Question

What is the molecular formula for a compound that is 26.37 carbon 5.541 hydrogen 52.70 oxygen and 15.38 nitrogen and has a molar mass of 182.16g

Answer 1

Answer: The molecular formula of the compound is $C_2H_5O_3N$

Explanation:

To know the molecular formula of the compound, we will follow some steps:

Step 1: Converting all these percentages into mass.

We take the total mass of the compound to be 100 grams, so, the percentages given for each element becomes its mass.

Mass of Carbon = $\frac{26.37}{100}\times 100g=26.37g$

Mass of Hydrogen = $\frac{5.541}{100}\times 100g=5.541g$

Mass of Oxygen = $\frac{52.7}{100}\times 100g=52.7g$

Mass of Nitrogen = $\frac{15.38}{100}\times 100g=15.38g$

Molar mass of Carbon = 12 g/mole

Molar mass of Hydrogen = 1 g/mole

Molar mass of Oxygen = 16 g/mole

Molar mass of Nitrogen = 14 g/mol

Step 2: Converting the given masses into their respective moles.

Moles of Carbon = $\frac{\text{Given mass of C}}{\text{Molar mass of C}}= \frac{26.37g}{12g/mole}=2.197moles$

Moles of Hydrogen = $\frac{\text{Given mass of H}}{\text{Molar mass of H}}= \frac{5.541g}{1g/mole}=5.541moles$

Moles of Oxygen = $\frac{\text{Given mass of O}}{\text{Molar mass of O}}= \frac{52.7g}{16g/mole}=3.29moles$

Moles of Nitrogen = $\frac{\text{Given mass of N}}{\text{Molar mass of N}}= \frac{15.38g}{14g/mole}=1.09moles$

Step 3: Now, calculating mole ratio, we divide each number of moles by the smallest number of moles calculated.

For Carbon = $\frac{2.197}{1.09}=2.01\approx 2$  

For Hydrogen = $\frac{5.541}{1.09}=5.08\approx 5$  

For Oxygen = $\frac{3.29}{1.09}=3.01\approx 3$

For Nitrogen = $\frac{1.09}{1.09}=1$

The ratio of C : H : O : N = 2 : 5 : 3 : 1

Step 4: Writing the mole ratio of the element as the subscripts in molecular formula.

Molecular formula of the compound : $C_2H_5O_3N$

Hence, the molecular formula of the compound is $C_2H_5O_3N$