Question

The elemental analysis of an organic solid extracted from gum arabic (a gummy substance used in adhesives, inks, and pharmaceuticals) showed that it contained 40.0 percent by mass C, 6.7 percent by mass H, and 53.3 percent by mass O. A solution of 0.561 g of the solid in 24.9 g of the solvent diphenyl gave a freezing-point depression of 1.5°C. Calculate the molar mass and molecular formula of the solid. (Kf for diphenyl is 8.00°C/m.)

Answer 1

Answer:

The molar mass of the organic solid is 120.16 g/mol.

The molecular formula of an organic solid is $C_4H_8O_4$

Explanation:

Let the molecular mass of an organic solid be $C_xH_yO_z$

$\Delta T_b=K_b\times m$

$Delta T_b=K_b\times \frac{\text{Mass of solid}}{\text{Molar mass of solid}\times \text{Mass of diphenyl in Kg}}$

where,

$\Delta T_f$ =Elevation in boiling point = $=1.5^oC$

Mass of organic solid= 0.561 g

Mass of diphenyl = 24.9 g = 0.0249 kg (1 kg = 1000 g)

$K_b$ = boiling point constant = 8.00 °C/m

m = molality

Now put all the given values in this formula, we get

$1.5^oC=8.00 ^oC/m\times \frac{0.561 g}{\text{Molar mass of solid}\times 0.0249 kg}$

${\text{Molar mass of solid}}=120.16 g/mol$

$\%=\frac{\text{Number of atoms}\times \text{mass of an atom}}{\text{molas mass of compound}}\times 100$

Percentage of carbon in an organic solid = 40.0%

$40\%=\frac{x\times 12 g/mol}{120.16 g/mol}\times 100$

x = 4.0

Percentage of hydrogen in an organic solid = 6.7%

$6.7\%=\frac{y\times 1 g/mol}{120.16 g/mol}\times 100$

y = 8.0  

Percentage of hydrogen in an organic solid = 6.7%

$53.3\%=\frac{x\times 12 g/mol}{120.16 g/mol}\times 100$

y = 4.0

The molecular formula of an organic solid is $C_4H_8O_4$