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

Explanation

` d_1 = 5.46 gm // dm^3`
`T_1 = 27^@ C = 300 K `
`P_1 = 2 ` bar
` P_2 =1.013 ` bar (STP)
` T_2 = 273 K (STP)`
` d_2 =?`
We know that density d = `(P M)/(RT)`.
`d_1 = (P_1 M )/( RT_1) ,d_2 = (P_2 M)/( RT_2)`
` (d_1)/(d_2 ) = ((P_1 M )/( RT_1))/( (P_2 M )/(RT_2))= (P_1 T_1)/(P_2 T_1)`
`(d_1)/(d_2) = (P_1 T_2)/( P_2 T_1) `
` (5.46 )/( d_2) = ( 2 xx 273 )/( 1.013 xx 300 )`
` ( 5.46 )/( d_2) = ( 546 )/( 303.9 ) `
` d_2 = ( 303 .9 )/( 100 )`
` = 3.039 gm //dm^3`