Density of a gas is found to be `5.46//dm^(3)` at `27^(@)C` at 2 bar pressure What will be its density at `STP` ? .

Explanation

We know that density `(rho)` of a gas `prop = (1)/("Volume")`
`:. rho_(1) prop 1//V_(1)` and `rho_(2) prop 1//V_(2)`. Also `(rho_(1))/(rho_(2)) = (V_(2))/(V_(1))`
According to combined gas law.
`(P_(1)V_(1))/(T_(1)) = (P_(2)V_(2))/(T_(1)) = (P_(1)rho_(2))/(T_(1)) = (P_(2)rho_(1))/(T_(2))`
`(rho_(1))/(rho_(2)) = (P_(1)T_(2))/(P_(2)T_(1))` or `rho_(2) = (rho_(1)P_(2)T_(1))/(P_(1)T_(2))`
According to available data :
`rho_(1) = 5.46 g//dm^(3), T_(1) = 27 + 273 = 300 K , P_(1) = 2 "bar"`
`rho_(2) = ? , T_(2) = 0+273 = 273 K, P_(2) = 1.01325 "bar"`
`:. rho_(2) = ((5.46 g//dm^(3)) xx (300 K) xx (1.01325 "bar"))/((2 "bar") xx (273 K)) = 3.04 g//dm^(3)`