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Chapter 3: Problem 14

How many moles of cobalt (Co) atoms are there in \(6.00 \times 10^{9}\) (6 billion) Co atoms?

Short Answer

Expert verified
There are approximately \(9.96 \times 10^{-14}\) moles of Cobalt atoms

Step by step solution

01

Identify Given Value and Conversion Factor

First, we have the given number of Cobalt atoms which is \(6.00 \times 10^{9}\). We will use Avogadro's number \(6.02214076 \times 10^{23}\) as the conversion factor, noting that 1 mole of any substance contains approximately this many entities.
02

Set Up the Conversion

To convert atoms to moles, use the relationship that 1 mole of atoms is equivalent to Avogadro's number of atoms. The conversion set up will be: \[\frac{{6.00 \times 10^{9} \, atoms}}{{1}} \times \frac{1 \, mole}{{6.02214076 \times 10^{23} \, atoms}}\]
03

Calculate

Performing the multiplication and division gives approximately \(9.9647 \times 10^{-14}\) moles of Cobalt.

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Most popular questions from this chapter

Calculate the percent composition by mass of all the elements in calcium phosphate \(\left[\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}\right],\) a major component of bone.

(a) For molecules having small molecular masses, mass spectrometry can be used to identify their formulas. To illustrate this point, identify the molecule that most likely accounts for the observation of a peak in a mass spectrum at 16 amu, 17 amu, 18 amu, and 64 amu. (b) Note that there are (among others) two likely molecules that would give rise to a peak at 44 amu, namely, \(\mathrm{C}_{3} \mathrm{H}_{8}\) and \(\mathrm{CO}_{2} .\) In such cases, a chemist might try to look for other peaks generated when some of the molecules break apart in the spectrometer. For example, if a chemist sees a peak at 44 amu and also one at 15 amu, which molecule is producing the 44 -amu peak? Why? (c) Using the following precise atomic masses \(-\mathrm{H}\) ( 1.00797 amu), \({ }^{12} \mathrm{C}(12.00000 \mathrm{amu}),\) and \({ }^{16} \mathrm{O}(15.99491 \mathrm{amu})-\) how precisely must the masses of \(\mathrm{C}_{3} \mathrm{H}_{8}\) and \(\mathrm{CO}_{2}\), be measured to distinguish between them?

The molar mass of caffeine is \(194.19 \mathrm{~g}\). Is the molecular formula of caffeine \(\mathrm{C}_{4} \mathrm{H}_{5} \mathrm{~N}_{2} \mathrm{O}\) or \(\mathrm{C}_{8} \mathrm{H}_{10} \mathrm{~N}_{4} \mathrm{O}_{2} ?\)

Use the formation of water from hydrogen and oxygen to explain the following terms: chemical reaction, reactant, product.

Describe the steps involved in the mole method.
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