How to convert mol/m^2 to total mass ( e.g gram, kg etc )?
$\rm \frac{mol}{m^2}$ shows the amount of $\rm{NO_2}$ in the atmosphere over a square meter of surface area - in mols.

The molar mass of the $\rm{NO_2}$ is $14+2\cdot 16=46$. It means, the mass of 1 mol of $\rm{NO_2}$ is $\rm{46g}$.

The surface area of the Earth is 510million $\rm{km^2}$. Thus, 1 $\rm \frac{mol}{m^2} \rm{NO_2}$ translates to $\rm{46 \frac{g}{m^2} \cdot 5.1 \cdot 10^8 km^2}$, what means a total mass of $23.46\cdot 10^9 \rm t$ in the whole atmosphere.

Here we assumed a constant distribution of the $\rm {NO_2}$ in the atmosphere, which is typically not the case in earth science-related problems. Also your research question is about the visualization of a highly non-level distribution. Here you need to integrate (or, considering your digital evironment, sum).