Question

A 5.25g sample of magnesium sulfate hydrate is heated until the masses stabilize. If the residue has a mass of 2.56g, answer the following. What is the mass of the hydrate?

Answer 1

A hydrate is a compound that contain (loose) molecules of water. When the molecules are removed (usually by heat), the hydrate becomes the anhydrous (no water) compound.
An example is copper sulphate, which is a blue crystal when there are 5 molecules attached to the compound (CuSO4.5H2O0. When it is anhydrous, it becomes a white powder.

This question is not too clearly written by asking the mass of the hydrate, which is given as 5.25 g. But it would be understood that it is the number of water molecules in the hydrate that is required.
It is a logical problem to do because Magnesium Sulphate has more than one possible hydrates, so determining the number is logical.

What we need to know is that the mass of the hydrate and the mass of the anhydrous ("when the mass is stable") substance is proportional to the molecular masses.

So we set up the equation, assuming x molecules of H2O in the hydrate and calculate the molecular masses:
\(\Large \frac{24+32+4*16+(16+2)x}{24+32+4*16}=\frac{5.25}{2.56}\)

Solve for x and round to the nearest integer.