Question

A mercury manometer is used to measure pressure in the container illustrated. Calculate the pressure exerted by the gas if atmospheric pressure is 751 torr and the distance labeled is 176 mm.

Answer 1

Answer:

Pressure exerted by the gas is 574.85 torr

Explanation:

Atmospheric pressure = 751 torr

but 1 torr = 1 mmHg

therefore,

atmospheric pressure = 751 mmHg

1 mmHg = 133.3 Pa

therefore,

atmospheric pressure = 751 x 133.3 = 100108.3 Pa

distance labeled (tube section with mercury) = 176 mm

the pressure within the tube will be

$P_{tube}$ = ρgh

where ρ is the density of mercury = 13600 kg/m^3

h is the labeled distance = 176 mm = 0.176 m

g is acceleration due to gravity = 9.81 m/s^2

$P_{tube}$  = 13600 x 9.81 x 0.176 = 23481.216 Pa

The general equation for the pressure in the manometer will be

$P_{atm}$ = $P_{tube}$ + $P_{gas}$

where $P_{atm}$  is the atmospheric pressure

$P_{tube}$  is the pressure within the tube with mercury

$P_{gas}$ is the pressure of the gas

substituting, we have

100108.3 = 23481.216 + $P_{gas}$

$P_{gas}$ = 100108.3 - 23481.216 = 76627.1 Pa

This pressure can be stated in mmHg as

76627.1 /133.3 = 574.85 mmHg

and also equal to 574.85 torr