Which of the following expressions is correct ( `n = no`. of moles of the gas, `N_(A) =` Avogadro constant `m = mass` of 1 molecule of the gas, N = no of molecules of the gas) ? .

Options

A. `n = mN_(A)`
B. `m = N_(A)`
C. `N = nN_(A)`
D. `m = n//N_(A)`

Explanation

To solve the question regarding the correct expression among the given options, we will analyze the relationships between the number of moles, number of molecules, and Avogadro's constant step by step.

### Step 1: Understanding Moles and Molecules
- The number of moles (n) of a substance is defined as the amount of substance that contains as many entities (atoms, molecules, etc.) as there are atoms in 12 grams of carbon-12.
- Avogadro's constant (NA) is the number of entities in one mole of a substance, which is approximately \(6.022 \times 10^{23}\) entities/mole.

### Step 2: Relationship Between Moles and Molecules
- The total number of molecules (N) in a given number of moles (n) can be calculated using the formula:
\[ N = n \times N_A \]
where:
- \(N\) = total number of molecules
- \(n\) = number of moles
- \(N_A\) = Avogadro's constant

### Step 3: Analyzing the Given Options
- We need to identify which expression correctly represents the relationship between the number of moles, number of molecules, and Avogadro's constant.
- Based on our understanding from Step 2, the correct expression is:
\[ N = n \times N_A \]

### Step 4: Conclusion
- Therefore, the correct expression among the options provided is:
\[ N = n \times N_A \]
- This indicates that the total number of molecules (N) is equal to the number of moles (n) multiplied by Avogadro's constant (\(N_A\)).