Question

a. identify which apparatus pictured below shows a trapped gas sample with pressure greater than atmospheric pressure and which shows a trapped gas sample with pressure less than atmospheric pressure. then briefly explain how (and why) you can tell whether the pressure of the trapped gas is greater than or less than atmospheric pressure.
b. given that atmospheric pressure is 760.2 mm hg, calculate the total gas pressure inside the tube pictured at right, with the water level inside the tube 15.3 cm above the surrounding water.
c. given that atmospheric pressure is 760.2 mm hg, calculate the total gas pressure inside the tube pictured at right, with the water level inside the tube 7.5 cm below the surrounding water.

Explanation:

Step1: Convert height of water column to equivalent mercury column height

The density of mercury (\(d_{Hg} = 13.6\ g/cm^{3}\)) and density of water (\(d_{water}=1\ g/cm^{3}\)). Using the formula \(P = h\times d\times g\) (since \(g\) is constant, \(h_{Hg}=\frac{h_{water}\times d_{water}}{d_{Hg}}\)).
For part b: \(h_{water}=15.3\ cm = 153\ mm\), \(h_{Hg}=\frac{153\ mm\times1}{13.6}\approx11.25\ mm\)
For part c: \(h_{water}=7.5\ cm = 75\ mm\), \(h_{Hg}=\frac{75\ mm\times1}{13.6}\approx5.51\ mm\)

Step2: Calculate gas pressure

The relationship between gas pressure (\(P_{gas}\)), atmospheric pressure (\(P_{atm}\)) and the pressure due to the liquid column (\(P_{liquid}\)) is:

• If the liquid level is higher inside the tube (gas pressure is less than atmospheric pressure): \(P_{gas}=P_{atm}-P_{liquid}\)
• If the liquid level is lower inside the tube (gas pressure is greater than atmospheric pressure): \(P_{gas}=P_{atm}+P_{liquid}\)

For part b: \(P_{atm} = 760.2\ mm\ Hg\), \(P_{gas}=760.2\ mm\ Hg - 11.25\ mm\ Hg=748.95\ mm\ Hg\)
For part c: \(P_{gas}=760.2\ mm\ Hg+ \frac{75}{13.6}\ mm\ Hg\approx760.2 + 5.51=765.71\ mm\ Hg\)

Answer:

b. \(748.95\ mm\ Hg\)
c. \(765.71\ mm\ Hg\)