Question

When lithium metal is heated strongly in an atmosphere of pure nitrogen, the product contains \(59.78 \%\) Li and \(40.22 \%\) N on a mass basis. Determine the empirical formula of the compound.

Short answer

The empirical formula of the compound formed when lithium metal is heated strongly in an atmosphere of pure nitrogen is Li3N.

Step-by-step solution

Convert mass percentages to grams

Since percentages are given, we can assume that we have 100 grams of the compound. This means there are 59.78 grams of Li and 40.22 grams of N in the compound.

Convert grams to moles

We need to convert grams of Li and N to moles. The molar mass of Li is approximately 6.94 g/mol, and the molar mass of N is approximately 14.01 g/mol. For Li: moles of Li \(=\frac{59.78\,\text{g}}{6.94\,\text{g/mol}}\approx8.61\,\text{moles}\) For N: moles of N\(= \frac{40.22\,\text{g}}{14.01\,\text{g/mol}}\approx 2.87\,\text{moles}\)

Find the mole ratio of Li to N

It is now necessary to find the mole ratio of Li to N. To do so, divide both numbers of moles by the smallest number of moles. \(\frac{8.61\,\text{moles}}{2.87\,\text{moles}}\approx3.00\) \(\frac{2.87\,\text{moles}}{2.87\,\text{moles}}\approx1.00\) The mole ratio is approximately 3:1.

Write the empirical formula

Using the mole ratio, we can now write the empirical formula of the compound: Empirical Formula: Li3N. Thus, the empirical formula of the compound is Li3N.

Key concepts

Mole Ratio

The mole ratio is a crucial step in determining the empirical formula of a compound. This concept helps chemists understand the proportion of each element within a compound based on their moles. To find the mole ratio, you first need to convert the mass of each element into moles, as the number of moles directly reflects the number of atoms.
The mole ratio is established by dividing each element's mole value by the smallest mole value in the dataset. For instance, if you have 8.61 moles of lithium (Li) and 2.87 moles of nitrogen (N), you divide both by 2.87, yielding a mole ratio of approximately 3:1. This indicates that for every one nitrogen atom, there are three lithium atoms in the compound, leading to the empirical formula of Li3N.
Understanding mole ratios helps chemists predict and balance chemical reactions, making this concept fundamental in stoichiometry.

Molar Mass

Molar mass is the mass of one mole of a given substance, usually measured in grams per mole (g/mol). It provides a bridge between the mass of a substance and the amount of its constituent particles, or moles.
To find the molar mass of an element, you simply look at its atomic mass on the periodic table. For example, lithium (Li) has an approximate molar mass of 6.94 g/mol and nitrogen (N) around 14.01 g/mol.
In the given exercise, the molar mass is used to convert the mass percentages of elements (Li and N) into moles. By dividing the mass of each element in grams by its molar mass, you obtain the number of moles of each element, which is an essential step for calculating the empirical formula.
Molar mass is not only important in determining empirical formulas but is also valuable in various applications like calculating the concentrations of solutions.

Chemical Composition Analysis

Chemical composition analysis involves determining the percentage by mass of each element in a compound. This analysis is fundamental for understanding the makeup of a substance and is the initial step towards finding the empirical formula.
For instance, if you know that a compound contains 59.78% lithium and 40.22% nitrogen, you can assume an initial 100 g sample for easy calculations. This converts directly to 59.78 g of lithium and 40.22 g of nitrogen.
To perform chemical composition analysis, after obtaining the percentage composition, you convert it to mass, then to moles using molar masses. The mole values are then used to find the mole ratio, which helps derive the empirical formula.
Understanding chemical composition analysis allows chemists to assess the purity of compounds, identify substances, and contribute to quality control in chemical manufacturing.