Epsom salts, a strong laxative used in veterinary medicine, is a hydrate, which means that a certain number of water molecules are included in the solid structure. The formula for Epsom salts can be written as MgSO4⋅xH2O, where x indicates the number of moles of H2O per mole of MgSO4. When 6.073 g of this hydrate is heated to 250 ∘C, all the water of hydration is lost, leaving 2.966 g of MgSO4.
What is the value of x?
molar mass MgSO4 ... 120.4 g
... moles MgSO4 ... 2.966 g / 120.4 g
molar mass H2O ... 18.02 g
... moles H2O ... (6.073 g - 2.966 g) / 18.02 g
x = (moles H2O) / (moles MgSO4)
To determine the value of x, we need to calculate the amount of water that was lost during heating. We can then compare this value to the amount of magnesium sulfate remaining to find the ratio of water to magnesium sulfate.
1. Calculate the molar mass of magnesium sulfate (MgSO4):
- Mass of Mg = 24.31 g/mol
- Mass of S = 32.07 g/mol
- Mass of 4 O = 16.00 g/mol x 4 = 64.00 g/mol
- Molar mass of MgSO4 = 24.31 + 32.07 + 64.00 = 120.38 g/mol
2. Convert the mass of magnesium sulfate remaining (2.966 g) to moles:
- Moles of MgSO4 = Mass / Molar mass = 2.966 g / 120.38 g/mol ≈ 0.02465 mol
3. Calculate the amount of water lost during heating by subtracting the mass of magnesium sulfate remaining (2.966 g) from the initial mass of the hydrate (6.073 g):
- Mass of water lost = Initial mass - Mass of MgSO4 left = 6.073 g - 2.966 g = 3.107 g
4. Convert the mass of water lost to moles:
- Moles of water lost = Mass / Molar mass = 3.107 g / 18.02 g/mol ≈ 0.1722 mol
5. Finally, determine the ratio of moles of water to moles of MgSO4 by dividing the moles of water lost by the moles of MgSO4:
- x = Moles of water lost / Moles of MgSO4 = 0.1722 mol / 0.02465 mol ≈ 7
Therefore, the value of x is approximately 7.
To find the value of x in the formula MgSO4⋅xH2O, we need to use the given information and perform a series of calculations.
Step 1: Calculate the mass of water lost during heating
The mass of the hydrate before heating is 6.073 g, and the mass of anhydrous MgSO4 after heating is 2.966 g. Therefore, the mass of water lost during heating can be calculated as follows:
Mass of water lost = Mass of hydrate before heating - Mass of anhydrous MgSO4
Mass of water lost = 6.073 g - 2.966 g
Mass of water lost = 3.107 g
Step 2: Convert mass of water lost to moles
To calculate the number of moles of water lost, we need to divide the mass by the molar mass of water, which is approximately 18.015 g/mol.
Number of moles of water lost = Mass of water lost / Molar mass of water
Number of moles of water lost = 3.107 g / 18.015 g/mol
Number of moles of water lost = 0.1722 mol
Step 3: Convert moles of water lost to moles of MgSO4
Since the ratio of water to MgSO4 in the formula is x, the number of moles of MgSO4 is equal to the number of moles of water lost.
Number of moles of MgSO4 = Number of moles of water lost
Number of moles of MgSO4 = 0.1722 mol
Step 4: Calculate the molar mass of MgSO4
The molar mass of MgSO4 can be calculated by adding the atomic masses of each element in the compound.
Molar mass of MgSO4 = (1 mol Mg) + (1 mol S) + (4 mol O)
Molar mass of MgSO4 = (24.305 g/mol) + (32.06 g/mol) + (4 * 16.00 g/mol)
Molar mass of MgSO4 = 120.366 g/mol
Step 5: Calculate the value of x
Now, we can find the value of x by dividing the number of moles of MgSO4 by the molar mass of MgSO4.
x = Number of moles of MgSO4 / Molar mass of MgSO4
x = 0.1722 mol / 120.366 g/mol
x ≈ 0.00143
Therefore, the value of x in the formula MgSO4⋅xH2O is approximately 0.00143.