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

Explanation

Let `rho_(1)=5.46 g dm^(-3)`, `P_(1)= 2"bar"`, `T_(1)=27^(@)C=300K`
At `STP`
`rho_(2)=?`
`P_(2)=1 "bar"`
`T_(2)=0^(@)C=273.15K`
Hence
`rho_(1)=(P_(1)M)/(RT_(1))`, `rho_(2)=(P_(2)M)/(RT_(2))`
or `(rho_(1))/(rho_(2))=(P_(1)T_(2))/(T_(1)P_(2))` or `rho_(2)=(rho_(1)T_(1)P_(2))/(P_(1)T_(2))`
Substituting the values, we have
`rho_(2)=(5.46xx300xx1)/(2xx273.15)=3.0 g dm^(-3)`
Hence, density of gas at `STP` is `3.0 g dm^(-3)`