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?
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To find the value of x in the formula Na2CO3·x H2O, we can use the given information about the mass of washing soda and the mass of Na2CO3 left after heating.
Step 1: Calculate the number of moles of Na2CO3 left after heating.
We can find the number of moles from the mass using the molar mass of Na2CO3.
The molar mass of Na2CO3 can be calculated by adding the atomic masses of sodium (Na), carbon (C), and oxygen (O):
Molar mass of Na2CO3 = (2 x atomic mass of Na) + atomic mass of C + (3 x atomic mass of O)
Using the atomic masses from the periodic table:
Molar mass of Na2CO3 = (2 x 22.99 g/mol) + 12.01 g/mol + (3 x 16.00 g/mol)
Molar mass of Na2CO3 = 22.99 g/mol + 12.01 g/mol + 48.00 g/mol
Molar mass of Na2CO3 = 82.00 g/mol
Now, we can calculate the moles of Na2CO3:
Moles of Na2CO3 = Mass of Na2CO3 / Molar mass of Na2CO3
Moles of Na2CO3 = 0.825 g / 82.00 g/mol
Moles of Na2CO3 = 0.010 mol
Step 2: Calculate the moles of water lost during heating.
Since the mass of the washing soda (Na2CO3·x H2O) has decreased by the mass of Na2CO3, the mass difference corresponds to the water lost during heating.
Mass of water lost = Mass of washing soda - Mass of Na2CO3
Mass of water lost = 2.228 g - 0.825 g
Mass of water lost = 1.403 g
Step 3: Calculate the moles of water lost.
We can calculate the moles of water lost using the molar mass of water (H2O).
The molar mass of water (H2O) can be calculated by adding the atomic masses of hydrogen (H) and oxygen (O):
Molar mass of H2O = (2 x atomic mass of H) + atomic mass of O
Using the atomic masses from the periodic table:
Molar mass of H2O = (2 x 1.01 g/mol) + 16.00 g/mol
Molar mass of H2O = 2.02 g/mol + 16.00 g/mol
Molar mass of H2O = 18.02 g/mol
Now, we can calculate the moles of water lost:
Moles of water lost = Mass of water lost / Molar mass of H2O
Moles of water lost = 1.403 g / 18.02 g/mol
Moles of water lost = 0.078 mol
Step 4: Calculate the value of x.
The value of x represents the number of moles of H2O per mole of Na2CO3.
The moles of Na2CO3 (0.010 mol) and the moles of water lost (0.078 mol) are in a ratio of 1: x.
Therefore, we can write the following equation:
0.010 mol Na2CO3 / 1 = 0.078 mol H2O / x
Simplifying the equation by cross-multiplying:
0.010 mol Na2CO3 * x = 0.078 mol H2O * 1
x = (0.078 mol H2O * 1) / 0.010 mol Na2CO3
x = 7.8
Therefore, the value of x is 7.8.
So the formula for washing soda is Na2CO3·7.8 H2O, indicating that each mole of Na2CO3 is associated with 7.8 moles of water.
mass water expelled is
2.228-0.825 = ?, then
mols H2O = ?g/18 = ?
0.825/molar mass Na2CO3 = ?
Now find the ratio of the two. This USUALLY is done to make Na2CO3 = 1.00 and x some whole number.