Mass Units

Kilogram

The kilogram (kg) is the SI base unit of mass (m). A kilogram was originally defined as being the mass of one litre of water. The more modern version of this definition agrees with this original definition within 30 parts per million [1].

A good way to visualize kilograms is to look at it in terms of water. Since litres can be considered in terms of metres cubed, kilograms of water can be compared to litres or metres cubed to better visualize quantity. For example, 1000 kilograms of water would fit in a 1 metre cubed volume or 1 kilogram of water would fit in a 0.001 metre cubed volume. Now consider an Olympic size swimming pool, about 25 metres by 50 metres, that has a depth of 0.8 metres. That volume, which is equal to 1000 metres cubed, would hold 1,000,000 kilograms of water [2].

[3]

Since the kilogram already has a prefix as part of its name, SI prefixes are concatenated with the unit gram instead. For instance, one-millionth of a kilogram is 1 milligram, not 1 microgram. The kilogram is a widely used measurement in science, engineering and commerce world wide [1].

Kilogram per Cubic Metre

The kilogram per cubic metre (kg/m³) is a SI derived unit used for measuring density (ρ). The kilogram per cubic metre is already written in SI base units [4].

Given that density is a ratio of mass to volume, the quantitative value of kilograms per cubic metre will be constant for a material in constant pressure and temperature no matter how much of the material there is [5]. An example of this would be iron. The density of iron, near room temperature and at atmospheric pressure, is about 7874 kg/m³ [6]. Another example would be copper which, under the same conditions, has a density of 8960 kg/m³ [6].

Mole

The mole is a SI base unit of amount of substance. One mole is define as being 6.022·10²³ particles, which can be atoms, molecules, ions or electrons [7].

The mole is used in chemistry as a way to conveniently express amounts of reactants and products in chemical reactions. As an example, the chemical equation 2H₂+O₂ → 2H₂O can be interpreted to mean that for 2 mol of dihydrogen and 1 mol dioxygen, 2 mols of water will form [7].

Mole per Cubic Metre

The mole per cubic metre is a SI derived unit for measuring amount-of-substance concentration. It expresses the number of atoms of a substance per unit of volume [8].

Since one mole is approximately 6.022·10²³, 1 mol/m³ represents 6.022·10²³ atoms of substance in one cubic metre of space [8].

References

[1] “Kilogram,” Wikipedia, 06-Aug-2021. [Online]. Available: https://en.wikipedia.org/wiki/Kilogram. [Accessed: 11-Aug-2021].

[2] “How to visualise a 1 million kg? What on earth is this heavy,” Quora. [Online]. Available: https://www.quora.com/How-do-I-visualise-a-1-million-kg-What-on-Earth-is-this-heavy. [Accessed: 11-Aug-2021].

[3] L. H. Taylor, “How big is an olympic-size pool?,” LiveAbout. [Online]. Available: https://www.liveabout.com/how-big-is-olympic-size-pool-2737098. [Accessed: 11-Aug-2021].

[4] “Kilogram per cubic metre,” Wikipedia, 17-Mar-2020. [Online]. Available: https://en.wikipedia.org/wiki/Kilogram_per_cubic_metre. [Accessed: 13-Aug-2021].

[5] “Density,” Wikipedia, 11-Jul-2021. [Online]. Available: https://en.wikipedia.org/wiki/Density. [Accessed: 13-Aug-2021].

[6] “Density of ELEMENTS CHART,” Density of Elements Chart – Angstrom Sciences Elements Density Table. [Online]. Available: https://www.angstromsciences.com/density-elements-chart. [Accessed: 13-Aug-2021].

[7] “Mole (unit),” Wikipedia, 28-Jun-2021. [Online]. Available: https://en.wikipedia.org/wiki/Mole_(unit). [Accessed: 13-Aug-2021].

[8] T. T. Contributor, “What is mole per meter cubed (avogadro constant)? - definition from whatis.com,” WhatIs.com, 24-Mar-2011. [Online]. Available: https://whatis.techtarget.com/definition/mole-per-meter-cubed-Avogadro-constant. [Accessed: 13-Aug-2021].