The elemental analysis of an organic solid extracted from gum arabic showed that it contained 40.0% C, 6.7% H, and 53.3% O. A solution of 0.650 g of the solid in 27.8 g of the solvent diphenyl gave a freezing point depression of 1.56 °C. Calculate the molar mass and determine the molecular formula of the solid (kf for diphenyl is 8.00 °C/m). To earn full credit, clearly show your work with units and proper significant figures

The molar mass of the organic solid is 119.9g/mol.

The molecular formula of an organic solid is C4H8O4

Explanation:

Step 1

We find the Molar mass

From the above question, we are given:

A solution of 0.650 g of the solid in 27.8 g of the solvent diphenyl gave a freezing point depression of 1.56 °C. Calculate the molar mass and determine the molecular formula of the solid (kf for diphenyl is 8.00 °C/m)

A freezing point depression = 1.56 °C.

Mass of organic solid= 0.650 g

Mass of diphenyl = 27.8 g

Converting to kilograms

1000g = 1kg

27.8g =

Cross Multiply

= 27.8g × 1 kg/1000g

= 0.0278kg

Boiling point constant = 8.00 °C/m

Molar mass of the organic compound = Boiling point constant × Mass of solid /Freezing point depression × Mass of diphenyl

Molar mass of the organic compound =

8.00 °C/m × 0.650g/1.56°C × 0.0278kg

= 5.2 g°C/m ÷ 0.043368 g°C

= 119.9040767 g/mol

Approximately = 119.9 g/mol

Step 2

Find the Molecular formula

Molecular formula = CxHyOz

Let x = Carbon, y = Hydrogen, z = Oxygen

For x = Carbon

Atomic mass of Carbon = 12.01078

x = % of Carbon in the compound × Molar mass of the organic compound/atomic mass of Carbon

x = 40% × 119.9 g/mol / (12.01078

x = 3.99

x = Approximately = 4

For y = Hydrogen

Atomic mass of Hydrogen = 1.007947

y = % of Hydrogen in the compound × Molar mass of the organic compound/Atomic mass of Hydrogen

x = 6.7% × 119.9 g/mol) / 1. 007947

x = 7.97

x is Approximately = 8

For z = Oxygen

Atomic mass of Oxygen = 15.99943

z = % of Oxygen in the compound × Molar mass of the organic compound/Atomic mass of Oxygen

z = 53.3% × 119.9 g/mol /15.99943

z = 3.99

z is approximately ≈ 4

Therefore,

The molar mass of the organic solid is 119.9 g/mol.

The molecular formula of an organic solid is C4H8O4

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