Question

A compound containing only C, H, and O, was extracted from the bark of the sassafras tree. The combustion of 56.5 mg produced 153 mg of CO₂ and 31.4 mg of H₂O. The molar mass of the compound was 162 g/mol. Determine its empirical and molecular formulas.

Answer 1

Given

Mass of sample = 56.5 mg = 0.0565 g

Mass of CO ₂ = 153 mg = 0.153 g

Mass of H₂O = 31.4 mg = 0.0314 g

one molecule of CO ₂ contain one C atom.

No. of moles of C = no. of moles of CO ₂

We have, no. of moles = Mass / molar mass

No. of moles of C = no. of moles of CO ₂ = 0.153 g / 44.010 g /mol

No. of moles of C = no. of moles of CO ₂ = 0.003476 mol

Mass of C in the sample = No. of moles of C Molar Mass

Mass of C in the sample = 0.003476 mol   12.01 g / mol = 0.04175 g

One molecule of water contain 2 H atoms.

moles of H = 2 no. of moles of water

  moles of H = 2 no. of moles of water = 2 (0.0314 g / 18.015 g / mol )

moles of H = 0.003486 mol

Mass of H in the sample = moles of H molar mass

Mass of H in the sample = 0.003486 mol 1.0079 g /mol = 0.003514 g

Total mass of C & H in the sample = 0.04175 g + 0.003514 g = 0.04526 g

We have given, Mass of sample = 0.0565 g

Mass of O = Mass of sample - Total mass of C & H in the sample

Mass of O = 0.0565 g - 0.04526 g = 0.01124 g

Moles of O = 0.01124 g / 16.00 g / mol = 0.0007025 mol

Now, calculate ratio of number of moles of C:H:O

0.003476 / 0.0007025 = 4.95 mol C 5

0.003486 / 0.0007025 = 4.96 mol H 5

0.0007025 / 0.0007025 = 1.00 mol O.

In compound, C,H & O are present in the ratio 5 : 5: 1.

Empirical formula of compound is C₅H₅O.

Now, we can determine molecular formula as shown below.

Empirical formula mass = ( 5 12.01 ) + ( 5 1.0079 ) + ( 1 16.00 ) = 81.09 g / mol

We have relation , Molecular formula = A empirical formula

Where A is the ratio of molar mass of substance to the empirical formula mass.

Therefore,A = Molecular formula mass / empirical formula mass

A = 162.00 g / mol / ( 81.09 g / mol )

A = 1.9977 2

Hence, Molecular formula =A x empirical formula

Molecular formula of compound =2 C₅H₅O .= C₁₀H₁₀O₂ .

ANSWER : Molecular formula of compound is C₁₀H₁₀O₂ .