The Stern Volmer plot is the plot is that of Io/I vs Concentration as said . But it can be also expressed as (Io-I)/I=K[Q]. This is a particular case of the plot of (Io-I)/(I-I∞)=K[Q] where I∞ is the remaining intensity for an infinite concentration of quencher [Q]. It can be the blank fluorescence, if any, or the fluorescence of the quenched fluorophore, if any.  This last relation is quite general since (Io-I) is proportional to [FQ] and (I-I∞) is proportional to [F] as long as the signal I, fluorescence, absorbance, scattering is proportional to concentration.  Interestingly you can have a straight line in two cases : if you have a static quenching mechanism or a dynamic quenching mechanism. In your case a static quenching is the more probable. You will not get a straight line if both mechanisms act together. Indeed there is non more a linearity between concentrations and signals.

The y-axis is the ratio of the unquenched fluorescence intensity divided by the quenched fluorescence intensity. The x-axis is the quencher concentration. The y-intercept is 1. The slope is the Stern-Volmer constant.

Check this paper. It is given in detail. Organometallics, 34, 4491, 2015.

The Stern Volmer plot is the plot is that of Io/I vs Concentration as said . But it can be also expressed as (Io-I)/I=K[Q]. This is a particular case of the plot of (Io-I)/(I-I∞)=K[Q] where I∞ is the remaining intensity for an infinite concentration of quencher [Q]. It can be the blank fluorescence, if any, or the fluorescence of the quenched fluorophore, if any.  This last relation is quite general since (Io-I) is proportional to [FQ] and (I-I∞) is proportional to [F] as long as the signal I, fluorescence, absorbance, scattering is proportional to concentration.  Interestingly you can have a straight line in two cases : if you have a static quenching mechanism or a dynamic quenching mechanism. In your case a static quenching is the more probable. You will not get a straight line if both mechanisms act together. Indeed there is non more a linearity between concentrations and signals.

Can I use Stern - Volmer equation to fit the Fluorescence quenching response (FQR) vs gas partial pressure instead of FQR vs solution concentration?

I don't see why not. Gas partial pressure is equivalent to concentration.

You can refer the following literature if u have further difficulties.

https://www.ncbi.nlm.nih.gov/m/pubmed/28441541/

https://www.researchgate.net/publication/318896704_Molecular_interaction_between_human_serum_albumin_HSA_and_phloroglucinol_derivative_that_show_selective_anti-proliferative_potential