[Co = 59 amu]. The mass percent composition of a substance is 24.7% Ca, 1.24% H, 14.8% C and 59.3% O. Calculate the molecular formula of the substance if its molecular mass is 162 u.

To find the molecular formula of the substance with a molecular mass of 162 u, we first need to determine the number of moles of each element based on their mass percent composition.

Step 1: Convert Mass Percent to Grams

Assuming we have 100 grams of the substance, the mass of each element is as follows:

• Calcium (Ca): 24.7 g
• Hydrogen (H): 1.24 g
• Carbon (C): 14.8 g
• Oxygen (O): 59.3 g

Step 2: Calculate Moles of Each Element

Next, we convert grams to moles using the atomic masses:

• Ca: 40.08 g/mol
• H: 1.01 g/mol
• C: 12.01 g/mol
• O: 16.00 g/mol

Now, we calculate the moles:

• Moles of Ca = 24.7 g / 40.08 g/mol ≈ 0.615 moles
• Moles of H = 1.24 g / 1.01 g/mol ≈ 1.228 moles
• Moles of C = 14.8 g / 12.01 g/mol ≈ 1.233 moles
• Moles of O = 59.3 g / 16.00 g/mol ≈ 3.706 moles

Step 3: Find the Simplest Ratio

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

• Ca: 0.615 / 0.615 = 1
• H: 1.228 / 0.615 ≈ 2
• C: 1.233 / 0.615 ≈ 2
• O: 3.706 / 0.615 ≈ 6

Step 4: Write the Empirical Formula

The simplest whole number ratio gives us the empirical formula:

Empirical Formula: CaH₂C₂O₆

Step 5: Determine the Molecular Formula

Next, we calculate the molar mass of the empirical formula:

• Ca: 40.08 g/mol
• H: 2 × 1.01 g/mol = 2.02 g/mol
• C: 2 × 12.01 g/mol = 24.02 g/mol
• O: 6 × 16.00 g/mol = 96.00 g/mol

Total molar mass of the empirical formula = 40.08 + 2.02 + 24.02 + 96.00 = 162.12 g/mol.

Final Calculation

Since the empirical formula mass (162.12 g/mol) is very close to the given molecular mass (162 u), the molecular formula is the same as the empirical formula:

Molecular Formula: CaH₂C₂O₆