How many sodium atoms are there in 100.0 grams of sodium

How many sodium atoms are there in 100.0 grams of sodium?

The correct answer and explanation is:

To determine how many sodium atoms are in 100.0 grams of sodium, we follow these steps:

Step-by-step Solution:

1. Find the molar mass of sodium (Na):
   • Sodium has a molar mass of approximately 22.99 g/mol.
2. Convert grams to moles: Moles of Na=Mass of NaMolar mass of Na=100.0 g22.99 g/mol≈4.35 mol\text{Moles of Na} = \frac{\text{Mass of Na}}{\text{Molar mass of Na}} = \frac{100.0 \, \text{g}}{22.99 \, \text{g/mol}} \approx 4.35 \, \text{mol}
3. Use Avogadro’s number to find number of atoms:
   • Avogadro’s number = 6.022 × 10²³ atoms/mol
   Number of atoms=4.35 mol×6.022×1023 atoms/mol≈2.62×1024 atoms\text{Number of atoms} = 4.35 \, \text{mol} \times 6.022 \times 10^{23} \, \text{atoms/mol} \approx 2.62 \times 10^{24} \, \text{atoms}

✅ Final Answer:

There are approximately 2.62 × 10²⁴ sodium atoms in 100.0 grams of sodium.

🧪 Explanation (300 words):

To understand how many atoms are in a given mass of an element, we must link mass to the microscopic scale using moles and Avogadro’s number. A mole is a unit in chemistry that represents 6.022 × 10²³ particles, typically atoms or molecules. This concept is similar to using the term “dozen” to represent 12 items — only the mole represents an incredibly large number of particles.

Sodium (Na) is a metallic element with a molar mass of 22.99 grams per mole, which means that one mole of sodium atoms weighs 22.99 grams. If we have 100 grams of sodium, we divide that by 22.99 to get the number of moles of sodium present in that sample. That calculation gives us about 4.35 moles.

Now, using Avogadro’s number, we know that each mole contains 6.022 × 10²³ atoms. So, multiplying 4.35 moles by this constant gives the total number of sodium atoms: approximately 2.62 × 10²⁴.

This large number highlights how incredibly tiny individual atoms are. Even a small mass of a pure element contains an astronomically large number of atoms. This concept is critical in chemistry, where reactions occur at the atomic level, and quantities of substances are most meaningfully measured in moles. It allows chemists to predict how much of a substance is needed or will be produced in a chemical reaction.