Find the best solutions to your problems with the help of IDNLearn.com's experts. Ask your questions and receive accurate, in-depth answers from our knowledgeable community members.

Use the periodic table to determine how many atoms of phosphorus (P) are in a sample that has a mass of [tex]172.90 \, \text{g}[/tex].

A. [tex]3.48 \times 10^{21}[/tex] atoms
B. [tex]1.97 \times 10^{22}[/tex] atoms
C. [tex]3.36 \times 10^{24}[/tex] atoms
D. [tex]1.04 \times 10^{26}[/tex] atoms


Sagot :

Sure, I'd be happy to help you figure this out!

To determine the number of atoms of phosphorus in a sample with a mass of [tex]\(172.90 \, \text{g}\)[/tex], we need to follow these steps:

1. Determine the molar mass of phosphorus:
The atomic mass of phosphorus is [tex]\(30.974 \, \text{g/mol}\)[/tex]. This value is obtained from the periodic table.

2. Calculate the number of moles of phosphorus:
To find the number of moles, we use the formula:
[tex]\[ \text{moles of phosphorus} = \frac{\text{mass of sample}}{\text{molar mass of phosphorus}} \][/tex]
Plugging in the values, we get:
[tex]\[ \text{moles of phosphorus} = \frac{172.90 \, \text{g}}{30.974 \, \text{g/mol}} \approx 5.582 \, \text{moles} \][/tex]

3. Calculate the number of atoms of phosphorus:
We know that one mole of any substance contains [tex]\(6.022 \times 10^{23}\)[/tex] atoms (Avogadro's number). So, to find the number of atoms, we multiply the number of moles by Avogadro's number:
[tex]\[ \text{atoms of phosphorus} = \text{moles of phosphorus} \times 6.022 \times 10^{23} \, \text{atoms/mol} \][/tex]
Substituting the number of moles we estimated:
[tex]\[ \text{atoms of phosphorus} = 5.582 \, \text{moles} \times 6.022 \times 10^{23} \approx 3.362 \times 10^{24} \, \text{atoms} \][/tex]

4. Simplify to match the given options:
By simplifying the scientific notation to match the closest option:
[tex]\[ \text{atoms of phosphorus} \approx 3.36 \times 10^{24} \, \text{atoms} \][/tex]

From the choices given:

[tex]\[ 3.48 \times 10^{21} \, \text{atoms}, \quad 1.97 \times 10^{22} \, \text{atoms}, \quad 3.36 \times 10^{24} \, \text{atoms}, \quad 1.04 \times 10^{26} \, \text{atoms} \][/tex]

The correct answer is:

[tex]\[ \boxed{3.36 \times 10^{24}} \][/tex]
Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. Find the answers you need at IDNLearn.com. Thanks for stopping by, and come back soon for more valuable insights.