What is the number of atoms in 46 g of sodium-23 (N = Avogadro constant)?
2N
Understanding Atoms in Sodium-23
This question asks us to find the total number of atoms present in a given mass of sodium-23. To solve this, we need to use the concept of molar mass and Avogadro's constant, which connects the macroscopic world (mass in grams) to the microscopic world (number of atoms).
Key Concepts: Molar Mass and Avogadro's Constant
- Molar Mass: The molar mass of an element or compound is the mass of one mole of that substance. For an element, the molar mass in grams per mole (g/mol) is numerically equal to its atomic mass number. For sodium-23, the atomic mass number is 23. Therefore, the molar mass of sodium-23 is approximately 23 g/mol.
- Avogadro's Constant (N): Avogadro's constant is the number of particles (atoms, molecules, ions, etc.) in one mole of a substance. Its value is approximately \(6.022 \times 10^{23}\) particles/mol. The question uses the symbol 'N' to represent this constant. So, 1 mole of any substance contains N particles.
Calculating the Number of Moles
First, we need to determine how many moles are present in 46 g of sodium-23. We can do this using the formula:
Number of moles = Mass of substance / Molar mass of substance
Given:
- Mass of sodium-23 = 46 g
- Molar mass of sodium-23 = 23 g/mol
Calculation:
Number of moles = \(\frac{46 \text{ g}}{23 \text{ g/mol}}\) = 2 moles
So, 46 g of sodium-23 corresponds to 2 moles of sodium-23.
Calculating the Number of Atoms
Now that we know the number of moles, we can find the number of atoms using Avogadro's constant (N). Since 1 mole of any substance contains N particles (in this case, atoms), 2 moles will contain 2 times N particles.
Number of atoms = Number of moles \(\times\) Avogadro's constant (N)
Given:
- Number of moles = 2 moles
- Avogadro's constant = N atoms/mol
Calculation:
Number of atoms = \(2 \text{ moles} \times N \text{ atoms/mol}\) = \(2N\) atoms
Therefore, there are \(2N\) atoms in 46 g of sodium-23.
Summary of Calculation Steps
| Step | Description | Calculation |
|---|---|---|
| 1 | Identify the given mass | 46 g |
| 2 | Determine the molar mass of sodium-23 | 23 g/mol |
| 3 | Calculate the number of moles | \(\frac{46 \text{ g}}{23 \text{ g/mol}} = 2 \text{ moles}\) |
| 4 | Relate moles to number of atoms using Avogadro's constant (N) | Number of atoms = Number of moles \(\times\) N |
| 5 | Final Calculation for number of atoms | \(2 \text{ moles} \times N \text{ atoms/mol} = 2N \text{ atoms}\) |
Final Answer on Sodium Atoms
Based on the calculations, the number of atoms in 46 g of sodium-23 is \(2N\).
Revision Table: Atoms and Moles
| Concept | Definition | Relationship |
|---|---|---|
| Mole | Unit for amount of substance, contains Avogadro's number of particles. | 1 mole = N particles |
| Molar Mass | Mass of one mole of a substance. | Mass of substance = Number of moles \(\times\) Molar Mass |
| Avogadro's Constant (N) | Number of particles in one mole (\(\approx 6.022 \times 10^{23}\)). | Number of particles = Number of moles \(\times\) N |
Additional Information on Isotopes and Molar Mass
Sodium-23 is a specific isotope of sodium. Isotopes are atoms of the same element that have the same number of protons but different numbers of neutrons. The number '23' in sodium-23 refers to its mass number (protons + neutrons). The atomic mass of sodium (as found on the periodic table, which is an average of naturally occurring isotopes) is approximately 22.99 u, which is very close to 23. For calculations involving a specific isotope like sodium-23, we often use its mass number as the numerical value for its molar mass in g/mol.
Understanding the relationship between mass, moles, and the number of particles is fundamental in chemistry calculations and stoichiometry. These conversions allow chemists to predict the amounts of reactants and products in chemical reactions.
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