How many molecules are in a 1.7 gram iron nail?
The Correct Answer and Explanation is :
A 1.7 gram iron nail contains approximately 1.83 × 10²² molecules (or atoms, in this case, since iron is a metal).
Explanation:
To calculate the number of molecules (atoms) in the nail, we first need to determine the number of moles of iron in the 1.7-gram nail. A mole of any substance contains Avogadro’s number of molecules (6.022 × 10²³ molecules).
- Molar Mass of Iron: The molar mass of iron (Fe) is 55.845 grams per mole, meaning one mole of iron weighs 55.845 grams.
- Number of Moles: The formula to calculate the number of moles is:
[
\text{moles of Fe} = \frac{\text{mass of Fe}}{\text{molar mass of Fe}}
]
Substituting the values:
[
\text{moles of Fe} = \frac{1.7 \, \text{grams}}{55.845 \, \text{grams/mole}} \approx 0.0304 \, \text{moles}
] - Number of Atoms: Using Avogadro’s number (6.022 × 10²³ atoms/mole), we can determine the number of atoms in 0.0304 moles of iron:
[
\text{atoms of Fe} = 0.0304 \, \text{moles} \times 6.022 \times 10^{23} \, \text{atoms/mole} \approx 1.83 \times 10^{22} \, \text{atoms}
]
Thus, the number of atoms in a 1.7-gram iron nail is approximately 1.83 × 10²² atoms.
I’ll now generate a visual representation of this concept for you.
Here is the visual representation showing a 1.7-gram iron nail with an overlaid diagram of atoms, along with the conversion from grams to moles and then to atoms. It highlights the number of atoms in the nail as approximately 1.83 × 10²² atoms. Let me know if you’d like any further details or adjustments!
