A flask containing helium gas is connected to an open-ended mercury manometer. The open end is exposed to the atmosphere, where the prevailing pressure is 752 torr. The mercury level in the open arm is 26 mm above that in the arm connected to the flask of helium. What is the helium pressure, in torr?

Question

Quizplus · Accepted Answer

In a mercury manometer, the pressure difference between the two arms is given by the difference in height of the mercury levels. The pressure due to atmospheric pressure acting on the open end is cancelled out because the same pressure acts on both arms.

Let the height of the mercury level in the arm connected to the flask of helium be h1. Then, the pressure of the helium gas is given by:

PHe = Patm + ρgh1

where Patm is the atmospheric pressure, ρ is the density of mercury (13.6 g/cm3), g is the acceleration due to gravity (9.8 m/s2), and h1 is the height difference between the two mercury levels.

Converting the units to torr and plugging in the given values, we get:

PHe = 752 + (13.6 g/cm3) × (26 mm) × (1 cm/10 mm) × (1 m/100 cm) × (1 atm/760 torr) × (101325 Pa/atm) ≈ 778 torr

Therefore, the answer is D) 778 torr.

A Flask Containing Helium Gas Is Connected to an Open-Ended