Question

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.

Explanation:

Step1: Convert the height of water column to mm

Since \(1\ cm = 10\ mm\), then \(h = 15.3\ cm=153\ mm\)

Step2: Use the pressure - relation formula \(P_{gas}+P_{water}=P_{atm}\)

The pressure of water column \(P_{water}=
ho_{water}gh\), and the pressure of mercury column \(P_{Hg}=
ho_{Hg}gh\). The ratio of densities \(\frac{
ho_{water}}{
ho_{Hg}}=\frac{1}{13.6}\). So the pressure of \(153\ mm\) water column in terms of mercury is \(h_{Hg}=\frac{h_{water}}{13.6}\)

Substitute \(h_{water} = 153\ mm\) into the formula: \(h_{Hg}=\frac{153}{13.6}\ mm\approx11.25\ mm\)

Step3: Calculate the gas pressure

From \(P_{gas}+P_{water}=P_{atm}\), we can express \(P_{gas}=P_{atm}-P_{water}\) (in terms of \(Hg\)). Given \(P_{atm} = 760.2\ mm\ Hg\) and \(P_{water}\approx11.25\ mm\ Hg\)

\(P_{gas}=760.2 - 11.25=748.95\ mm\ Hg\)

Answer:

\(748.95\ mm\ Hg\)