4.64 g of Na2So4 * xH2O were heated to yield 2.84 g of Na2So4. What is the value of x?
4.64g represents the mass of sodium sulfate combined with water.
If the heating yields 2.84g of sodium sulfate, that means that the difference in mass was entirely water.
Therefore 4.64 - 2.84 = 1.8g water.
However, this doesn't tell us the coefficient of water - that is, the ratio of water molecules to sodium sulfate molecules. To determine this, we need to work in moles. Working in moles allows us to ignore the difference in mass between the two molecules, and work only in the number of molecules that we actually have.
We need to determine the molar mass of each molecule - that is, the weight of one mole of that substance. You can do this by adding the mass of each constituent element.
Water = 18
Sodium Sulfate = 142
1.8g / 18 = .1mol water
2.84 / 142 = .02mol sodium sulfate.
Therefore, each .02mol of sodium sulfate corresponds to .1mol of water.
If we multiply both sides until we reach an integer coefficient, we find that this is a ratio of 1 to 5.
The value of x is 5.