Gas (Helium) Pycnometer Theory and Practice PDF

IOI lnstruQuest, Inc. January. 2019 Gas (Helium) Pycnometer Theory and Practice By Jan Malczyk Gas (helium) pycno...

IOI lnstruQuest, Inc. January. 2019 Gas (Helium) Pycnometer Theory and Practice By Jan Malczyk Gas (helium) pycnometer is a laboratory or lield instrument that measures volume (density) of materials using gas displacement method by employing the ideal gas law, pV = nRT. The basic operation relics on having a user accessible sample chamber, and an added volume (referenc e chamber). otlen more then one. There are usually al least three valves used: the first (VI) to provid~ gas to the sample chamber. the second (V2) to allow expansion of the gas from sample to reference chamber, and the third (V3) to release the gas to atmosphere to establish atmospheric pressure Pa value. Pressure Transducer V1 V2 Gas In Ve Vr Sample Reference Chamber Chamber Simolilied flow diaeram of a eas ovcnometer desien The typical pycnometer operation consists of three steps: I. Opening the VI valve. pressurization of sample chamber to the pressure Pp, and closing VI valve. 2. Expansion of the gas to the reference chamber by opening valve V2 (V3 and VI stay closed). Alter the depressurization. the same pressure Pd will be in both chambers, Ve and Yr. 3. Rekase of gas 10 the atmosphere by opening valves V3 and V2. The transducer will read the atmospheric pressure. Pa. The underlying theory will be easier to understand by placing an object into the sample chamber and writing the mass balance equations, as the amount of gas in the first step must be equal to the amount of gas in step 2, obviously assuming no additional sources or leaks. Step1 Step2 V2. Vc-Vobj Vr Vc-Vobj Vr  + Yr) Pp(Vc- Yobj) Pa Yr Pd(Yc- Yobj~- ()) -'- --- -'- +- -= --- --= - RT RT RT er volume h) (number of moles) in the redw.:ed sample chamb The equation I states. that the amount of gas pressu re in the Vr volume muS t amount or gas al atmospheric the object volume at the pressure Pp and the.. after expansion to the pressure Pd. be equal to the amount of gas in both chambers trivial of tempe rature during the experiment. the sought Vobj volume. after Assuming turthcr constancy manipulations, can be calculated as follows: u b' u Vr(P d-Pa ) (2) YO'/) = yC- Pp- Pd using an yed by the gas ·expansion pycnomcter. When The equation (2) is the working equation emplo pressu re value of IO 1.32_5 is around the standard atmospheric absolute pressure transducer. the Pa pressure ucer (rclercnced to zero at atmosp~enc pressure transd kPa. When a pycnometcr uses a gauge type re values from It is important to remember. that the pressu pressure). then the Pa value is set to zero. gauge pressure transd ucers or pressure the pressu re values or absolute pressure transducers are higher then gauges by IO 1.325 kPa. ined first. Since and Vr must be known and need to be determ In order to obtain the Vobj from eq. 2, the Ve d. Typic ally, one exper iment is conducted iments are neede then: are two unknowns, two independent exper vs Vr: the above equation yields relationship of Ve with empty Ve. Since the Vobj = 0 in this case, (3) e Vsphere. is volume, typically a calibrated sphere of volum In the second experiment, an object of known becom es: used. The equation (2) for the second experiment Pd- 2 Pa 2 (4) Vsphere =Ye -Yr P2 p-P2d allows calculation of Vr: Solving the system of two equations (3) and (4) Yr= Ysphere (5) P1d - P,a P2d - P2a P1p- P1d P2 p- P2d Vr values into (3) yields the Ve value. Plugging the Ve and Substituting the found Vr value into equation e Vobj. the sought o~ject volum the working equation (2) allows calculation of be easily calculated using the density Knowing the object mass, m, its density, d, can definition d = m/Vobj [mass/volume). to solve. The this simple theory, here is an easy problem In case you think that you have understood l repetitions of the basic cycles where each consists of severa diagram below shows two hypothetical runs, measu red pressu re values are presented to atmos phere). The (pressurization, expansion, and releasing gas e and which is explanation) which run is done with the sampl as red and green circles. Can you tell (with s the same? ing everything else remain without the sample in the sample chamber, assum 2