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 Na2CO3·x H2O, where x is the number of moles of H2O per mole of Na2CO3. When a 2.228 g sample of washing soda is heated at 125°C, all the water of hydration is lost, leaving 0.825 g of Na2CO3. What is the value of x?
To find the value of x in the formula Na2CO3·x H2O, we need to determine the moles of water and moles of Na2CO3 present in the given sample.
Let's calculate the moles of Na2CO3:
The molar mass of Na2CO3 is:
2(atomic mass of Na) + atomic mass of C + 3(atomic mass of O)
= 2(22.99 g/mol) + 12.01 g/mol + 3(16.00 g/mol)
= 46.00 g/mol + 12.01 g/mol + 48.00 g/mol
= 106.01 g/mol
Now, let's calculate the moles of Na2CO3 in the sample:
moles of Na2CO3 = mass of Na2CO3 in grams / molar mass of Na2CO3
moles of Na2CO3 = 0.825 g / 106.01 g/mol
Next, we need to determine the moles of water that were lost during heating. The difference between the initial mass and final mass of the compound represents the mass of water lost.
The mass of water lost = initial mass - final mass
= 2.228 g - 0.825 g
Now, calculate the moles of water:
moles of water = mass of water lost / molar mass of water
molar mass of water = 2(atomic mass of H) + atomic mass of O
= 2(1.01 g/mol) + 16.00 g/mol
= 2.02 g/mol + 16.00 g/mol
= 18.02 g/mol
moles of water = (2.228 g - 0.825 g) / 18.02 g/mol
Finally, we can determine the value of x by comparing the moles of water lost to the moles of Na2CO3:
moles of water / moles of Na2CO3 = x
Substituting the calculated values:
(2.403 / 106.01) = x
Simplifying,
x ≈ 0.0226
Therefore, the value of x is approximately equal to 0.0226 in the formula Na2CO3·x H2O.