Chapter 3, Problem 3.51P

Interpretation Introduction

Interpretation:

The molecular formula of cortisol that contains $69.6\text{ \% C}$ , $8.34\text{ \% H}$, and $\text{22}\text{.1 \% O}$ is to be determined.

Concept introduction:

An empirical formula gives the simplest whole number ratio of atoms of each element present in a molecule. The molecular formula tells the exact number of atoms of each element present in a molecule.

Following are the steps to determine the molecular formula of a compound when the percentage of each element is given,

Step 1: Assume $100.0\text{ g}$ of the compound and express mass percent of each element directly as a mass in grams.

Step 2: Divide mass of each element by its molar mass to convert the mass of the element to moles.  The formula to calculate moles from the mass is as follows:

$\text{Amount}\left(\text{mol}\right)=\left(\text{Given mass}\left(\text{g}\right)\right)\left(\frac{1\text{ mol}}{\text{No}\text{. of grams}}\right)$ (1)

Step 3: The number of moles of the elements is the fractional amounts, thus, write the calculated amount $\left(\text{mol}\right)$ of each element as the subscript of the element’s symbol to obtain a preliminary formula for the compound.

Step 4: Convert the moles of each element to the whole number subscripts. The steps for this math conversion are as follows:

(a) Each subscript is divided by the smallest subscript.

(b) If the whole number is not obtained after division, multiply the obtained subscripts by the smallest integer. This gives the empirical formula of the compound.

Step 5: Add the molar mass of each element multiplied by its number of atoms present in the empirical formula to obtain the empirical formula mass for the compound.

Step 6: Divide the molar mass of the compound by its empirical formula mass to obtain the whole number. The formula to calculate the whole number multiple is as follows:

$\text{Whole}-\text{number multiple}=\frac{\text{Molar mass of compound}}{\text{Empirical formula mass}}$ (2)

Step 7: Multiply the whole number with the subscript of each element present in the empirical formula. This gives the molecular formula of the compound.