When 6.724 g of one of the hydrates of sodium sulfate (Na2SO4) was heated to drive off its water of hydration, the residue of anhydrous sodium sulfate has a mass of 2.964 g. What is the value of x in the formula for the hydrate, Na2SO4•xH2O?
6.724g hydrate
-2.964g anhdrous Na2SO4
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3.760g H2O driven off.
Convert to mols.
3.760/18 = ? mols H2O
2.964/molar mass Na2SO4= ?
Now find the ratio of the water to 1.00 mol Na2SO4.
To find the value of x in the formula for the hydrate Na2SO4•xH2O, we need to determine the amount of water that was associated with the initial mass of the hydrate and then calculate x.
First, calculate the mass of water lost by subtracting the mass of the anhydrous sodium sulfate from the initial mass of the hydrate:
Mass of water lost = Initial mass of hydrate - Mass of anhydrous sodium sulfate
Mass of water lost = 6.724 g - 2.964 g
Mass of water lost = 3.76 g
Now, we know that the molar mass of water (H2O) is approximately 18.015 g/mol. To determine the number of moles of water lost, divide the mass of water lost by the molar mass of water:
Number of moles of water lost = Mass of water lost / Molar mass of water
Number of moles of water lost = 3.76 g / 18.015 g/mol
Number of moles of water lost ≈ 0.2086 mol
Since the empirical formula of the hydrate is already given as Na2SO4•xH2O, it means that 1 mole of Na2SO4 is associated with x moles of water.
Therefore, we can say:
Number of moles of Na2SO4 = Number of moles of water lost
Number of moles of Na2SO4 = x moles of water
0.2086 mol = x moles of water
To find the value of x, we can equate the equation in terms of moles:
x = 0.2086 mol
So, the value of x in the formula for the hydrate Na2SO4•xH2O is approximately 0.2086.