The ratio of oxygen to nitrogen by mass in \(\mathrm{NO}_{2}\) is \(2.29 .\) The ratio of fluorine to nitrogen by mass in \(\mathrm{NF}_{3}\) is \(4.07 .\) Find the ratio of oxygen to fluorine by mass in \(\mathrm{OF}_{2}\).

Chemical stoichiometry refers to the quantitative relationship between the elements within compounds or between compounds in a chemical reaction. Understanding stoichiometry is essential for predicting the amounts of substances consumed and produced in reactions. Imagine a recipe—it tells you how much of each ingredient you need for the desired outcome. Stoichiometry serves a similar purpose but for chemical reactions, providing a 'recipe' based on the balanced chemical equations.

In the case of determining the mass ratio of oxygen to fluorine in \textbf{OF}\(_2\), we start by looking at the relative amounts of each element in different compounds and then, as a ‘recipe’, convert them into the desired mass ratio. This process involves using a common reference—the mass of nitrogen, which links the two original compounds (\textbf{NO}\(_2\) and \textbf{NF}\(_3\)) to determine the ratio in \textbf{OF}\(_2\). This approach is a practical application of stoichiometry, including the mass relationships between elements in a compound.

Mass-to-mass conversion is a pivotal process in chemical stoichiometry that allows us to convert the mass of one substance into the equivalent mass of another substance via a common reference. In the exercise, nitrogen serves as this reference point, allowing us to understand the relationship between the masses of oxygen and fluorine.

We use given mass ratios to perform these conversions. By creating a fraction that shows the mass of one element over the mass of another, and then dividing one fraction by another, we can cancel out the common element (nitrogen in our exercise). This calculation is crucial because it transcends simply comparing the masses in one compound to comparing the masses in different compounds, thereby determining the sought-after mass ratio in chemical reactions or compounds not directly stated.

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It plays a fundamental role in converting between the mass of a substance and the number of moles. Since the molar mass of an element is numerically equivalent to its atomic weight found on the periodic table, it allows us to use a substance's formula to determine the total molar mass of a compound.

For instance, to find the molar mass of \textbf{NO}\(_2\) or \textbf{NF}\(_3\), one would sum the molar masses of the constituent elements—nitrogen (N), oxygen (O), and fluorine (F), each taken with its respective numbers of atoms in the molecular formula. The molar mass concept is essential when interpreting the mass ratios because it gives a relationship between a substance's mass in the lab and its amount in moles, which is a bridge between the macroscopic and microscopic worlds of chemistry.