Answer to Question #340727 in General Chemistry for Onie

Question

An organic compound contains carbon(71,17%),hydrogen(5.12%) with the remainder nitrogen.Dissolving 0.177 g of the compound in 10 g of benzene gives a solution with a vapour pressure of 94.16 mmHg at 25°C .(The vapor pressure of pure benzene at this temperature is 95.26 mmHg.)What is the molecular formula for the compound?

Answer 1

Solution:

Raoult's law states that a solvent's partial vapour pressure in a solution is equal or identical to the vapour pressure of the pure solvent multiplied by its mole fraction in the solution.

Raoult's law can be expressed as: P_solution = χ_solvent × P°_solvent

P_solution = 94.16 mmHg

P°_solvent = P°_benzene = 95.26 mmHg

Therefore,

χ_solvent = χ_benzene = (P_solution / P°_benzene) = (94.16 mmHg / 95.26 mmHg) = 0.98845

χ_benzene = 0.98845

Moles of benzene = Mass of benzene / Molar mass of benzene

The molar mass of benzene is 78.11 g mol⁻¹

Therefore,

Moles of benzene = (10 g) / (78.11 g mol⁻¹) = 0.128 mol

Moles of benzene = 0.128 mol

χ_benzene = (Moles of benzene) / (Moles of benzene + Moles of organic compound)

0.98845 = (0.128) / (0.128 + Moles of organic compound)

0.1295 = 0.128 + Moles of organic compound

Moles of organic compound = 0.0015 mol

Molar mass of organic compound = Mass of organic compound / Moles of organic compound

Mass of organic compound = 0.177 g

Moles of organic compound = 0.0015 mol

Therefore,

Molar mass of organic compound = (0.177 g) / (0.0015 mol) = 118 g mol⁻¹

Molar mass of organic compound = 118 g mol⁻¹

w(C) = 71.17% or 0.7117

w(H) = 5.12% or 0.0512

w(N) = 100% − w(C) − w(H) = 100% − 71.71% − 5.12% = 23.17% or 0.2317

Convert the %values to grams:

Mass of C = w(C) × Mass of organic compound = 0.7117 × 0.177 g = 0.12597 g C

Mass of H = w(H) × Mass of organic compound = 0.0512 × 0.177 g = 0.00906 g H

Mass of N = w(N) × Mass of organic compound = 0.2317 × 0.177 g = 0.04101 g N

Molar mass of carbon (C) is 12.0107 g mol⁻¹

Molar mass of hydrogen (H) is 1.00784 g mol⁻¹

Molar mass of nitrogen (N) is 14.0067 g mol⁻¹

Convert grams to moles:

Moles of C = (0.12597 g C) × (1 mol C / 12.0107 g C) = 0.01049 mol C

Moles of H = (0.00906 g H) × (1 mol H / 1.00784 g H) = 0.00899 mol H

Moles of N = (0.04101 g N) × (1 mol N / 14.0067 g N) = 0.00293 mol N

Divide all moles by the smallest of the results:

C : 0.01049 / 0.00293 = 3.58

H : 0.00899 / 0.00293 = 3.07

N : 0.00293 / 0.00293 = 1.00

C : H : N = 3.58 : 3.07 : 1.00 = 7.16 : 6.14 : 2.00 ≈ 7 : 6 : 2

Thus, the empirical formula of organic compound is C₇H₆N₂

Empirical formula mass of organic compound = 7×Ar(C) + 6×(H) + 2×(N) =

Empirical formula mass of organic compound = 7×12.0107 + 6×1.00784 + 2×14.0067 = 118.14 (g mol^-1)

Empirical formula mass of organic compound = 118.14 g mol⁻¹

Molar mass / Empirical formula mass = n formula units/molecule

(118 g mol⁻¹) / (118.14 g mol⁻¹) ≈ 1 formula units/molecule

Finally, derive the molecular formula for organic compound from the empirical formula by multiplying each subscript by one: (C₇H₆N₂)₁ = C₇H₆N₂

Thus, the molecular formula for the compound is C₇H₆N₂

Answer: The molecular formula for the compound is C₇H₆N₂