Question

Molecular Formula from Elemental Analysis and Molecular Mass Determination An unidentified covalent molecular compound contains only carbon, hydrogen, and oxygen. When 7.80 mg of this compound is burned, 18.12 mg of CO2 and 1.98 mg of H2O are produced. The freezing point of camphor is lowered by 26.4°C when 3.236 g of the compound is dissolved in 17.25 g of camphor (Kf = 40.0°C kg/mol). What is the molecular formula of the unidentified compound? Choose appropriate coefficients in the molecular formula below. CHOD Submit Answer) Incorrect. Tries 3/5 Previous Tries

Answer 1

Step 1:
use:
Δ Tf = Kf*mb
26.4 = 40.0 *mb
mb= 0.66 molal


m(solvent)= 17.25 g
= 1.725*10^-2 kg

use:
number of mol,
n = Molality * mass of solvent in Kg
= (0.66 mol/Kg)*(1.725*10^-2 Kg)
= 1.138*10^-2 mol

mass(solute)= 3.236 g


use:
number of mol = mass / molar mass
1.138*10^-2 mol = (3.236 g)/molar mass
molar mass = 284.2 g/mol

Step 2:
let in compound number of moles of C, H and O be x, y and z respectively

Number of moles of CO2 = mass of CO2 / molar mass CO2
= 0.01812/44
= 4.118*10^-4

Number of moles of H2O = mass of H2O / molar mass H2O
= 0.00198/18
= 1.1*10^-4

Since 1 mol of CO2 has 1 mol of C
Number of moles of C in CO2= 4.118*10^-4
so, x = 4.118*10^-4

Since 1 mol of H2O has 2 mol of H
Number of moles of H = 2*1.1*10^-4 = 2.2*10^-4

Molar mass of O = 16 g/mol


mass O = total mass - mass of C and H
= 0.0078 - 4.118*10^-4*12 - 2.2*10^-4*1
= 2.638*10^-3

number of mol of O = mass of O / molar mass of O
= 2.638*10^-3/16.0
= 1.649*10^-4
so, z = 1.649*10^-4
Divide by smallest:
C: 4.118*10^-4/1.649*10^-4 = 5/2
H: 2.2*10^-4/1.649*10^-4 = 4/3
O: 1.649*10^-4/1.649*10^-4 = 1

Multiply by 6 to get simplest whole number ratio:
C: 5/2*6 = 15
H: 4/3*6 = 8
O: 1*6 = 6

So empirical formula is:C15H8O6

Molar mass of C15H8O6,
MM = 15*MM(C) + 8*MM(H) + 6*MM(O)
= 15*12.01 + 8*1.008 + 6*16.0
= 284.214 g/mol

Now we have:
Molar mass = 284.2 g/mol
Empirical formula mass = 284.214 g/mol
Multiplying factor = molar mass / empirical formula mass
= 284.2/284.214
= 1

So molecular formula is:C15H8O6
Answer: C15H8O6