An easy approach for reading manometers to determine gas pressure

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RON DELORENZO Middle Georgia College Cochran, Georgia 31014

An Easy Approach for Reading Manometers to Determine 6as Pressure: The Analogy of the Child's Seesaw Ira Batra Garde The Phillips Exeter Academy Exeter. NH 03833

While studying ideal gases, a discussion of pressure and its measurement is in order. The text I am using in introductory chemistry devotes several pages to the instruments used to measure pressure, including open-ended and closed-ended manometers. The hook's discussion of how to read manometers is somewhat difficult to follow. I used the simple analogy of a child's seesaw, which for my students eliminated confusion on how to read manometers, hoth open-ended and closed-ended. This analogy works a t hoth the qualitative and quantitative levels. All children, one would hope, have played on seesaws. Children know from this experience that the end of the plank supporting the heavier child is pushed downwards, while the lighter child offers little resistance and is wafted high up into the air (see Fig. 1). In the case of an open-ended manometer, atmospheric pressurt, represents o w child, and the gas whose presiure is tu he measured rwresenrs the other child. 'I'hr two tops uf the mercury colunh represent the seats on the seesaw. If the gas pressure equals atmospheric pressure, then the tops of the mercury column will he at the same level (see Fig. 2).

796

Journal of Chemical Education

Figure 1. The child's seesaw

,

... .

"CHILD = GdS

Figure 2. Openended manometer ( P

= Patmsm) Q=:

"CMLD" = A M $ -

If the eas nressure is ereater than atmos~hericpressure, then t h e i a s is the "heavyer chi1d"and atmospheri&ressure can he renresented hv the "linhter child". The mercury level side will settle a c a level below the level bf the on the mercury on the side of the atmosphere. The difference, in millimeters, between the two levels of mercury represents the amount by which the gas' pressure isgreater than atmospheric pressure. So the difference (A mmHg) is added to the atmospheric pressure t o obtain the pressure of the gas, "the heavier child" (see Fig. 3). Likewise, if the mercury levels settle in such a way that the levelon the gas side is higher than the level of mercury on the side of the atmosphere, the gas must he the "lighter child" since he or she is wafted unwards due to the nreater weight of his or her playmate, the airnosphere. In thiscase, the &fference in mercury levels (A m m H d must be subtracted from atmospheric pr&sure in order obtain a smaller pressure for the gas (see Fig. 4).

Figure 3. opewended manometer (Pas > P-M)

.. "KAVB1 CHILD' =

Figure 4. Openended manometer (P,,

< Pd,,-).

Thus, this simple analogy helps the student to quickly assess whether to add or tosubtract the difference inmercury levels to the atmospheric pressure in order to obtain the pressure of the gas. The decision is based on whether the gas is "heavier" or "lighter" than the atmosphere, an assessment which is easy to make visually if one has the seesaw analogy in mind. I t is important to point out that with an open-ended manometer one can only determine the 'pressure of the gas of interest relative to atmospheric pressure. The actual value of atmospheric pressure must be determined independently using a Toricellian barometer, which, in fact, also works by measuring a pressure difference, the difference between the atmosphere and a vacuum. In the case of a closed-ended manometer, the gas whose pressure is being measured is the only child on the seesaw. His or her absent playmate is represented by a vacuum. Therefore, the mercury level on the side of the gas is always lower than the mercury level on the side of the vacuum. Since the gas is always the "heavier child", the difference in mercury levels (A mmHg) represents the amount by which the gas pressure is greater than the pressure exerted by the vacuum. Since the pressure exerted by the vacuum is esseutially zero, the difference in mercury levels represents the pressure exerted by the gas (see Fig. 5). The seesaw analogy was well received by my students. The analogy contributes in an important way to the discussion of gases because it gives the student a sense that particles with weight are present in the "empty space" ahove the mercury columns. Indeed, the students conclude that there must be more than "empty space" above the mercury columns if this analogy can he used. Also important is the fact that the analogy has both qualitative and quantitative applications. I t assists in the intuitive appreciation of whether the gas pressure of interest is more or less than the reference pressure. This qualitative comprehension naturally aids the students in the quantitative decision of whether to add the difference in mercury levels to the reference pressure or to subtract the difference (A mmHg) from the reference pressure. In addition, the analogy triggers memories of more carefree days. Also, talking about lighter and heavier children touches apoint of concern to many adolescents, and the connection with body weight therefore serves to rivet their attention. After using this analogy in class, I included the following question on my exam covering the Ideal Gas Laws. The atmos~hericDressure is 783 mmHe. The eas side of an open-endedmanometer ha* a mercwy Ie\el ~ h i r his b mm h h r w thr mercury level un theupen.ended a~deafthemanometbr. What is the pressure of the gas?

The circumstances described are the same as those represented in Figure 3. The gas is the "heavier child" relative to the atmosphere, and it is heavier by the difference between the two mercury levels, (A mmHg = 5 mmHg). Therefore,

+

P,, = Patmoapher. 5 mmHg = 788 mmHg

Figure 5. Closed-ended manometer

Twenty-two of my 24 students answered the question completely correctly. Many drew accurate diagrams to help themselves visualize the situation described in the auestion, a response that supports the visual strength of thisanalogy: The two students who were not com~letelvcorrect showed they understood how to read manometers but made emharrassing arithmetic errors.

Volume 63

Number 9

September 1986

797