# Introduction

One way to solve what substance has been created in a laboratory is to measure its density. Object's density is its weight divided by its volume. Weight of the substance is relatively easy to measure when compared to the measurement of volume. The problem with volume measurement is that object or substance isn't usually in a form of a regular shape but as a deformerd object or as a powder. Using classical method such as water diplacement isn't usually good enough since water could interact and become stuck on the sample surface.  Gas pycnometry solves this by utilizing an inert gas and Boyle's gas law. This article will describe basic theory of Boyle's gas law and a simple pycnometer setup.

# Boyles's law

Boyle's law (or Boyle-Mariotte law) states that if temperature and the amount of gas remain constant then pressure multiplied by volume remains constant. This is described with the following equation.

$PV=k$

Since pressure multiplied by volume remains constant, different conditions with differing pressure and volume can be compared using following equation.

$P_1V_1 = P_2V_2$

# Determining the volume of a sample using Boyle's law

Using two conjoined chambers (A and B) and inert gas the volume of a sample can be determinated using Boyle's law.

$P_1(V_1-V_S) = P_2(V_2-V_S)$ $V_S=\frac{P_2V_2-P_1V_1}{P_2-P_1}$

In which

Pis pressure inside chamber A

Pis pressure inside chamber A+B

V1 is volume of Chamber A

Vis volume of chamber A+B

VS is volume of the sample.

# Gas pycnometer

A gas pycnometer consists of two chambers, a sample chamber A and expansion chamber B (Figure 1). Chambers are joined to a gas source and vacuum source. Before pretreatment dry sample is placed inside chamber A. During sample's pretreatment the gas chamber A  is flushed with a inert gas, usually helium. Flushing removes any air particles stuck on the sample's surface or on pores. The flushing is done 2-3 times. After pretreatment is over, measurement phase 1 begins. Figure 1. Schematic illustration of gas pycnometer setup. (Figure: Erkka Koskenniemi)

## Measurement Phase 1

In phase 1, chamber A is filled with inert gas and Chamber B is emptied using vacuum (Figure 2). The pressure of the chamber A is measured. Figure 2.  Phase 1: Chamber A is filled with gas. (Figure: Erkka Koskenniemi)

## Measurement Phase 2

In Phase 2, the valve between chambers A and B is opened which allows gas inside chamber A to flow to Chamber B (Figure 3). The combined pressure of chambers A+B is measured. After measurements are done, the volume of the sample is calculated using Boyle's gas law. Some gas pycnometers do not use two chambers. Instead they use a chamber which volume can be altered in order to get two different conditions that are necessary for the calculations. Figure 3. Phase 2: Gas is let into chamber B. (Figure: Erkka Koskenniemi)

# References

  1 C. L. Bielders, L. W. De Backer. B. Delvaux, Particle Density of Volcanic Soils Measured with a Gas Pycnometer, Soil Science Society of America Journal, 1990, 54, 822-826 (https://doi.org/10.2136/sssaj1990.03615995005400030034x)  1 2 S. Tamari, A. Aguilar-Chavez. Optimum Design of Gas Pycnometers for Determining the Volume of Solid Particles, Journal of Testing and Evaluation, 2005, 33, 135-138 (https://doi.org/10.1520/JTE12674)  1 H. T. Nguyen, J.C Horn, M.Bleakney, D. W. Siderius, L Espinal, Langmuir, Understanding Material Characteristics through Signature Traits from Helium Pycnometry, 2019, 35 2115-2122. (https://pubs.acs.org/doi/10.1021/acs.langmuir.8b03731)  1 L. E. Flint, A.L. Flint, Methods of soil analysis Part 4 Physical Methods, Soil Science Society of America, Michigan, 2002 (https://doi.org/10.2136/sssabookser5.4.c11)

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