What percent of a sample of nitrogen must be allowed to escape if its temperature, pressure, and volume are to be changed from `220^(@)C`, `3 atm`, and `1.65 L` to `110^(@)C`, `0.7 atm`, and `1 L`, respectively?

Options

A. `41.4%`
B. `8.18%`
C. `4.14%`
D. `81.8%`

Explanation

Let `P_(1)=3 atm`, `T_(1)=220+273=493 K`,`V_(1)=1.65 L`
`P_(2)=0.7 atm`, `T_(2)=110+273=383 K`, `V_(2)=1 L`
Using the gas `PV=nRT` equation , we get
`n_(1)=(P_(1)V_(1))/(RT_(1))` and `n_(2)=(P_(2)V_(2))/(RT_(2))`
Thus, fraction remaining is
`(n_(2))/(n_(1))=(P_(2)V_(2))/(RT_(2))xx(RT_(1))/(P_(1)V_(1))=(0.7xx1)/(Rxx383)xx(Rxx493)/(3xx1.65)=0.182`
Fraction escaped `=1-0.182=0.818`
Percentage escaped `=0.818xx100=81.8%`
So the correct choice is (`d`).