Question

A cylinder contains nitrogen gas and a small amount of liquid water at a temperature of 25ºC (the vapour pressure of water is 23.8 mm Hg). The total pressure is 600 mm Hg. A piston is pushed into the cylinder until the volume is halved. What is the final total pressure?

Answer 1

According to the Dalton's law, the total pressure in the cylinder is the sum of the pressure of the nitrogen and the water vapour.

${ P }_{ total }\quad =\quad { P }_{ { N }_{ 2 } }\quad +\quad { P }_{ { H }_{ 2 }O }$

From the given,  

Total pressure = 600

${ P }_{ { H }_{ 2 }O }$ = 23.8

Substitute the given values 600 = ${ P }_{ { N }_{ 2 } }$+ 23.8

${ P }_{ { N }_{ 2 } }$ = 576.2 mmHg

According to the Boyle's law pressure of nitrogen will be doubled.

Therefore,

${ P }_{ { N }_{ 2 } }\quad =\quad 2\quad \times \quad 576.2\\\\ { P }_{ { N }_{ 2 } }\quad =\quad 1152.4\quad mmHg$

Total pressure = 1152.4 + 23.8

Total pressure = 1176.2 mmHg