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Chapter 2: Problem 68

A sample of ethanol (ethyl alcohol), \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH},\) contains \(4.2 \times 10^{23}\) hydrogen atoms. How many \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\) molecules are in this sample?

Short Answer

Expert verified
There are \(7 \times 10^{22}\) \(\mathrm{C}_{2}\mathrm{H}_{5}\mathrm{OH}\) molecules.

Step by step solution

01

Understanding the problem

We need to determine how many molecules of ethanol, \(\mathrm{C}_{2}\mathrm{H}_{5}\mathrm{OH}\), contain \(4.2 \times 10^{23}\) hydrogen atoms. Ethanol has the chemical formula \(\mathrm{C}_{2}\mathrm{H}_{5}\mathrm{OH}\), which means each molecule of ethanol contains 6 hydrogen atoms.
02

Calculate the number of hydrogen atoms per ethanol molecule

Each ethanol molecule \(\mathrm{C}_{2}\mathrm{H}_{5}\mathrm{OH}\) consists of 6 hydrogen atoms due to its structure: \(\mathrm{H}_{5}\) from the ethyl group and an additional \(\mathrm{OH}\) group. Thus, each ethanol molecule has a total of 6 hydrogen atoms.
03

Set up the relationship for molecules to hydrogen atoms

Since one ethanol molecule contains 6 hydrogen atoms, the number of ethanol molecules is the total number of hydrogen atoms divided by 6.
04

Perform the calculation

To find the number of \(\mathrm{C}_{2}\mathrm{H}_{5}\mathrm{OH}\) molecules, divide the total hydrogen atoms \(4.2 \times 10^{23}\) by the number of hydrogen atoms per molecule, which is 6:\[\frac{4.2 \times 10^{23}}{6} = 0.7 \times 10^{23} = 7 \times 10^{22}\]Thus, there are \(7 \times 10^{22}\) ethanol molecules.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding the Chemical Formula
A chemical formula is a notation used to express the types and numbers of atoms in a molecule. For ethanol, the chemical formula is written as \(\mathrm{C}_{2}\mathrm{H}_{5}\mathrm{OH}\). This formula tells us several key things about the ethanol molecule:
  • The \(\mathrm{C}_{2}\) indicates that there are two carbon atoms.
  • The \(\mathrm{H}_{5}\) shows that there are five hydrogen atoms attached to the carbon chain.
  • The \(\mathrm{OH}\) group adds an additional hydrogen and an oxygen atom, totaling six hydrogen atoms in one ethanol molecule.
This informative system allows chemists to quickly understand the composition and structure of molecules by reading the formula.
Exploring Molecules
Molecules are a group of atoms bonded together, representing the smallest identifiable unit of a chemical compound that can take part in a chemical reaction. Ethanol is one such molecule, made up of carbon, hydrogen, and oxygen atoms.
A single molecule of ethanol consists of:
  • 2 Carbon atoms (\(\mathrm{C}_{2}\))
  • 6 Hydrogen atoms (\(\mathrm{H}_{6}\))
  • 1 Oxygen atom (\(\mathrm{O}\))
These atoms are bound together to create a complete unit of ethanol. Understanding the concept of molecules helps us comprehend how atoms interact to form substances. Every substance around us, including ethanol, is made up of these versatile molecules.
Role of Hydrogen Atoms
Hydrogen atoms are the simplest type of atom, consisting of just one proton and one electron. In our example of ethanol, hydrogen plays a crucial role due to its presence in significant numbers relative to other atoms.
Since an ethanol molecule, \(\mathrm{C}_{2}\mathrm{H}_{5}\mathrm{OH}\), contains 6 hydrogen atoms, calculating the total number of ethanol molecules in a sample directly involves understanding this composition:
  • If you know the total hydrogen atoms in a sample, you can determine the number of ethanol molecules by dividing the hydrogen count by 6.
  • This relationship is fundamental in stoichiometry, involving the balancing and calculation of atoms in a chemical reaction.
Hydrogen's abundance in ethanol makes it a vital focal point for understanding molecular quantities in a sample.
The Ethanol Compound
Ethanol, often recognized as the active ingredient in alcoholic beverages, has a wide range of applications beyond consumption. Chemically, it is an organic compound that belongs to the alcohol group.
The characteristics of ethanol include:
  • A colorless volatile liquid at room temperature.
  • Flammable, with a characteristic pleasant odor.
  • Used as a solvent in the manufacture of varnishes and perfumes.
  • A fuel or fuel additive due to its ability to combust.
Understanding ethanol is not only essential for its application in chemistry labs but also for its numerous practical uses in everyday life. This compound is a frequent subject of study in chemistry due to its practical applications and its contribution to numerous chemical processes.

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Most popular questions from this chapter

Give the formulas for the following compounds. a. hydrogen peroxide b. magnesium phosphate c. lead(IV) phosphide d. calcium carbonate

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Glauber's salt has the formula \(\mathrm{Na}_{2} \mathrm{SO}_{4} \cdot 10 \mathrm{H}_{2} \mathrm{O}\). What is the chemical name of this substance?

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Balance the following equations. a. \(\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}+\mathrm{H}_{3} \mathrm{PO}_{4} \longrightarrow \mathrm{Ca}\left(\mathrm{H}_{2} \mathrm{PO}_{4}\right)_{2}\) b. \(\mathrm{MnO}_{2}+\mathrm{HCl} \longrightarrow \mathrm{MnCl}_{2}+\mathrm{Cl}_{2}+\mathrm{H}_{2} \mathrm{O}\) c. \(\mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3}+\mathrm{I}_{2} \longrightarrow \mathrm{NaI}+\mathrm{Na}_{2} \mathrm{~S}_{4} \mathrm{O}_{6}\) d. \(\mathrm{Al}_{4} \mathrm{C}_{3}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{Al}(\mathrm{OH})_{3}+\mathrm{CH}_{4}\) e. \(\mathrm{NO}_{2}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{HNO}_{3}+\mathrm{NO}\)
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