To determine the value of x in the formula (Na2SO4路xH2O), we need to calculate the molar mass of the hydrated sodium sulphate (Na2SO4路xH2O).
Let's break down the molar mass calculation step-by-step:
1. Sodium (Na) has a molar mass of 23.0 g/mol.
2. Sulfur (S) has a molar mass of 32.0 g/mol.
3. Oxygen (O) has a molar mass of 16.0 g/mol.
4. Hydrogen (H) has a molar mass of 1.0 g/mol.
The molar mass of sodium sulphate (Na2SO4) is calculated as follows:
(2 脳 Na) + S + (4 脳 O)
(2 脳 23.0) + 32.0 + (4 脳 16.0)
46.0 + 32.0 + 64.0
142.0 g/mol
Now, let's find the molar mass of water (H2O):
2 脳 H + O
(2 脳 1.0) + 16.0
2.0 + 16.0
18.0 g/mol
Considering the hydrated formula of sodium sulphate (Na2SO4路xH2O), the total molar mass is:
142.0 + (x 脳 18.0) g/mol
Next, we have to find the moles of hydrated sodium sulphate used by using the given mass of 3.22g:
Moles = Mass / Molar mass
Moles = 3.22g / (142.0 + (x 脳 18.0)) g/mol
The mass of the anhydrous sodium sulphate (Na2SO4) is given as 1.42g. The molar mass of anhydrous sodium sulphate is 142.0 g/mol.
Now, we can set up an equation based on the conservation of mass:
Moles of hydrated sodium sulphate = Moles of anhydrous sodium sulphate
Therefore, we can write the equation as follows:
3.22g / (142.0 + (x 脳 18.0)) g/mol = 1.42g / 142.0 g/mol
Cross-multiplying the equation, we get:
(3.22g)(142.0 g/mol) = (1.42g)(142.0 + (x 脳 18.0)) g/mol
Simplifying, we have:
457.24 = 201.24 + (x 脳 25.56)
Rearranging the equation, we get:
(x 脳 25.56) = 457.24 - 201.24
(x 脳 25.56) = 256.0
Finally, divide both sides of the equation by 25.56 to solve for x:
x = 256.0 / 25.56
Calculating, we find:
x = 10
Therefore, the value of x in the formula Na2SO4路xH2O is 10.