A hydrate of copper(II) chloride has the following formula: CuCl2 # x H2O. The water in a 3.41-g sample of the hydrate is driven off by heating. The remaining sample has a mass of 2.69 g. Find the number of waters of hydration (x) in the hydrate.

Video transcript

Welcome back everyone to another video. A hydrate of copper two chloride has the following formula. Copper two chloride X hydrate the water in a 3.41 g sample of the hydrate is driven off by heating. The remaining sample has a mass of 2.69 g. Find the number of waters of hydration acts in the hydrate. And we are given for answer choices A four B 3d 2 and D one. So let's solve this problem. First of all, we have our substance. We are going to write the formula here. We don't know the number of water molecules attached to the hydrate. Specifically, we are heating it, right. So we're taking the solid form and when we heat it, we're basically separating copper two chloride and X amount of water. In this case, we can use water vapor, right? We're heating at a higher temperature. We're going to use gas and for copper to chloride, we're going to use the solid warm and because it's a salt, now, essentially, we want to identify a and we are given the mass of the sample, we can easily find the mass of water according to the law of mass conservation. So mass of the sample is given. So we're going to find the mass of water 3.3 0.41 g. That's the total mass of the sample. If we subtract 2.69 g, which is the mass of copper two chloride, we will get the mass of water, which is 0.72 g. Now let's find the number of moles of water. And we can do that by dividing the mass of water by its molar mass. We have 0.72 g. We need to divide that by 18.015 g per mole. That's the molar mass of water. And if we calculate the result, we get 0.040 moles. And similarly, we want to identify the number of moles of copper to chloride because we're interested in the ratio. Once again, we know the mass of copper two chloride. That's 2.69 g. We need to divide that number by the molar mass of copper two chloride. That's 134.45 grams from all. Now, if we do the math here we end up with 0.020 moles. And eventually, if we have most of both, we can find the ratio. So we take the number of moles of water. And if we divide by the number of moles of copper to chloride, we take 0.040 moles divided by 0.020 moles. And this gives us 2.0 meaning X should be two because we have the molar ratio of a 1 to 2 or basically 2 to 1 if we start with X, right. So X is equal to two. And we can easily tell that based on our answer, the correct choice or the correct answer to this problem would be option C the value of X is two. Thank you for watching.