Well, essentially that's because it remains solid and we get water vapor afterwards. So if we find the difference between 14.79 and 7.23 we will get the mass of water, which essentially corresponds to seven point 56 rams, right, based on the law of mass conservation, the sum of the masses of products must be equal to the sum of the masses of the reactants. So now that we have mass of each, we can find most of each, the number of moles of magnesium sulfate would simply be the ratio between its mass and molar mass. So we take 7.23 g and we divide by the molar mass of magnesium sulfate, which is 120 137 grams. For more, this gives us the number of moles of magnesium sulfate. We end up with 0.0601 moles. And now we find the number of moles of water, we already have the mass 7.56 g. And we divide by 18.015 g per mole, which is the molar mass of water. Now, let's perform the calculation. We get 0.420 moles. And eventually to find the X, we simply want to see that there are X moles of water per one mole of magnesium sulfate. So X is simply the ratio between 0.420 moles and 0.0601 moles. Why? Well, essentially this is because we will turn our denominator into one. So we will get the number of moles of water per mole of magnesium sulfate. And we end up with seven, which essentially corresponds to the answer choice B Thank you for watching.