Chapter 3, Problem 3.43P

(a)

Interpretation Introduction

Interpretation:

The empirical formula of the compound that contains $\text{0}\text{.039 mol}$ of iron atoms and $\text{0}\text{.052 mol}$ of oxygen atoms 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 moles/fractional amount of each element is given,

Step 1: Write the 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 2: 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.

(b)

Interpretation Introduction

Interpretation:

The empirical formula of the compound that contains $0.903\text{ g}$ of phosphorous and $6.99\text{ g}$ of bromine 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.

(c)

Interpretation Introduction

Interpretation:

The empirical formula of a hydrocarbon that contains $79.9\text{ mass \%}$ carbon is to be determined.

Concept introduction:

Hydrocarbons are compounds that contain carbon and hydrogen atoms. 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 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 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:

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

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.