Very briefly and physically speaking, it obviously depends on the ability of the sensor channel to detect some spectral response from the interactions between very tiny molecules like SO2 and incident wavelength. However, usually these molecules concentrations are also associated to some other kinds of particulated matter or aerossol concentrations with higher diameter (ex.PM2.5 or higher).
The simple answer in "NO" just because the width of the Landsat channels is quite big. For the task you approach you need data from other RS instruments such as OMI or TROPOMI, but the spatial resolution is not so fine (15km x 15km).
First of all, thanks to all of you for taking your time to respond this question.
Hristo Nikolov, the research that we are designing is for Puerto Rico. The ideal scenario was 90sq km because we want to study a specific community, but I guess we can work with an image that indicates SO2 and NO2 with patches that cover a wider area. The main island is 9,104 sq km. Do you understand that is a good size for Landsat 8?
OMI and TROPOMI are not the best choices since it takes longer to process.