What Unit of Measurement Pertains to the Number of Microscopic Molecules in a Sample?

SI unit of amount of substance

"Nmol" redirects here. For the mathematical technique, meet Method of lines.

mole
Unit system	International organization of units (SI)
Unit of measurement of	Amount of substance
Symbol	mol

The mole, symbol mol, is the SI base of operations unit of amount of substance.^{[one] [ii] [3]} The quantity corporeality of substance is a mensurate of how many elementary entities of a given substance are in an object or sample. Depending on what the substance is, an unproblematic entity may be an cantlet, a molecule, an ion, an ion pair, or a subatomic particle such equally an electron. For example, if beaker A contains 10 moles of water (a chemic chemical compound) and chalice B contains 10 moles of mercury (a chemical element), they comprise equal amounts of substance and chalice B contains exactly 1 cantlet of mercury for each molecule of water in chalice A, despite the ii beakers containing different volumes and very different masses of liquid.

The mole is defined as exactly 6.022140 76 ×ten²³ elementary entities. This definition was adopted in Nov 2018 and came into force on the xx May 2019, superseding the previous definition of the mole every bit a number of elementary entities equal to that in 12 grams of carbon-12, the most common isotope of carbon. Because a dalton, a unit ordinarily used to measure diminutive mass, is exactly 1/12 of the mass of a carbon-12 atom, the definition of the mole in identify before 2019 entailed that the mass of one mole of a compound or element in grams was numerically equal to the boilerplate mass of i molecule or atom of the substance in daltons and that the number of daltons in a gram was equal to the number of elementary entities in a mole. Because the mass of a nucleon (i.e. a proton or neutron) is approximately 1 dalton and the nucleons is an atom's nucleus make up the overwhelming majority of its mass, the pre-2019 definition also entailed that the mass of i mole of a substance was roughly equivalent to the number of nucleons in one atom or molecule of that substance. For case, a water molecule formed from the near common isotope of oxygen and of hydrogen contains 10 protons and viii neutrons and has a full mass of 18.015 daltons, meaning a mole of water has a mass of eighteen.015 grams, while an atom of the only stable isotope of aureate contains 79 protons and 118 neutrons and has a mass of 196.96657 daltons, meaning a mole of gold has a mass of 196.96657 grams.

The number of elementary entities in ane mole is known as the Avogadro number. Prior to 2019, it could merely exist estimated based on experimental data. The value half-dozen.022140 76 ×10²³ was adopted based on the best estimates bachelor in 2018, allowing the new definition to very closely judge the earlier definition and avert the need to recalibrate measuring equipment or update published data tables.

The mole is widely used in chemistry as a convenient style to express amounts of reactants and products of chemical reactions. For case, the chemical equation 2H₂ + O_ii → 2H_iiO can be interpreted to mean that for each 2 mol dihydrogen (H₂) and ane mol dioxygen (O₂) that react, ii mol of water (H₂O) class. The mole may also exist used to mensurate the amount of atoms, ions, electrons, or other entities. The concentration of a solution is commonly expressed past its molarity, divers equally the amount of dissolved substance in mole(due south) per unit volume of solution, for which the unit typically used is moles per litre (mol/L), commonly abbreviated Thousand.

The term gram-molecule (grand mol) was formerly used for "mole of molecules",^[4] and gram-atom (g cantlet) for "mole of atoms". For instance, 1 mole of MgBr₂ is 1 gram-molecule of MgBr₂ but 3 gram-atoms of MgBr₂.^{[five] [six]}

Concepts [edit]

Nature of the particles [edit]

The mole is essentially a count of particles.^[vii] Usually the particles counted are chemically identical entities, individually distinct. For case, a solution may contain a certain number of dissolved molecules that are more than or less contained of each other. Still, in a solid the constituent particles are fixed and bound in a lattice arrangement, yet they may be separable without losing their chemical identity. Thus the solid is equanimous of a certain number of moles of such particles. In all the same other cases, such as diamond, where the entire crystal is substantially a unmarried molecule, the mole is notwithstanding used to express the number of atoms bound together, rather than a count of multiple molecules. Thus, mutual chemic conventions apply to the definition of the elective particles of a substance, in other cases exact definitions may exist specified. The mass of 1 mole of a substance is equal to its relative diminutive or molecular mass in grams.

