Problem 48 - Chemistry The Molecular Nature of Matter

Question

Nail polish remover is usually the volatile liquid ethyl acetate, \(\mathrm{CH}_{3} \mathrm{COOC}_{2} \mathrm{H}_{5} .\) In this compound, what is the (a) atom ratio of \(\mathrm{C}\) to \(\mathrm{O}\) ? (c) atom ratio of \(\mathrm{C}\) to \(\mathrm{H}\) ? (b) mole ratio of \(\mathrm{C}\) to \(\mathrm{O}\) ? (d) mole ratio of \(\mathrm{C}\) to \(\mathrm{H}\) ?

Step-by-Step Solution

Answer

Atom ratio of C to O is 2:1, atom ratio of C to H is 2:3, mole ratio of C to O is 2:1, and mole ratio of C to H is 2:3.

Step 1: Identify the Molecular Formula

The molecular formula for ethyl acetate is given as \(\mathrm{CH}_{3}\mathrm{COOC}_{2}\mathrm{H}_{5}\). This formula indicates the number of each type of atom in a molecule of ethyl acetate. Based on that formula, we can tally the count of carbon (C), hydrogen (H), and oxygen (O) atoms.

Step 2: Count the Atoms of Each Element

In the molecular formula, there are a total of 4 carbon (C) atoms: two from \(\mathrm{CH}_{3}\) and two from \(\mathrm{C}_{2}\mathrm{H}_{5}\), a total of 6 hydrogen (H) atoms: three from \(\mathrm{CH}_{3}\) and three from \(\mathrm{C}_{2}\mathrm{H}_{5}\), and 2 oxygen (O) atoms from \(\mathrm{COO}\).

Step 3: Calculate the Atom Ratio of C to O

To calculate the atom ratio of carbon to oxygen (C:O), simply divide the number of carbon atoms by the number of oxygen atoms. With 4 carbon atoms and 2 oxygen atoms, the atom ratio of C to O is \(\frac{4}{2} = 2\).

Step 4: Calculate the Atom Ratio of C to H

Similarly, to find the atom ratio of carbon to hydrogen (C:H), divide the number of carbon atoms by the number of hydrogen atoms. With 4 carbon atoms and 6 hydrogen atoms, the atom ratio of C to H is \(\frac{4}{6}\), which can be simplified to \(\frac{2}{3}\).

Step 5: Explain Mole Ratio

The mole ratio of elements in a compound is the same as the atom ratio because a mole is simply a defined number of molecules (Avogadro's number, 6.022 x \(10^{23}\) molecules), and all molecules of ethyl acetate have the same atomic composition.

Key Concepts

Molecular Formula

Understanding the molecular formula of a compound is essential for grasping the basics of chemistry. The molecular formula represents the exact number of atoms of each element present in a single molecule of a compound. For ethyl acetate, the molecular formula is \(CH_3COOC_2H_5\). In this notation, the subscript numbers indicate the quantity of each type of atom within the molecule. Knowing this facilitates calculations and predictions about the behavior of the compound in reactions.

When dealing with molecular formulas, it is crucial to remember that they provide a direct look into the composition of a molecule, showing us how to count the atoms for various calculations, such as determining the atom and mole ratios involved in the chemical substance and understanding its proportion in stoichiometric equations.

Atom Ratio Calculations

Atom ratio calculations are a fundamental aspect of stoichiometry. They involve quantifying the proportion of one type of atom to another within a compound. Take ethyl acetate as an example; the molecular formula \(CH_3COOC_2H_5\) reveals that the atom ratio calculations will depend on the count of each element's atoms.

The process includes counting the number of atoms for each element and then expressing the relationship between them as a ratio. For instance, comparing carbon atoms to oxygen atoms or carbon atoms to hydrogen atoms sets the stage for understanding the proportions in which elements combine to form a chemical substance.

Stoichiometry

Stoichiometry lies at the heart of chemical reactions. It is the study of the quantitative relationships, or ratios, of reactants and products in chemical reactions. Stoichiometry depends heavily on the mole concept, which relates masses of different substances in a reaction based on their molecular weights. From the perspective of a molecular formula like that of ethyl acetate, stoichiometry allows us to predict how much of each reactant is needed and what quantity of products will be formed under ideal conditions.

Understanding the stoichiometry of a compound such as ethyl acetate requires one to use mole ratios, which can be deduced from the atom ratios. These mole ratios become critical when scaling reactions to larger or smaller quantities and when determining the limiting reactants in a chemical process.

Ethyl Acetate Properties

Ethyl acetate, commonly used as a solvent in nail polish removers, showcases interesting chemical and physical properties. Its molecular formula, \(CH_3COOC_2H_5\), not only defines its composition but also influences its behavior. Ethyl acetate is known for its fast evaporation rate, pleasant smell, and relatively low toxicity, making it suitable for use in personal care products. It is also a polar solvent, which means it can dissolve a wide range of organic compounds.

Moreover, it finds applications in the field of chromatography, where it is used as an eluting agent due to its ability to interact with varying substances. Knowledge of ethyl acetate's properties is crucial when considering its interactions with other chemicals and its suitability for different applications in laboratories and industries.