Problem 119 - General Chemistry: Principles and Modern Applications

Question

Three of the following formulas might be either an empirical or a molecular formula. The formula that must be a molecular formula is (a) \(\mathrm{N}_{2} \mathrm{O} ;\) (b) \(\mathrm{N}_{2} \mathrm{H}_{4}\) (c) \(\mathrm{NaCl} ;\) (d) \(\mathrm{NH}_{3}\)

Step-by-Step Solution

Answer

The formula that must be a molecular formula is (d) \(\mathrm{NH}_{3}\).

Step 1: Understand the formulas

Consider each of the provided formulas: (a) \(\mathrm{N}_{2} \mathrm{O}\), (b) \(\mathrm{N}_{2} \mathrm{H}_{4}\), (c) \(\mathrm{NaCl}\), (d) \(\mathrm{NH}_{3}\). Each of these represents a compound composed of different elements.

Step 2: Analyze each formula

Analyze each formula to determine if it could be an empirical formula, i.e., the simplest, reduced ratio of elements, or if it must be a molecular formula, i.e., the actual number of atoms in a molecule of the compound. (a) \(\mathrm{N}_{2} \mathrm{O}\) - This could be an empirical formula because it exhibits a whole number ratio of elements. Also, it could be a molecular formula representing the exact number of atoms in molecular nitrogen monoxide.(b) \(\mathrm{N}_{2} \mathrm{H}_{4}\) - This could also be an empirical formula because it exhibits a whole number ratio of elements. Also, it could be a molecular formula representing the exact number of atoms in a molecule of hydrazine.(c) \(\mathrm{NaCl}\) - Similarly, this could be an empirical or molecular formula because it represents a 1:1 ratio of sodium to chlorine atoms, as in a molecule of sodium chloride.(d) \(\mathrm{NH}_{3}\) - Evidently, this must be a molecular formula representing the exact number of atoms in a molecule of ammonia, since there's no simpler whole number ratio for \(\mathrm{NH}_{3}\).

Step 3: Identify the molecular formula

After analyzing each option, it can be identified that option (d) \(\mathrm{NH}_{3}\) must definitely be a molecular formula as it represents the exact composition of ammonia, with no further scope for simplification.

Key Concepts

Empirical Formula

An empirical formula represents the simplest whole-number ratio of the elements in a chemical compound. This means you break down the compound into its most reduced ratio without changing the relative proportions of the elements involved. Consider it the "basic recipe" for a compound.
For example, in the formula \(\mathrm{N}_2\mathrm{O}\), the elements nitrogen and oxygen are in a 2:1 ratio. This can be both an empirical formula if it truly reflects the simplest ratio, and a molecular formula if this is the actual number of atoms in a single molecule.
If you have hydrogen peroxide, with a molecular formula of \(\mathrm{H}_2\mathrm{O}_2\), its empirical formula would be \(\mathrm{HO}\) because the 2:2 ratio reduces to 1:1.When identifying an empirical formula, ask yourself: Can these elemental ratios be simplified any further? If the answer is no, then it's likely an empirical formula.

Molecular Formula

The molecular formula of a compound depicts the actual number of each type of atom in a single molecule of the compound. Unlike the empirical formula, which is the simplest ratio, the molecular formula discloses the exact composition and the actual size of the molecule.
Look at \(\mathrm{NH}_3\), ammonia's molecular formula. This tells us each molecule contains three hydrogen atoms and one nitrogen atom. Since there’s no simpler whole-number ratio than what \(\mathrm{NH}_3\) provides, it serves strictly as a molecular formula.
The molecular formula is essential for understanding the compound's specific properties and interactions. In larger molecules, like glucose \(\mathrm{C}_6\mathrm{H}_{12}\mathrm{O}_6\), knowing the molecular formula helps chemists determine structural formulas and predict physical behaviors.To differentiate, remember: Molecular formulas display the specifics of the molecule itself, whereas empirical formulas are only about the proportions.

Chemical Compounds

Chemical compounds are substances formed when two or more different elements are chemically bonded together. They come with distinct properties and compositions defined by their chemical formulas, whether empirical or molecular.
Every compound is unique, and knowing the correct formula is crucial to identify the compound accurately. Compounds like \(\mathrm{NaCl}\) or sodium chloride demonstrate a simple one-to-one chemical composition often shared between the empirical and molecular formulas.Understanding chemical compounds requires examining both their formulas and their actual structure. The molecular structure reveals how atoms connect and interact, contributing to the compound's characteristics.
For students studying chemistry, recognizing the difference in formula types and understanding their significance helps unravel the complex identities of compounds, leading to deeper insights into molecular chemistry and reactions.