### Video Transcript

An analyst heated a sample of 50.0 grams hydrated salt until all the water was dried out. The mass of solid remaining was 35.0 grams. What was the percent of water by mass in the original sample? A) 13 percent, B) 30 percent, C) 35 percent, D) 70 percent, or E) 87 percent.

We can imagine the analyst weighing out 50.0 grams of the salt and putting in a crucible. By heating the sample, water is encouraged to escape. After sufficient heating, the analyst may have taken the crucible away from the heat, let it cool down, and weigh it. They would’ve returned it to the heat for a little bit longer and then weighed it again. If the mass was constant, then they would’ve known that the hydrated salt had been fully dehydrated.

A good example of a hydrated salt is copper sulfate pentahydrate. The mass of the hydrated salt is due to the salt itself, the copper sulfate, and the water. After heating, all the water would’ve gone, leaving behind only the salt as the remaining solid. So, the mass of water released when we heat the sample is simply the mass of the hydrated salt minus the mass of the residual solid, which is 50.0 grams minus 35.0 grams which evaluates to 15.0 grams.

So, we have the mass of water in the original sample and we have the mass of the original sample overall. Therefore, the percentage of water by mass in our hydrated salt is simply the mass of water we’ve just calculated divided by the mass of the sample multiplied by 100 percent. At this point, it’s very important not to put in the wrong number. The mass of sample refers to the mass of the hydrated salt. We’re not looking at the mass of solid remaining.

What you should plug in is 15 grams for the mass of the water and 50 grams for the mass of the sample, which evaluates to 0.3 times 100 percent which is 30 percent. So, in this case, where we had 50 grams of hydrated salt and heated it until there was only 35 grams of dry solid remaining, the percentage of water by mass in the original sample was 30 percent.