Question

Analysis of a certain compound yielded the following percentages of the elements by mass: nitrogen, 29.16\%; hydrogen, 8.392\%; carbon, 12.50\%; oxygen, 49.95\%. Determine the empirical formula of the compound.

Short answer

The empirical formula for the given compound is N2H8CO3.

Step-by-step solution

Convert percentages to grams

For simplicity, we assume we have 100 grams of the compound. Then the given percentages are equal to the mass values in grams of the respective elements. Therefore, we have: - Nitrogen: 29.16 g - Hydrogen: 8.392 g - Carbon: 12.50 g - Oxygen: 49.95 g

Find the moles of each element

To find the moles of each element, we will divide the mass (in grams) by their respective atomic masses: Moles of Nitrogen = \(\frac{29.16\text{ g}}{14.01\text{ g/mol}} = 2.08\text{ mol}\) Moles of Hydrogen = \(\frac{8.392\text{ g}}{1.01\text{ g/mol}} = 8.31\text{ mol}\) Moles of Carbon = \(\frac{12.50\text{ g}}{12.01\text{ g/mol}} = 1.041\text{ mol}\) Moles of Oxygen = \(\frac{49.95\text{ g}}{16.00\text{ g/mol}} = 3.12\text{ mol}\)

Find the molar ratios

Now divide the moles of each element by the smallest found moles to find the molar ratios: Molar ratio of Nitrogen = \(\frac{2.08\text{ mol}}{1.041\text{ mol}} = 2\) Molar ratio of Hydrogen = \(\frac{8.31\text{ mol}}{1.041\text{ mol}} = 8\) Molar ratio of Carbon = \(\frac{1.041\text{ mol}}{1.041\text{ mol}} = 1\) Molar ratio of Oxygen = \(\frac{3.12\text{ mol}}{1.041\text{ mol}} = 3\)

Determine the empirical formula

Based on the molar ratios determined in the previous step, the empirical formula of the compound can be written as: N2H8C1O3. However, the common notation simply omits the "1" subscript for single atoms. Thus, the empirical formula for the given compound is N2H8CO3.

Key concepts

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. Understanding stoichiometry is essential for predicting how much product will form from a given amount of reactants, which is key for many practical applications like creating recipes for industrial chemical processes or even cooking.

For example, when determining the empirical formula of a compound, stoichiometry comes into play as we use the mass percentages of each element to calculate the moles of those elements present in a sample of the compound. The empirical formula, which provides the simplest whole-number ratio of the elements in the compound, is derived using the stoichiometric calculations. These steps bring us closer to understanding the fundamental composition of a substance and how various elements combine to form complex molecules.

Stoichiometry is not only about balancing equations but also about the deeper understanding of the conservation of mass and the mole concept, ensuring that the atoms involved in reactions are accounted for from reactants to products. It's akin to ensuring every piece of a puzzle is placed correctly; without adherence to stoichiometric principles, we might end up with an incomplete picture of our chemical reaction.

Mole Concept

The mole concept is a cornerstone in the study of chemistry, providing a bridge between the microscopic world of atoms and molecules and the macroscopic world we observe. It defines a mole as Avogadro’s number (\(6.022 \times 10^{23}\) entities) of particles, which could be atoms, molecules, ions, or other chemical units, and is used to conveniently count these particles just as one might use a dozen to count eggs or people.

By using the mole concept, we can convert the mass of an element (in grams) to the number of moles, as seen in the exercise. This enables us to compare the ratios of atoms involved in a compound on a mole-to-mole basis, which is essential for determining the chemical formula. It’s a bit like counting the number of each type of fruit in a mixed basket to determine the contents without guessing based on the weight alone.

Furthermore, understanding the mole concept allows us to delve further into the realm of stoichiometry, as it provides the underlying basis for the calculations and conversions between mass and number of particles — an indispensable skill for any budding chemist or anyone involved in scientific endeavors concerning chemical quantities.

Chemical Composition Analysis

Chemical composition analysis provides a deeper insight into the make-up of a substance, revealing the proportions of the different elements present in a compound. This is akin to looking at a recipe and its ingredients list to determine what and how much is needed to create a dish.

In the given exercise, the process begins by converting the percent composition data into mass, assuming a 100-gram sample, which simplifies the math without losing the proportionality. Examining the mass percentage of each element leads to the understanding of how much of each element is present in a given amount of the compound. From there, we convert those masses to moles to contemplate the actual number of atoms, underlining the connection between quantitative and qualitative analysis.

Chemical composition analysis is a critical tool when experimenting or in industry applications such as quality control, where precise knowledge of a compound's makeup is essential. Whether a student is working on a laboratory synthesis or a manufacturer is assessing product consistency, chemical composition analysis guides decisions and ensures that outcomes are predictable and repeatable.