Question

A sample of sulfur dioxide occupies a volume of 561 mL at 48° C and 792 mm Hg. What volume will the sulfur dioxide occupy in ml at 4° C and 1 atm? Round to the nearest two decimal places.

Answer 1

There are two stages of the gas:

At first stage

$V_1=561 ml$

$P_1=792 mmHg$

$T_1=48^o C= 321K$

At second stage:

$P_2=1atm=760mmHg$

$T_2=4^o C=277 K$

$V_2=V_2(let)$

Here we use Ideal gas eqn

PV=nRT

n=$\dfrac{PV}{RT}$

In both the stages moles are constants, so

$\Rightarrow$ $n_1=n_2$

$\Rightarrow$ $\dfrac{P_1V_1}{RT_1}=\dfrac{P_2V_2}{RT_2}$

As R is constant both the sides,so

$\Rightarrow V_2=\dfrac{P_1V_1T_2}{T_1P_2}$

$\Rightarrow V_2=\dfrac{792\times561\times277}{321\times760}=$ 504.49 ml