What is the number of atoms present in 46 g of sodium 23, expressed in terms of Avogadro constant N?

Introduction / Context:
This question is a straightforward application of the mole concept. It asks how many atoms of an element are present in a given mass when the molar mass and Avogadro constant are known. Such questions are foundational for stoichiometry, limiting reagent problems, and understanding chemical equations quantitatively.

Given Data / Assumptions:

• Element considered is sodium 23, meaning its atomic mass is 23 g per mole.
• Given mass of sodium is 46 g.
• Avogadro constant is represented by N, which is the number of particles in 1 mole.
• We assume sodium is in atomic form, so each particle is an atom.

Concept / Approach:
Number of moles is calculated by dividing the given mass by molar mass. Once the number of moles is known, the total number of atoms is obtained by multiplying the number of moles by Avogadro constant. In symbols: moles = given mass / molar mass number of atoms = moles * N We then simplify this expression and match it with the symbolic options given (N/2, N, 2N, 23 N).

Step-by-Step Solution:
Step 1: Calculate the number of moles of sodium. molar mass of sodium 23 = 23 g per mole. given mass = 46 g. moles of sodium = 46 / 23 = 2 moles. Step 2: Find the number of atoms. Each mole contains N atoms. Therefore, number of atoms in 2 moles = 2 * N = 2N. Step 3: Match the result with the options. 2N corresponds exactly to option C.

Verification / Alternative Check:
As a quick sanity check, if 23 g of sodium contains N atoms, then doubling the mass to 46 g while keeping the same substance should double the number of atoms. So the answer must be twice N, that is 2N. This proportional reasoning confirms the result without needing to redo the full calculation.

Why Other Options Are Wrong:
Option A: N/2 would correspond to half a mole, which would be 11.5 g of sodium, not 46 g. Option B: N corresponds to one mole, which is 23 g, again not matching 46 g. Option D: 23 N would be 23 times Avogadro constant, which would require 23 moles of sodium, that is 23 * 23 = 529 g, far more than 46 g.

Common Pitfalls:
Misreading the question and treating 23 as a multiplier for N instead of as the molar mass is a common mistake. Another error is to forget to divide the mass by molar mass before multiplying by N, leading to expressions like 46 N instead of 2N. Carefully keeping the steps in the right order prevents such mistakes.

Final Answer:
The number of atoms in 46 g of sodium 23 is 2N.