Question

Question 5.9 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?

Class XI States of Matter Page 153

Answer 1

concept :- we know,
$d=\frac{PM}{RT}\\\\d\:\:\:\alpha\frac{P}{T}$
for same gas at different temperature and pressure .
$\frac{d_2}{d_1}=\frac{P_2T_1}{P_1T_2}$
STP means gas at 1 bar pressure and 273K temperature.

here, d1 = 5.46 g/dm³ , d2 = ?
T1 = 27°C or 300K , T2 = 0°C or 273K
P1 = 2bar and P2 = 1 bar

d2 = d1.P2.T1/P1.T2
= 1 × 300 × 5.46/2 × 273
= 3 g/dm³

Answer 2

Answer: $3.0gdm^{-3}$

Explanation:-

$d=\frac{PM}{RT}$

d= density

M= molar mass

R= constant

T= temperature

For same gas at different temperature and pressure:

$\frac{d_2}{d_1}=\frac{P_2T_1}{P_1T_2}$

STP means gas is at 1 bar pressure and 273 K temperature.

$d_1=5.46 gdm^{-3}$

$d_2$= ?

$T_1=27^0C=27+273=300K$  

$T_2= 0^0C=0+273=273K$

$P_1 = 2bar$ and $P_2=1 bar$  

$d_2=d_1\times {\frac{P_2T_1}{P_1T_2}$

$d_2=5.46\times {\frac{1\times 300}{2\times 273}$

$d_2= 3gdm^{-3}$