Molecular Empirical Formula

The problem asks for the empirical formula mass of an organic compound (X) based on the mass of the compound combusted and the masses of carbon dioxide ( ) and water ( ) produced.

Concept Used:

The solution uses the principle of combustion analysis to determine the empirical formula. In combustion analysis:

1. All the carbon present in the organic compound is converted into .
2. All the hydrogen present in the organic compound is converted into .
3. If the compound contains oxygen, its mass is found by subtracting the masses of carbon and hydrogen from the total mass of the organic compound.
4. The empirical formula is the simplest whole-number ratio of atoms of the elements present in the compound. This ratio is found by converting the mass of each element to moles and then finding their simplest ratio.

Step-by-Step Solution:

Step 1: Calculate the mass of carbon (C) from the mass of produced.

The molar mass of is . In one mole of , there is one mole of C atoms (12 g).

Step 2: Calculate the mass of hydrogen (H) from the mass of produced.

The molar mass of is . In one mole of , there are two moles of H atoms (2 g).

Step 3: Calculate the mass of oxygen (O) by difference.

The total mass of the compound is the sum of the masses of C, H, and O.

Step 4: Convert the mass of each element into moles.

Step 5: Determine the simplest whole-number ratio of the moles.

To find the simplest ratio, divide the number of moles of each element by the smallest value obtained in Step 4 (which is approximately 0.0332).

• For C:
• For H:
• For O:

The simplest whole-number ratio of C : H : O is 1 : 2 : 1. Therefore, the empirical formula of the compound (X) is .

Step 6: Calculate the empirical formula mass.

The mass of the empirical formula is the sum of the atomic masses of the atoms in it.

The empirical formula mass of compound (X) is 30 g mol .