#### Question

The density of a gas is found to be 5.46 g/dm^{3} at 27 °C at 2 bar pressure. What will be its density at STP?

#### Solution 1

Given

`d_1= 5.46 "g/dm"^3`

`p_1` = 2bar

`T_1 = 27 ^@C` = (27 + 273) K = 300 K

`p_2` = 1 bar`

`T_2` = 273 K

`d_2= ?`

The density (*d*_{2}) of the gas at STP can be calculated using the equation,

`d = (Mp)/(RT)`

`:. d_1/d_2 = ((Mp_1)/(RT_1))/((Mp_2)/(RT_2))`

`=> d_1/d_2 = (p_1T_2)/(p_2T_1)`

`=> d_2 = (p_2T_1d_1)/(p_1T_2)`

`= (1xx300 xx 5.46)/(2xx273)`

`= 3 gdm^(-3)`

Hence, the density of the gas at STP will be 3 g dm^{–3}.

#### Solution 2

`d = (MP)/(RT)` For the same gas at different temperature and pressure, `d_1/d_2 = P_1/T_1 xx T_2/P_2`

Here d_1 = 5.46 g `dm^(-3)`, `T_1 = 27^@C = 300 K`, `P_1= 2 "bar"`

At STP, `d_2 = ? `, `T_2 = 0 ^@C = 273 K`, `P_2` = 1 bar

`:. (5.46 g dm^(-3))/(d^2) = "2 bar"/(300 K) xx (273 K)/"1 bar"` or `d_2 = 3 gdm^(-3)`