Chapter 3, Problem 3.129P

Interpretation Introduction

Interpretation:

From the combustion analysis data of ferrocene, the empirical formula of ferrocene is to be determined.

Concept introduction:

An empirical formula gives the simplest whole number ratio of atoms of each element present in a compound.

Following are the steps to determine the empirical formula of a compound when the masses of each element are given,

Step 1: 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:

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

Step 2: 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 3: 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.

The number of moles is calculated by the formula as given below:

  $\text{Number of moles}=\frac{\text{given mass of sample}\left(\text{g}\right)}{\text{molar mass (g/mol)}}$        (1)

The formula to calculate the mass from moles is given as follows:

  $\text{Mass of a given sample}\left(\text{g}\right)=\left(\text{molecular mass}\left(\text{g/mol}\right)\right)\left(\text{number of moles}\right)$        (2)