Chemical formulas concisely express the composition of a compound, detailing the elements present and their relative quantities. Understanding the difference between empirical and molecular formulas is necessary to correctly interpret the makeup of any substance, including \(\text{N}_2\text{O}_4\). The distinction lies in whether the formula shows the actual count of atoms in a molecule (molecular) or simply the smallest possible whole-number ratio of those atoms (empirical). This concept is central to describing chemical structures accurately.
Understanding Chemical Formulas
A molecular formula provides the exact number of each type of atom found in a single molecule of a compound. For example, the molecular formula for glucose is \(\text{C}_6\text{H}_{12}\text{O}_6\). This explicitly states that one molecule contains six carbon atoms, twelve hydrogen atoms, and six oxygen atoms, representing the compound as it physically exists.
In contrast, the empirical formula shows the simplest whole-number ratio of atoms in a compound. It is derived by dividing the subscripts in the molecular formula by the greatest common divisor. Using the glucose example (\(\text{C}_6\text{H}_{12}\text{O}_6\)), dividing the subscripts by six yields the empirical formula \(\text{CH}_2\text{O}\). This represents the most reduced 1:2:1 ratio for carbon, hydrogen, and oxygen atoms.
The empirical formula can be the same for multiple different compounds, indicating they share the same elemental ratio but not necessarily the same molecular structure or mass. For instance, both ethylene (\(\text{C}_2\text{H}_4\)) and butene (\(\text{C}_4\text{H}_8\)) share the empirical formula \(\text{CH}_2\). While the empirical formula gives compositional information, the molecular formula reveals the true number of atoms in the molecule.
Analyzing the Structure of Dinitrogen Tetroxide
Applying these concepts to \(\text{N}_2\text{O}_4\), the formula indicates that a single unit contains two nitrogen atoms and four oxygen atoms. Because this represents the actual, non-simplified count of atoms bonded together, \(\text{N}_2\text{O}_4\) is definitively the molecular formula for dinitrogen tetroxide.
To determine the corresponding empirical formula, the subscripts in \(\text{N}_2\text{O}_4\) must be reduced to their lowest whole-number ratio. The greatest common divisor for the subscripts (2 and 4) is 2. Dividing by 2 yields the empirical formula \(\text{NO}_2\).
The simplest ratio of nitrogen to oxygen in the compound is 1:2. The molecular formula \(\text{N}_2\text{O}_4\) is a whole-number multiple (specifically, a multiple of 2) of its empirical formula, \(\text{NO}_2\). \(\text{N}_2\text{O}_4\) is often described as a dimer, composed of two identical \(\text{NO}_2\) units bonded together.
The Equilibrium with Nitrogen Dioxide
The empirical formula for dinitrogen tetroxide, \(\text{NO}_2\), also represents a stable, distinct molecule called nitrogen dioxide. These two compounds exist in a dynamic equilibrium. In this system, two molecules of the brown-colored nitrogen dioxide (\(\text{NO}_2\)) reversibly combine to form one molecule of the colorless dinitrogen tetroxide (\(\text{N}_2\text{O}_4\)).
This equilibrium is highly sensitive to temperature changes, which affect the ratio between the two molecules. The reaction forming the larger \(\text{N}_2\text{O}_4\) molecule from two \(\text{NO}_2\) molecules is exothermic, meaning it releases heat. Consequently, cooling the mixture favors the production of the colorless \(\text{N}_2\text{O}_4\), causing the mixture’s color to lighten.
Conversely, heating the system shifts the equilibrium in the opposite direction, favoring the endothermic decomposition of \(\text{N}_2\text{O}_4\) back into the brown \(\text{NO}_2\). This increase in nitrogen dioxide concentration is observed as the gas mixture becoming noticeably darker brown.