What would be the mass of a bag of anhydrous magnesium sulfate, MgSO4, if it contained the same amount of magnesium as a 1.00kg bag of Epsom Salts, MgSO4 . 7H2O?
So I calculated the mass of MgSO4 (120.37g/mol) and the mass of 7H2O (126.14g/mol). Then I divided the mass of MgSO4 by MgSO4 . 7H20 multiplied by 100%. My answer was 95.426%. But how do I get the amount of magnesium?
I posted an answer but deleted it. Here is what I would do. There is a shorter way but I don't believe teachers are using gravimetric factors now--pity.
How much Mg is in the 1 kg bag of MgSO4.7H2O. That will be
1.00 kg x (1 mol/molar mass MgSO4.7H2O) x (24.30 g Mg/1 mol Mg) = g Mg in the 1.00 kg bag.
Now convert that g Mg into MgSO4 and you will have your answer.
The EASY way of doing it is
1.00 Kg x (molar mass MgSO4/molar mass MgSO4.7H2O) = ??
Try it both ways. The answer should be the same. Check my work.
To find the mass of a bag of anhydrous magnesium sulfate, MgSO4, that contains the same amount of magnesium as a 1.00 kg bag of Epsom Salts, MgSO4 . 7H2O, we need to calculate the molar mass of both compounds and compare the amount of magnesium in each.
1. Find the molar mass of Epsom Salts (MgSO4 . 7H2O):
- The molar mass of magnesium sulfate (MgSO4) is:
- Magnesium (Mg): 24.31 g/mol
- Sulfur (S): 32.06 g/mol
- Oxygen (O) (4 atoms): 15.999 g/mol
Total molar mass of MgSO4: 24.31 + 32.06 + (15.999 x 4) = 120.37 g/mol
- The molar mass of water (H2O) is 18.015 g/mol.
- Since there are 7 water molecules (H2O) in Epsom Salts, multiply the molar mass of water by 7:
18.015 x 7 = 126.105 g/mol
- To find the molar mass of Epsom Salts (MgSO4 . 7H2O), add the molar mass of magnesium sulfate and the molar mass of water molecules:
120.37 + 126.105 = 246.475 g/mol
2. Calculate the molar mass of anhydrous magnesium sulfate (MgSO4):
- The molar mass of anhydrous magnesium sulfate is the same as that of magnesium sulfate without the water molecules, which is 120.37 g/mol (as calculated above).
3. Calculate the amount of magnesium in the 1.00 kg bag of Epsom Salts:
- To find the amount of magnesium in the bag, we need to calculate the ratio of the molar masses of magnesium in each compound:
(Ratio of MgSO4 . 7H2O to MgSO4) = (molar mass of magnesium sulfate) / (molar mass of anhydrous magnesium sulfate)
= (120.37 g/mol) / (120.37 g/mol) = 1:1
- Since the ratio of magnesium in both compounds is 1:1, the mass of magnesium in the 1.00 kg bag of Epsom Salts is 1.00 kg.
4. Determine the mass of the bag of anhydrous magnesium sulfate containing the same amount of magnesium:
- The bag of anhydrous magnesium sulfate would also have a mass of 1.00 kg.
Therefore, the mass of the bag of anhydrous magnesium sulfate would be 1.00 kg.
To determine the mass of a bag of anhydrous magnesium sulfate (MgSO4) that would contain the same amount of magnesium as a 1.00 kg bag of Epsom Salts (MgSO4 . 7H2O), we need to consider their respective molecular formulas and the molar mass of each compound.
1. Begin by determining the molar mass of Epsom Salts (MgSO4 . 7H2O):
- The molar mass of magnesium sulfate (MgSO4) is calculated by summing the atomic masses of its constituent elements:
- The atomic mass of magnesium (Mg) is approximately 24.31 g/mol.
- The atomic mass of sulfur (S) is approximately 32.07 g/mol.
- The atomic mass of oxygen (O) is approximately 16.00 g/mol.
- Multiply the atomic mass of each element by the number of atoms in the formula:
- Mg: 1 atom x 24.31 g/mol = 24.31 g/mol
- S: 1 atom x 32.07 g/mol = 32.07 g/mol
- O: 4 atoms x 16.00 g/mol = 64.00 g/mol
- Sum the individual masses to obtain the molar mass of MgSO4:
- Molar mass of MgSO4 = (24.31 g/mol) + (32.07 g/mol) + (64.00 g/mol) = 120.38 g/mol
- The formula for Epsom Salts (MgSO4 . 7H2O) indicates that it contains 7 water molecules (H2O), each with a molar mass of 18.02 g/mol.
- Calculate the total molar mass of Epsom Salts by adding the contribution of MgSO4 and 7H2O:
- Molar mass of Epsom Salts = (1 mol of MgSO4) + (7 mol of H2O) = (120.38 g/mol) + (7 * 18.02 g/mol) = 246.32 g/mol
2. Now, we can calculate the mass of anhydrous magnesium sulfate (MgSO4) required to have the same amount of magnesium as the 1.00 kg bag of Epsom Salts:
- Since Epsom Salts (MgSO4 . 7H2O) has a molar mass of 246.32 g/mol, we can find the number of moles in the 1.00 kg bag using the formula:
- Moles of Epsom Salts = Mass (in grams) / Molar mass = 1000 g / 246.32 g/mol ≈ 4.06 mol
- As per the chemical formula, each mole of Epsom Salts contains one mole of magnesium (Mg). Hence, we have 4.06 moles of magnesium in the 1.00 kg bag of Epsom Salts.
3. Next, we can calculate the mass of anhydrous magnesium sulfate (MgSO4) required to contain the same amount of magnesium:
- Since each mole of magnesium sulfate (MgSO4) contains one mole of magnesium (Mg), the molar mass of MgSO4 will be equal to the molar mass of magnesium (Mg).
- Therefore, the mass of the anhydrous magnesium sulfate will be equal to the molar mass of magnesium sulfate multiplied by the number of moles of magnesium present in the Epsom Salts:
- Mass of anhydrous MgSO4 = Molar mass of MgSO4 * Moles of magnesium
- Mass of anhydrous MgSO4 = 120.38 g/mol * 4.06 mol ≈ 489.23 g
Therefore, the mass of the bag of anhydrous magnesium sulfate required to contain the same amount of magnesium as the 1.00 kg bag of Epsom Salts is approximately 489.23 grams.