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Chapter 9: Problem 42

How many \(\mathrm{O}_{2}\) molecules are there in 1 mole of \(\mathrm{O}_{2}\) molecules? How many \(\mathrm{O}\) atoms are there in 1 mole of \(\mathrm{O}_{2}\) molecules?

Short Answer

Expert verified
In 1 mole of O鈧� molecules, there are \(6.022 \times 10^{23}\) O鈧� molecules and \(1.2044 \times 10^{24}\) O atoms.

Step by step solution

01

Recall the definition of a mole and Avogadro's number

A mole is the amount of substance that contains as many particles (such as atoms, molecules, ions, etc.) as there are in 12 grams of pure carbon-12. Avogadro's number (N鈧�) is the number of particles in one mole of a substance and is equal to 6.022 x 10虏鲁 particles per mole.
02

Find the number of O鈧� molecules in 1 mole of O鈧� molecules

Since there are 6.022 x 10虏鲁 particles in 1 mole of a substance, there are 6.022 x 10虏鲁 O鈧� molecules in 1 mole of O鈧� molecules.
03

Find the number of O atoms in 1 mole of O鈧� molecules

In one O鈧� molecule, there are 2 O atoms. Since there are 6.022 x 10虏鲁 O鈧� molecules in 1 mole of O鈧� molecules, we can multiply this number by the number of O atoms in each O鈧� molecule to find the number of O atoms in 1 mole of O鈧� molecules: \( (6.022 \times 10^{23}) \times 2 = 1.2044 \times 10^{24} \) O atoms. In conclusion, there are 6.022 x 10虏鲁 O鈧� molecules in 1 mole of O鈧� molecules, and there are 1.2044 x 10虏鈦� O atoms in 1 mole of O鈧� molecules.

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Key Concepts

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

Understanding the Mole Concept
The mole is a fundamental concept in chemistry. It provides a bridge between the atomic and macroscopic worlds. A mole represents a specific quantity of particles, be it atoms, molecules, or ions. This specific quantity is determined by Avogadro's number, which is 6.022 x 10虏鲁. This means one mole of any substance contains exactly 6.022 x 10虏鲁 particles.

This concept simplifies calculations in chemistry. Instead of counting individual atoms in reactions, we use moles. This way, large amounts can be expressed more conveniently, allowing chemists to describe chemical reactions, compositional details, and properties effectively.
  • The mole provides a way to convert between atoms/molecules and grams.
  • It's based on exactly 12 grams of carbon-12.
  • This concept applies universally to all chemical entities.
Molecules Calculation Made Simple
Calculating the number of molecules is easy once you have the mole concept down. If you know the amount of substance in moles, multiplying by Avogadro's number gives you the total number of molecules.

In our example, if you have 1 mole of \(\mathrm{O}_{2}\), you simply multiply 1 mole by Avogadro's number:
\[ 1 \text{ mole} \times 6.022 \times 10^{23} \text{ molecules/mole} = 6.022 \times 10^{23} \text{ molecules} \]
  • This method works for any molecule or atom.
  • Just remember, one mole always equals 6.022 x 10虏鲁 entities.
  • Multiply the number of moles you have by Avogadro's number to get the total count.
Delving into Elementary Entities
Elementary entities can be any small unit of matter such as atoms, molecules, or ions. In chemistry, these tiny particles combine in various ways to form substances, and the mole connects these microscopic entities to macroscopic measurements.

For instance, in one molecule of \(\mathrm{O}_{2}\), there are two oxygen atoms. If given 1 mole of \(\mathrm{O}_{2}\) molecules, multiplying Avogadro's number by 2 gives the total number of oxygen atoms:
\[ 6.022 \times 10^{23} \text{ molecules} \times 2 \text{ atoms/molecule} = 1.2044 \times 10^{24} \text{ atoms} \]
  • This calculation helps determine the total number of elementary entities in compounds.
  • The method applies to any substance where multiple elementary entities form a larger molecule.

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Most popular questions from this chapter

Consider a \(5.00-\mathrm{g}\) sample of silver nitrate, \(\mathrm{AgNO}_{3}(s)\) (a) How many moles of \(\mathrm{AgNO}_{3}\) are in this sample? (b) How many moles of \(\mathrm{O}\) are in this sample? (c) How many grams of \(\mathrm{N}\) are in this sample? (d) How many Ag atoms are in this sample?

Suppose you run the reaction \(\mathrm{A}+2 \mathrm{~B} \rightarrow \mathrm{C}\) with \(\mathrm{B}\) as the limiting reactant and all of the reactants and products are solids. You desire to sell pure product \(C\). What problem are you going to encounter that you will have to spend money on to fix?

A \(2.000 \mathrm{~g}\) sample of a liquid compound that contains only carbon and hydrogen in its formula is subjected to combustion analysis. From the result, the lab determines that \(0.2874 \mathrm{~g}\) of the original sample's mass is due to hydrogen. (a) What is the percent by mass hydrogen for this sample? (b) What is the empirical formula for this compound? (c) The molar mass of this compound is determined to be about \(71 \mathrm{~g} / \mathrm{mol}\). What is the molecular formula for this compound?

The compound ibuprofen, used in some pain relievers, has the molecular formula \(\mathrm{C}_{13} \mathrm{H}_{18} \mathrm{O}_{2}\). If \(0.250 \mathrm{~g}\) of ibuprofen is burned in oxygen, how many grams of \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\) will be produced?

Chlorine \(\left(\mathrm{Cl}_{2}\right)\) and fluorine \(\left(\mathrm{F}_{2}\right)\) react to form \(\mathrm{ClF}_{3}\). A reaction vessel contains \(2.50\) moles of \(\mathrm{Cl}_{2}\) and \(6.15\) moles of \(\mathrm{F}_{2}\). (a) Write a balanced chemical equation for this reaction. (b) Which reactant is limiting?
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