Use The Periodic Table To Determine How Many Atoms Of Phosphorus (P) Are In A Sample That Has A Mass Of 172.90 G.A. 3.48 × 10 21 3.48 \times 10^{21} 3.48 × 1 0 21 Atoms B. 1.97 × 10 22 1.97 \times 10^{22} 1.97 × 1 0 22 Atoms C. 3.36 × 10 24 3.36 \times 10^{24} 3.36 × 1 0 24 Atoms D. $1.04
Understanding the Periodic Table and Atomic Mass
The periodic table is a tabular arrangement of the known chemical elements, organized by their atomic number (number of protons in the nucleus), electron configuration, and recurring chemical properties. The atomic mass of an element is the average mass of a single atom, taking into account the naturally occurring isotopes of the element. In this case, we are dealing with phosphorus (P), which has an atomic mass of approximately 30.97 g/mol.
Calculating the Number of Moles of Phosphorus
To determine the number of atoms of phosphorus in a sample, we first need to calculate the number of moles of phosphorus present. We can do this by dividing the mass of the sample (172.90 g) by the atomic mass of phosphorus (30.97 g/mol).
moles = mass / atomic mass
moles = 172.90 g / 30.97 g/mol
moles ≈ 5.59 mol
Understanding Avogadro's Number
Avogadro's number is a fundamental constant in chemistry, representing the number of particles (atoms or molecules) in one mole of a substance. It is defined as 6.022 x 10^23 particles per mole. This number is a conversion factor that allows us to convert between moles and particles.
Calculating the Number of Atoms of Phosphorus
Now that we have the number of moles of phosphorus, we can use Avogadro's number to calculate the number of atoms of phosphorus present in the sample.
atoms = moles x Avogadro's number
atoms = 5.59 mol x 6.022 x 10^23 atoms/mol
atoms ≈ 3.36 x 10^24 atoms
Evaluating the Answer Choices
Now that we have calculated the number of atoms of phosphorus, we can evaluate the answer choices to determine which one is correct.
- A. atoms: This answer is too low, as our calculation indicates a much larger number of atoms.
- B. atoms: This answer is still too low, but closer to our calculated value.
- C. atoms: This answer matches our calculated value exactly.
- D. atoms: This answer is close, but not as large as our calculated value.
Conclusion
Based on our calculation, the correct answer is C. atoms. This answer choice matches our calculated value exactly, indicating that the sample contains approximately 3.36 x 10^24 atoms of phosphorus.
Additional Considerations
When working with the periodic table and atomic masses, it's essential to consider the following:
- Atomic masses are averages, taking into account the naturally occurring isotopes of an element.
- The periodic table is a tabular arrangement of elements, organized by their atomic number, electron configuration, and recurring chemical properties.
- Avogadro's number is a fundamental constant in chemistry, representing the number of particles (atoms or molecules) in one mole of a substance.
By understanding these concepts and applying them to the problem at hand, we can accurately determine the number of atoms of phosphorus in a sample.
Q: What is the atomic mass of phosphorus?
A: The atomic mass of phosphorus is approximately 30.97 g/mol.
Q: How do I calculate the number of moles of phosphorus in a sample?
A: To calculate the number of moles of phosphorus, you need to divide the mass of the sample by the atomic mass of phosphorus. For example, if the mass of the sample is 172.90 g, you would divide it by 30.97 g/mol to get the number of moles.
Q: What is Avogadro's number?
A: Avogadro's number is a fundamental constant in chemistry, representing the number of particles (atoms or molecules) in one mole of a substance. It is defined as 6.022 x 10^23 particles per mole.
Q: How do I calculate the number of atoms of phosphorus using Avogadro's number?
A: To calculate the number of atoms of phosphorus, you need to multiply the number of moles by Avogadro's number. For example, if you have 5.59 mol of phosphorus, you would multiply it by 6.022 x 10^23 atoms/mol to get the number of atoms.
Q: What is the correct answer for the number of atoms of phosphorus in a sample with a mass of 172.90 g?
A: The correct answer is C. atoms.
Q: Why is it essential to consider the atomic mass of an element when calculating the number of moles?
A: The atomic mass of an element is essential because it takes into account the naturally occurring isotopes of the element. This means that the atomic mass is an average value, and using it ensures that your calculations are accurate.
Q: What is the significance of Avogadro's number in chemistry?
A: Avogadro's number is significant because it allows us to convert between moles and particles (atoms or molecules). This conversion factor is essential in chemistry, as it enables us to calculate the number of particles in a sample.
Q: Can I use Avogadro's number to calculate the number of atoms of any element?
A: Yes, you can use Avogadro's number to calculate the number of atoms of any element, as long as you know the number of moles of the element and its atomic mass.
Q: What are some common mistakes to avoid when calculating the number of atoms of an element?
A: Some common mistakes to avoid include:
- Not considering the atomic mass of the element
- Not using Avogadro's number to convert between moles and particles
- Not rounding calculations to the correct number of significant figures
Q: How can I apply the concepts learned in this article to real-world problems?
A: You can apply the concepts learned in this article to real-world problems by using the periodic table and atomic masses to calculate the number of atoms of an element in a sample. This can be useful in a variety of fields, including chemistry, physics, and materials science.