Question

To what temperature must a sample of nitrogen at 27°C and 0.625 atm be taken so that it’s pressure becomes 1.125 atm at constant volume?

Answer 1

The sample of nitrogen must be taken to 267
`^(0)\textrm{C}`.

Step-by-step explanation:

Let's assume nitrogen gas behaves ideally.

Here amount of nitrogen gas in both states remain constant.

So, in accordance with combined gas law for a given amount of an ideal gas in two different states:
`(P_(1)V_(1))/(T_(1))=(P_(2)V_(2))/(T_(2))`

where
`P_(1)` and
`P_(2)` are initial and final pressure respectively.
`V_(1)` and
`V_(2)` are initial and final volume respectively.
`T_(1)` and
`T_(2)` are initial and final temperature (in kelvin scale) respectively.

Here
`V_(1)=V_(2)` ,
`P_(1)=0.625atm` ,
`T_(1)=(273+27)K=300K` and
`P_(2)=1.125atm`

So
`T_(2)=(P_(2)T_(1))/(P_(1))=((1.125atm)* (300K))/((0.625atm))=540K`

540 K = (540-273)
`^(0)\textrm{C}` = 267
`^(0)\textrm{C}`

So the sample of nitrogen must be taken to 267
`^(0)\textrm{C}`.