Ideal Gas Equation

The correct option is(A): $1.5%5Ctimes%2010%5E%7B5%7D%20%5C%2C%20Pa$ .

From ideal gas law For container $A%2C%20n_%7B1%7D%3D%5Cfrac%7Bp_%7B1%7D%20V_%7B1%7D%7D%7BR%20T_%7B1%7D%7D$
For container $B$ , $n_%7B2%7D%3D%5Cfrac%7Bp_%7B2%7D%20V_%7B2%7D%7D%7BR%20T_%7B2%7D%7D$
After opening the value, $x$ moles of gas stream from container $A$ to container $B$ such that both container equalize at pressure $p$ .
Number of moles in container $A$ has changed to $n_%7B1%7D-x$ ,
i.e., $%5Cleft(n_%7B1%7D-x%5Cright)%3D%5Cfrac%7Bp%20%5Ccdot%20V_%7B1%7D%7D%7BR%20%5Ccdot%20T_%7B1%7D%7D$
$%5Ctherefore%20x%3Dn_%7B1%7D%3D%5Cfrac%7Bp%20%5Ccdot%20V_%7B1%7D%7D%7BR%20%5Ccdot%20T_%7B1%7D%7D%3D%5Cfrac%7B%5Cleft(p_%7B1%7D-p%5Cright)%20%5Ccdot%20V_%7B1%7D%7D%7BR%20%5Ccdot%20T_%7B1%7D%7D%20...$ (i)
Number of moles in container $6$ has changed to $n_%7B2%7D%2Bx$ ,
therefore $%5Cleft(n_%7B2%7D%2Bx%5Cright)%3D%5Cfrac%7Bp_%7B2%7D%20%5Ccdot%20V_%7B2%7D%7D%7BR%20%5Ccdot%20T_%7B2%7D%7D$
$%5Ctherefore%20x%3D%5Cfrac%7Bp%20%5Ccdot%20V_%7B2%7D%7D%7BR%20%5Ccdot%20T_%7B2%7D%7D-n_%7B2%7D%3D%5Cfrac%7B%5Cleft(p-p_%7Bz%7D%5Cright)%20V_%7B2%7D%7D%7BR%20%5Ccdot%20T_%7B2%7D%7D%20%5Cldots%20.%20.$ (ii)
Equating Eqs (i) and (ii), we get
$%5Cfrac%7B%5Cleft(p_%7B1%7D-p%5Cright)%20%5Ccdot%20V_%7B1%7D%7D%7BR%20%5Ccdot%20T_%7B1%7D%7D%3D%5Cfrac%7B%5Cleft(p-p_%7B2%7D%5Cright)%20%5Ccdot%20V_%7B2%7D%7D%7BR%20%5Ccdot%20T_%7B2%7D%7D$
$%5CRightarrow$ $%5Cleft(p_%7B1%7D-p%5Cright)%3D%5Cleft(p-p_%7B2%7D%5Cright)%20%5Ccdot%5Cleft(%5Cfrac%7BV_%7B2%7D%7D%7BV_%7B1%7D%7D%5Cright)%20%5Ccdot%5Cleft(%5Cfrac%7BT_%7B1%7D%7D%7BT_%7B2%7D%7D%5Cright)$
The pressure changes in the two containers are proportional
$%5Cleft(p_%7B1%7D-p%5Cright)%3D%5Cleft(p-p_%7B2%7D%5Cright)%20.%20K$
with $K%3D%5Cleft(%5Cfrac%7BV_%7B2%7D%7D%7BV_%7B1%7D%7D%5Cright)%20%5Ccdot%5Cleft(%5Cfrac%7BT_%7B1%7D%7D%7BT_%7B2%7D%7D%5Cright)$
$%3D4%5Cleft(%5Cfrac%7B300%7D%7B400%7D%5Cright)%3D3$
$p%3D%5Cfrac%7Bp_%7B1%7D%2Bp_%7B2%7D%20%5Ccdot%20K%7D%7B1%2BK%7D%3D%5Cfrac%7B5%20%5Ctimes%2010%5E%7B5%7D%2B1%20%5Ctimes%2010%5E%7B5%7D%7D%7B1%2B3%7D$
$%3D%5Cfrac%7B6%20%5Ctimes%2010%5E%7B5%7D%7D%7B4%7D%3D1.5%20%5Ctimes%2010%5E%7B5%7D%20Pa$

High-Yield Trend

Chapter Questions
1 MCQs

Official Solution

Ideal Gas Equation

High-Yield Trend

Chapter Questions 1 MCQs

Official Solution

Chapter Questions
1 MCQs