Molar mass [edit]

The tooth mass of a substance is the mass of one mole of that substance, in multiples of the gram. The amount of substance is the number of moles in the sample. For most applied purposes, the magnitude of tooth mass is numerically the same as that of the mean mass of ane molecule, expressed in daltons. For example, the molar mass of h2o is 18.015 thou/mol.^[8] Other methods include the utilise of the molar volume or the measurement of electric charge.^[eight]

The number of moles of a substance in a sample is obtained past dividing the mass of the sample by the molar mass of the compound. For example, 100 g of water is about five.551 mol of water.^[8]

The molar mass of a substance depends non merely on its molecular formula, but also on the distribution of isotopes of each chemical element present in information technology. For example, the mass of one mole of calcium-40 is 39.96259098±0.00000022 grams, whereas the mass of one mole of calcium-42 is 41.95861801±0.00000027 grams, and of ane mole of calcium with the normal isotopic mix is 40.078±0.004 grams.

Molar concentration [edit]

The molar concentration, also chosen molarity, of a solution of some substance is the number of moles per unit of measurement of volume of the terminal solution. In the SI its standard unit is mol/thou³, although more than practical units, such as mole per litre (mol/50) are used.

Molar fraction [edit]

The tooth fraction or mole fraction of a substance in a mixture (such as a solution) is the number of moles of the chemical compound in 1 sample of the mixture, divided past the total number of moles of all components. For example, if 20 grand of NaCl is dissolved in 100 g of water, the amounts of the two substances in the solution volition be (xx grand)/(58.443 g/mol) = 0.34221 mol and (100 g)/(eighteen.015 k/mol) = five.5509 mol, respectively; and the molar fraction of NaCl will be 0.34221/(0.34221 + v.5509) = 0.05807.

In a mixture of gases, the partial force per unit area of each component is proportional to its tooth ratio.

History [edit]

Avogadro, who inspired the Avogadro constant

The history of the mole is intertwined with that of molecular mass, atomic mass units, and the Avogadro number.

The start table of standard atomic weight (atomic mass) was published past John Dalton (1766–1844) in 1805, based on a system in which the relative atomic mass of hydrogen was defined as 1. These relative atomic masses were based on the stoichiometric proportions of chemical reaction and compounds, a fact that greatly aided their credence: Information technology was not necessary for a chemist to subscribe to diminutive theory (an unproven hypothesis at the time) to make applied use of the tables. This would lead to some defoliation between atomic masses (promoted past proponents of atomic theory) and equivalent weights (promoted by its opponents and which sometimes differed from relative diminutive masses by an integer gene), which would last throughout much of the nineteenth century.

Jöns Jacob Berzelius (1779–1848) was instrumental in the conclusion of relative atomic masses to ever-increasing accuracy. He was also the beginning pharmacist to use oxygen as the standard to which other masses were referred. Oxygen is a useful standard, as, unlike hydrogen, it forms compounds with most other elements, specially metals. Still, he chose to fix the atomic mass of oxygen as 100, which did not grab on.

Charles Frédéric Gerhardt (1816–56), Henri Victor Regnault (1810–78) and Stanislao Cannizzaro (1826–1910) expanded on Berzelius' works, resolving many of the issues of unknown stoichiometry of compounds, and the use of atomic masses attracted a large consensus by the time of the Karlsruhe Congress (1860). The convention had reverted to defining the diminutive mass of hydrogen as one, although at the level of precision of measurements at that fourth dimension – relative uncertainties of around one% – this was numerically equivalent to the later standard of oxygen = 16. Withal the chemical convenience of having oxygen every bit the primary atomic mass standard became ever more than evident with advances in analytical chemistry and the need for ever more accurate atomic mass determinations.

The proper noun mole is an 1897 translation of the German language unit of measurement Mol, coined by the chemist Wilhelm Ostwald in 1894 from the High german discussion Molekül (molecule).^{[9] [x] [11]} The related concept of equivalent mass had been in use at least a century earlier.^[12]

Standardization [edit]

Developments in mass spectrometry led to the adoption of oxygen-16 every bit the standard substance, in lieu of natural oxygen.^{[ citation needed ]}

The oxygen-sixteen definition was replaced with one based on carbon-12 during the 1960s. The mole was defined by International Bureau of Weights and Measures as "the corporeality of substance of a organization which contains equally many elementary entities as there are atoms in 0.012 kilogram of carbon-12." Thus, by that definition, ane mole of pure ¹²C had a mass of exactly 12 g.^{[4] [7]} The four unlike definitions were equivalent to inside 1%.

