If $14\text{g}$ of ${\text{N}}_2$ gas has '$n$ ' number of molecules, how many molecules are present in $46\text{g}$ of ${\text{NO}}_2$ gas?

Let's apply the mole concept step-by-step:
1. Molar mass of nitrogen gas (${\text{N}}_2$) = $2\times 14=28\text{g/mol}$.
2. Number of moles in $14\text{g}$ of ${\text{N}}_2$:

$$\text{Moles of }{\text{N}}_2=\frac{14\text{g}}{28\text{g/mol}}=0.5\text{mol}$$

We are given that $0.5\text{mol}$ contains $n$ molecules. Therefore, $1\text{mol}$ will contain $2n$ molecules.
3. Molar mass of nitrogen dioxide (${\text{NO}}_2$) = $14+(2\times 16)=14+32=46\text{g/mol}$.
4. Number of moles in $46\text{g}$ of ${\text{NO}}_2$:

$$\text{Moles of }{\text{NO}}_2=\frac{46\text{g}}{46\text{g/mol}}=1\text{mol}$$

Since $0.5\text{mol}$ corresponds to $n$ molecules, $1\text{mol}$ must correspond to:

$$\text{Number of molecules}=2\times n=2n$$