A crystalline compound when heated became anhydrous by losing 51.2% of the mass. On analysis, the anhydrous compound gave the following percentage composition. Mg=20%, S=26.66% O=53.33%. Calculate the molecular formula of the anhydrous compound and crystalline compound. The molecular mass of anhydrous compound is 120u.

To determine the molecular formula of the anhydrous compound and the original crystalline compound, we can follow a systematic approach. Let's break down the problem step by step.

Step 1: Calculate the Molar Mass of the Anhydrous Compound

We know that the molecular mass of the anhydrous compound is 120 u. Given the percentage composition, we can find the moles of each element in the compound.

Elemental Composition

• Magnesium (Mg): 20%
• Sulfur (S): 26.66%
• Oxygen (O): 53.33%

Calculating Moles of Each Element

Assuming we have 100 g of the anhydrous compound, the mass of each element can be calculated as follows:

• Mass of Mg = 20 g
• Mass of S = 26.66 g
• Mass of O = 53.33 g

Next, we convert these masses to moles using their respective atomic masses:

• Molar mass of Mg = 24.31 g/mol
• Molar mass of S = 32.07 g/mol
• Molar mass of O = 16.00 g/mol

Now, we calculate the moles:

• Moles of Mg = 20 g / 24.31 g/mol ≈ 0.82 mol
• Moles of S = 26.66 g / 32.07 g/mol ≈ 0.83 mol
• Moles of O = 53.33 g / 16.00 g/mol ≈ 3.33 mol

Finding the Simplest Ratio

To find the simplest whole number ratio, we divide each mole value by the smallest number of moles calculated:

• Mg: 0.82 / 0.82 = 1
• S: 0.83 / 0.82 ≈ 1.01 ≈ 1
• O: 3.33 / 0.82 ≈ 4.06 ≈ 4

This gives us a ratio of approximately 1:1:4, leading us to the empirical formula of the anhydrous compound as:

Step 2: Determine the Molecular Formula

Since the molar mass of the empirical formula (MgSO₄) can be calculated as follows:

• Molar mass of Mg = 24.31 g/mol
• Molar mass of S = 32.07 g/mol
• Molar mass of O = 4 × 16.00 g/mol = 64.00 g/mol

Adding these together gives:

This matches closely with the given molecular mass of 120 u, confirming that the molecular formula is indeed:

Step 3: Calculate the Crystalline Compound's Formula

We know that the crystalline compound loses 51.2% of its mass upon heating to become anhydrous. This means that the remaining mass is 48.8% of the original mass.

Finding the Mass of the Crystalline Compound

Let’s assume the mass of the anhydrous compound is 100 g. Therefore, the mass of the crystalline compound can be calculated as follows:

Calculating the Mass of Water Lost

The mass of water lost during the heating process can be calculated as:

• Mass of water = 204.88 g - 100 g = 104.88 g

Finding the Moles of Water

The molar mass of water (H₂O) is approximately 18.02 g/mol. Thus, the moles of water lost can be calculated as:

Finalizing the Crystalline Compound Formula

Since the empirical formula of the anhydrous compound is MgSO₄ and we have approximately 5.83 moles of water, we can express the crystalline compound as:

In summary, the molecular formula of the anhydrous compound is MgSO₄, and the formula for the crystalline compound is MgSO₄·6H₂O. This indicates that the crystalline form contains six water molecules for every formula unit of magnesium sulfate.