What is the formula of the hydrate?

Question

When 6.584f of one of the hydrates of sodium sulfate (Na2SO4) was heated to drive off all of its water of hydration, the residue of anhydrous sodium sulfate had a mass of 2.889g. What is the formula of the hydrate?

Answer 1

First use the weight of the sodium sulfate after all the water is gone to determine the moles of Na2SO4:

2.889g/[(2 x 23) + 32.06 + (4 x 16) = 0.0203 mole

The weight loss on heating can be used to determine the moles of water lost:

(6.584 - 2.889)/[(2 x 1.01) + 16] = 0.205 mole water

Now determine the ratio of Na2SO4 to water:

0.205/0.0203 = ~ 10.1

So: the ratio is 10 waters to one Na2SO4 or sodium sulfate decahydrate.