Question

a sealed - tube manometer as shown below can be used to measure pressures below atmospheric pressure. the tube above the mercury is evacuated. when there is a vacuum in the flask, the mercury levels in both arms of the u - tube are equal. if a gaseous sample is introduced into the flask, the mercury levels are different. the difference h is a measure of the pressure of the gas inside the flask. if h is equal to 3.55 cm, calculate the pressure in the flask in torr, pascals, and atmospheres.

Explanation:

Step1: Convert height from cm to mm

Since \(1\ cm = 10\ mm\), for \(h = 3.55\ cm\), we have \(h=3.55\times10 = 35.5\ mm\). In a manometer with evacuated arm, the pressure of the gas \(P = h\) (in torr). So \(P = 35.5\ torr\).

Step2: Convert from torr to atm

We know that \(1\ atm=760\ torr\). Using the conversion factor \(P(\text{atm})=\frac{P(\text{torr})}{760}\). Substitute \(P = 35.5\ torr\) into the formula: \(P(\text{atm})=\frac{35.5}{760}\approx0.0467\ atm\).

Step3: Convert from torr to Pa

We know that \(1\ torr = 133.322\ Pa\). Using the conversion factor \(P(\text{Pa})=P(\text{torr})\times133.322\). Substitute \(P = 35.5\ torr\) into the formula: \(P(\text{Pa})=35.5\times133.322 = 4732.931\ Pa\approx4730\ Pa\).

Answer:

Pressure \(= 35.5\ torr\), Pressure \(= 4730\ Pa\), Pressure \(= 0.0467\ atm\)