Question

A sample of gas at 398 K occupies a volume of 3 L
at a pressure of 0.867 x 100000Pa. Calculate its volume
at 100 kPa atmospheric pressure.

please answer it​

Answer 1

$\sf \bold {Given\::}$

$\bullet$ initial temperature = final temperature = 398K

$\bullet$ initial number of mole = final numbers of mole

$\bullet$ initial volume = $\sf V_{1}$ = 3L

$\bullet$ initial pressure = $\sf P_{1}$ = 0.867×100000 Pa = 0.867×10⁵Pa

$\bullet$ final pressure = $\sf P_{2}$ = 100kPa = 100000 Pa = 10⁵Pa

$\sf \bold {To\:find\::}$

$\bullet$ final volume = $\sf V_{2}$ =

$\sf \bold {Formula\:used\::}$

$\bullet$ PV = nRT

$\sf \bold {Solution\::}$

as number of mole & temperature remain constant

PV = nRT , can be written as PV = constant

Therefore, $\sf P_{1}$ × $\sf V_{1}$ = $\sf P_{2}$ × $\sf V_{2}$

Putting respective values, in above equation

We get ;

$\implies$ (0.867×10⁵) × (3) = (10⁵) × ($\sf V_{2}$)

$\implies$$\sf V_{2}$ = (0.867 ×3) × (10⁵÷10⁵)

$\implies$$\sf V_{2}$ = 2.601 L

$\sf \bold {ANSWER\::}$ final volume = $\sf \bold {2.601 L\::}$