Step 1: Recall Avogadro's number.
One mole of any substance contains $N_A=6.023\times 10^{23}$ particles. So if we know how many moles we have, we can find the number of molecules by multiplying by this number.
Step 2: Find the molar mass of nitrogen gas.
Nitrogen gas is $\mathrm{N_2}$, made of two nitrogen atoms. Each nitrogen atom weighs about $14\,\text{g/mol}$, so $\mathrm{N_2}$ has a molar mass of $28\,\text{g/mol}$.
Step 3: Write the moles formula.
Moles are found by dividing the given mass by the molar mass. \[ n=\frac{m}{M} \] We use this to convert grams into moles.
Step 4: Plug in the numbers.
The given mass is $2.8\,\text{g}$ and the molar mass is $28\,\text{g/mol}$. \[ n=\frac{2.8}{28}=0.1\ \text{mol} \]
Step 5: Convert moles to molecules.
Multiply the moles by Avogadro's number. \[ \text{Molecules}=0.1\times 6.023\times 10^{23} \]
Step 6: Compute the final count.
Multiplying gives \[ 6.023\times 10^{22} \] molecules, which is option 1. \[ \boxed{6.023\times 10^{22}} \]