Answer :
Answer:
The sample of nitrogen must be taken to 267 [tex]^{0}\textrm{C}[/tex].
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: [tex]\frac{P_{1}V_{1}}{T_{1}}=\frac{P_{2}V_{2}}{T_{2}}[/tex]
where [tex]P_{1}[/tex] and [tex]P_{2}[/tex] are initial and final pressure respectively. [tex]V_{1}[/tex] and [tex]V_{2}[/tex] are initial and final volume respectively. [tex]T_{1}[/tex] and [tex]T_{2}[/tex] are initial and final temperature (in kelvin scale) respectively.
Here [tex]V_{1}=V_{2}[/tex] , [tex]P_{1}=0.625atm[/tex] , [tex]T_{1}=(273+27)K=300K[/tex] and [tex]P_{2}=1.125atm[/tex]
So [tex]T_{2}=\frac{P_{2}T_{1}}{P_{1}}=\frac{(1.125atm)\times (300K)}{(0.625atm)}=540K[/tex]
540 K = (540-273) [tex]^{0}\textrm{C}[/tex] = 267 [tex]^{0}\textrm{C}[/tex]
So the sample of nitrogen must be taken to 267 [tex]^{0}\textrm{C}[/tex].