Finding Moles of He Atoms in 20 u Mass

The question asks for the number of moles of Helium (He) atoms present in a given mass of 20 u. Here, 'u' stands for unified atomic mass unit. Let's break down the concepts needed to solve this problem.

Understanding Atomic Mass and Moles

• Atomic Mass Unit (u): The atomic mass of an element or molecule is often expressed in atomic mass units (u). For Helium, the atomic mass is approximately 4 u. This means one Helium atom has a mass of about 4 u.
• Mole: A mole is a unit used to measure the amount of substance. One mole of any substance contains Avogadro's number of entities (atoms, molecules, ions, etc.). Avogadro's number is approximately $6.022 \times 10^{23}$.
• Molar Mass: The molar mass of an element is the mass of one mole of its atoms, expressed in grams per mole (g/mol). The numerical value of the molar mass in g/mol is equal to the atomic mass in u. For Helium, the molar mass is approximately 4 g/mol. This means 4 grams of Helium contain $6.022 \times 10^{23}$ Helium atoms (which is 1 mole of He atoms).

Calculating Moles from Mass in 'u'

We are given a total mass of 20 u for Helium atoms. We know that the mass of a single Helium atom is approximately 4 u. We can first find the total number of Helium atoms present in 20 u.

Step 1: Find the number of Helium atoms.

The number of atoms is the total mass divided by the mass of one atom.

Number of atoms = $\frac{\text{Total mass in u}}{\text{Mass of one atom in u}}$

Number of atoms = $\frac{20 \text{ u}}{4 \text{ u/atom}} = 5 \text{ atoms}$

So, a mass of 20 u of Helium corresponds to 5 Helium atoms.

Step 2: Convert the number of atoms to moles.

One mole contains Avogadro's number of atoms ($N_A = 6.022 \times 10^{23}$). To find the number of moles, we divide the number of atoms by Avogadro's number.

Number of moles = $\frac{\text{Number of atoms}}{\text{Avogadro's number} (N_A)}$

Number of moles = $\frac{5 \text{ atoms}}{6.022 \times 10^{23} \text{ atoms/mol}}$

Now, we perform the calculation:

Number of moles = $\frac{5}{6.022 \times 10^{23}}$ mol

Number of moles $\approx 0.8303 \times 10^{-23}$ mol

To express this in standard scientific notation, we move the decimal one place to the right and decrease the exponent by one.

Number of moles $\approx 8.303 \times 10^{-24}$ mol

Let's compare this result with the given options.

Our calculated value of approximately $8.3 \times 10^{-24}$ mol matches option 2.

Conclusion

To find the number of moles of He atoms in 20 u mass, we first determined the number of individual He atoms present in 20 u by dividing the total mass by the mass of a single He atom (20 u / 4 u = 5 atoms). Then, we converted the number of atoms to moles by dividing by Avogadro's number ($5 \text{ atoms} / 6.022 \times 10^{23} \text{ atoms/mol} \approx 8.3 \times 10^{-24} \text{ mol}$).