Question

The principal component of mothballs is naphthalene, a compound with a molecular mass of about 130 amu, containing only carbon and hydrogen. A 3.000-mg sample of naphthalene burns to give 10.3 mg of CO₂. Determine its empirical and molecular formulas.

a) Empirical formula: CH, Molecular formula: C₆H₆
b) Empirical formula: C₂H₂, Molecular formula: C₄H₄
c) Empirical formula: CH, Molecular formula: C₄H₄
d) Empirical formula: C₃H₃, Molecular formula: C₆H₆

Answer 1

The empirical formula of naphthalene is C5H4, and the molecular formula is C10H8.

Step-by-step explanation:

To determine the empirical and molecular formulas of naphthalene, we'll need to calculate the moles of carbon from the given mass of CO₂ produced and then the ratio of carbon to hydrogen atoms.

The molar mass of CO₂ is 44.01 g/mol, and the mass of carbon in CO₂ is the same as the mass of carbon in the naphthalene sample. From the 10.3 mg of CO₂, we calculate the moles of carbon:

• 10.3 mg CO₂ × (1 g / 1000 mg) × (1 mol CO₂ / 44.01 g CO₂) = 0.000234 moles of CO₂
• 0.000234 moles CO₂ × (1 mol C / 1 mol CO₂) = 0.000234 moles of C

Since the molecular mass of naphthalene is about 130 amu, we can use this information along with the empirical formula to obtain the molecular formula. The empirical formula mass of C5H4 is 64 amu (5 × 12 amu for carbon + 4 × 1 amu for hydrogen).

The ratio of the molecular mass to the empirical formula mass is 130 / 64, which is approximately 2. Thus, multiplying the empirical formula by this ratio gives us the molecular formula: C10H8

The closest match to this empirical and molecular formula set from the options given is: Empirical formula: C5H4, Molecular formula: C10H8