Problem 159 - Chemistry Matter and Change

Question

Which of the following formulas - NO, \(\mathrm{N}_{2} \mathrm{O}, \mathrm{NO}_{2}, \mathrm{N}_{2} \mathrm{O}_{4}\), and \(\mathrm{N}_{2} \mathrm{O}_{5}-\) represent the empirical and molecular for- mulas of the same compound? Explain your answer.

Step-by-Step Solution

Answer

NO is both the empirical and molecular formula of the compound.

Step 1: Understanding Empirical and Molecular Formulas

An empirical formula is the simplest whole-number ratio of atoms in a compound, while a molecular formula is the actual number of atoms of each element in a compound. Our task here is to identify compounds where both the empirical and molecular formulas are identical.

Step 2: Analyze Each Formula

We will examine each given formula: - **NO**: Empirical formula = Molecular formula (same ratio, 1:1) - **N₂O**: Empirical formula is NO (1:0.5 simplified to 2:1 with both being the simplest) - **NO₂**: Empirical formula is NO₂ (the ratio 1:2 is simplest and equivalent to molecular) - **N₂O₄**: Empirical formula is NO₂ (1:2) - **N₂O₅**: Empirical formula is N₂O₅ itself since simplified ratio remains 2:5.

Step 3: Comparison

Compare the empirical and molecular formulas that we deduced in the previous step. The compound where these formulas are identical represents the one with the same empirical and molecular formula.

Step 4: Identify the compound

Based on the comparison, the compound NO has both empirical and molecular formulas the same, meaning it does not need simplification.

Key Concepts

Chemical Compounds

In chemistry, a chemical compound refers to a substance composed of two or more different types of atoms bonded together. These atoms are linked through chemical bonds, creating compounds with distinct properties different from the elements that form them. For instance, water (\(\text{H}_2\text{O}\)) is a chemical compound made from hydrogen and oxygen.
Each compound has a fixed ratio of atoms, unique to its kind. This ratio determines whether a substance is an empirical formula, the simplest form, or its molecular formula, representing actual numbers of atoms in each molecule.

Simplest Whole-Number Ratio

The simplest whole-number ratio is all about reducing the numbers of atoms in a chemical compound to their smallest possible integer values. This simplified ratio gives you the empirical formula of the compound.
For example, when you take a compound like \(\text{N}_2\text{O}\), its simplest form is actually NO, showing a 1:0.5 ratio reduced to 2:1 as integers.
The principle behind this is to identify the smallest factor that all components can be divided by, helping chemists understand and communicate information about the composition of compounds easily.

Chemical Formulas

Chemical formulas are symbolic representations of the element composition within a compound. They use letters to denote elements and numbers to show the quantity of each element. These formulas help chemists quickly identify the types and ratios of atoms in compounds. The **empirical formula** shows the simplest ratio of elements, whereas the **molecular formula** provides the exact number of atoms in a single molecule.

• **NO** is both an empirical and molecular formula because the count for both elements in the compound doesn't simplify further.
• **N₂O₅** stands as a distinct molecular formula because its atom ratio doesn't change when simplified.

Understanding chemical formulas is crucial for studying reactions, stoichiometry, and compound identification.

Stoichiometry

Stoichiometry is the chemistry segment dedicated to the quantitative relationships between reactants and products in chemical reactions. It uses chemical formulas to calculate the masses, volumes, and amounts of substances involved in reactions.
Stoichiometry relies on the balance of atoms in reactions, ensuring that they are neither created nor destroyed. This is where empirical and molecular formulas find relevance, as they assist in aligning the proportions of reactants and products accurately.
In essence, stoichiometry is the math behind chemical interactions, providing insights into how much of each compound is required or produced, bridging theoretical chemistry with experimental results.