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

Answer:

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

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:            $\frac{P_{1}V_{1}}{T_{1}}=\frac{P_{2}V_{2}}{T_{2}}$

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 $T_{2}=\frac{P_{2}T_{1}}{P_{1}}=\frac{(1.125atm)\times (300K)}{(0.625atm)}=540K$

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

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