  The atmospheric metallicity greatly influences the composition of exoplanet
atmospheres. The effect of metallicity on the thermochemical equilibrium is
well studied, though its effect on the disequilibrium abundance is loosely
constrained. In this study, we have used the quenching approximation to study
the effect of metallicity on the quenched abundance for a range of parameters
(temperature: 500-2500 K, pressure: 10$^{-4}$-10$^3$ bar, metallicity: 0.1-1000
$\times$ solar metallicity). We determine the chemical timescale by finding
rate limiting steps in a reduced chemical network with a network analysis tool
and the thermochemical equilibrium abundance. The equilibrium abundance results
are similar to the literature. The CO, H$_2$O, and CO$_2$ abundances increase
with metallicity in the parameter range considered. The CH$_4$ abundance
increases with metallicity for CO/CH$_4$ $<$ 1 and is unaffected for CO/CH$_4$
$>$ 1. The chemical timescale of CO shows minimal change with the metallicity,
while the CH$_4$ chemical timescale is inversely proportional to atmospheric
metallicity. The quench level of CO shifts into the high-pressure region, and
the quench level of CH$_4$ shows complex behavior with metallicity. We
benchmarked the quenching approximation with the 1D photochemistry-transport
model for two test exoplanets (GJ 1214 b and HD 189733 b) and found it to be in
good agreement. We also found that the quenching approximation is a powerful
tool to constrain atmospheric parameters. We demonstrated this by constraining
the metallicity and transport strength for the test exoplanets HR 8799 b, HD
189733 b, GJ 436 b, and WASP-39 b.
