Determine the quantity of moles in 1.81×10^24 atoms of Na
The Correct Answer and Explanation is :
The correct answer is: 3.01 moles
To determine the quantity of moles in ( 1.81 \times 10^{24} ) atoms of sodium (Na), we can use Avogadro’s number, which is approximately ( 6.022 \times 10^{23} ) atoms/mole. This number represents the amount of atoms, ions, or molecules in one mole of a substance.
Calculation Steps:
- Identify the number of atoms: We have ( 1.81 \times 10^{24} ) atoms of sodium.
- Use Avogadro’s number: We know that one mole contains ( 6.022 \times 10^{23} ) atoms.
- Calculate the moles:
[
\text{Moles of Na} = \frac{\text{Number of atoms}}{\text{Avogadro’s number}} = \frac{1.81 \times 10^{24} \text{ atoms}}{6.022 \times 10^{23} \text{ atoms/mole}}
] [
\text{Moles of Na} = \frac{1.81}{6.022} \approx 3.01 \text{ moles}
]
Explanation:
The concept of a mole is fundamental in chemistry, allowing chemists to count quantities of atoms and molecules in a practical way. Since atoms and molecules are incredibly small and numerous, dealing with them one by one is impractical. Instead, using the mole provides a bridge between the atomic scale and the macroscopic scale we can measure in the laboratory.
Avogadro’s number is a constant that defines how many elementary entities (atoms, molecules, etc.) are in one mole of a substance. This constant is essential for converting between grams and moles because it provides a means to quantify large numbers of very small entities.
In this example, knowing that we have ( 1.81 \times 10^{24} ) atoms allows us to use Avogadro’s number to find out how many moles of sodium we actually have. This conversion is essential for various applications, including stoichiometry in chemical reactions, where precise quantities of reactants and products need to be calculated.
Thus, the quantity of moles in ( 1.81 \times 10^{24} ) atoms of Na is approximately 3.01 moles.