What is the value of X?

Question

Washing soda, a compound used to prepare hard water for washing laundry, is a hydrate, which means that a certain number of water molecules are included in the solid structure. Its formula can be written as Na2CO3x H2O, where x is the number of moles of H2O per mole of Na2CO3. When a 1.836 g sample of washing soda is heated at 125°C, all the water of hydration is lost, leaving 0.680 g of Na2CO3. What is the value of x?

Answer 1

Na2CO3 has a molecular weight of (rounding off values)

Sodium: 23 g/mole
Carbon: 12 g/mole
Oxygen: 16 g/mole

so 2*23 + 12 + 3*16 = 106 g/mole
Water is 18 g/mole.

you have 0.68 g of dry Na2CO3, and had (1.836 - 0.68) 1.156 g of water.

0.68 g of Na2CO3 is 0.0064 mole, and 1.156 g of water is 0.064 mole.

The ratio is pretty much equal to 10...

Answer 2

amount in grams of water = 1.836- 0.680 =
___ = 1.156 g
amount in mols of water = 1.156/(2*1.008+ 16.00)
___ = 0.0642 mol

amount in mols of Na2CO3 =
___ = 0.680/(2*22.99+ 12.01+ 3*16.00) =
___ = 0.00642 mol

There are (0.0642)/(0.00642) = 10 units of water for every unit of Na2CO3, which means that x = 10.

Answer 3

Na2CO3 has a molecular mass of 2*22.99+12.01+3*16
=105.99, or 106
H20 has an molecular mass of 2*1.008+16 = 18.016, or 18
(105.99+x*18.016)/1.836 = 105.99/0.68
18.016*x = 1.836*105.99/0.68 - 105.99
x = (1.836/0.68-1)*105.99/18.016

x=10