Scale basis	Scale basis relative to 12C = 12	Relative deviation from the 12C = 12 calibration
Diminutive mass of hydrogen = i	1.00794(7)	−0.788%
Atomic mass of oxygen = 16	15.9994(3)	+0.00375%
Relative atomic mass of 16O = 16	15.9949146221(15)	+0.0318%

Since the definition of the gram was not mathematically tied to that of the dalton, the number of molecules per mole Due north _A (the Avogadro constant) had to exist adamant experimentally. The experimental value adopted by CODATA in 2010 is N _A = (six.02214129±0.00000027)×10²³ mol⁻¹ .^[13] In 2011 the measurement was refined to (6.02214078±0.00000018)×10²³ mol⁻¹ .^[14]

The mole was made the 7th SI base of operations unit of measurement in 1971 by the 14th CGPM.^[15]

2019 redefinition of SI base units [edit]

In 2011, the 24th meeting of the General Conference on Weights and Measures (CGPM) agreed to a programme for a possible revision of the SI base unit definitions at an undetermined date.

On 16 November 2018, after a coming together of scientists from more than 60 countries at the CGPM in Versailles, France, all SI base units were divers in terms of physical constants. This meant that each SI unit of measurement, including the mole, would not exist defined in terms of any physical objects merely rather they would exist defined past constants that are, in their nature, verbal.^[2]

Such changes officially came into effect on 20 May 2019. Following such changes, "i mole" of a substance was redefined as containing "exactly half dozen.022140 76 ×10²³ uncomplicated entities" of that substance.^{[sixteen] [17]}

Criticism [edit]

Since its adoption into the International System of Units in 1971, numerous criticisms of the concept of the mole every bit a unit similar the metre or the 2nd have arisen:

• The number of molecules, electrons, etc. in a given corporeality of material is a dimensionless quantity that tin can be expressed simply as a number and therefore cannot be associated with a distinct base unit;^{[7] [eighteen] [19]}
• The official mole is based on an outdated continuum (non fully atomistic) concept of substance and logically cannot apply to electrons or dissolved ions since there is no electron or dissolved-ion substance;^[19]
• The SI thermodynamic mole is irrelevant to analytical chemistry and could cause avoidable costs to avant-garde economies;^[20]
• The mole is not a true metric (i.e. measuring) unit, rather it is a parametric unit, and corporeality of substance is a parametric base quantity;^[21]
• the SI defines numbers of entities as quantities of dimension ane, and thus ignores the ontological distinction between entities and units of continuous quantities.^[22]

In chemistry, information technology has been known since Proust's law of definite proportions (1794) that cognition of the mass of each of the components in a chemic system is not sufficient to define the arrangement. Amount of substance can exist described equally mass divided by Proust's "definite proportions", and contains information that is missing from the measurement of mass lonely. As demonstrated by Dalton'due south law of fractional pressures (1803), a measurement of mass is non even necessary to measure the amount of substance (although in do it is usual). There are many physical relationships between amount of substance and other physical quantities, the most notable 1 existence the ideal gas law (where the human relationship was first demonstrated in 1857). The term "mole" was showtime used in a textbook describing these colligative properties.^{[ citation needed ]}

Similar units [edit]

Like chemists, chemical engineers use the unit mole extensively, but dissimilar unit multiples may be more suitable for industrial use. For example, the SI unit for volume is the cubic metre, a much larger unit of measurement than the commonly used litre in the chemic laboratory. When amount of substance is likewise expressed in kmol (1000 mol) in industrial-scaled processes, the numerical value of molarity remains the same.

For convenience in avoiding conversions in the purple (or American customary units), some engineers adopted the pound-mole (notation lb-mol or lbmol), which is divers equally the number of entities in 12 lb of ¹²C. One lb-mol is equal to 453.59237 mol,^[23] which value is the same as the number of grams in an international avoirdupois pound.

In the metric system, chemic engineers once used the kilogram-mole (notation kg-mol), which is divers as the number of entities in 12 kg of ¹²C, and oft referred to the mole every bit the gram-mole (notation grand-mol), when dealing with laboratory data.^[23]

Late 20th-century chemical engineering science practice came to use the kilomole (kmol), which is numerically identical to the kilogram-mole, merely whose name and symbol adopt the SI convention for standard multiples of metric units – thus, kmol means 1000 mol. This is equivalent to the use of kg instead of grand. The employ of kmol is not only for "magnitude convenience" simply also makes the equations used for modelling chemic engineering science systems coherent. For instance, the conversion of a flowrate of kg/s to kmol/south only requires the molecular mass without the factor 1000 unless the bones SI unit of mol/s were to exist used.

Greenhouse and growth chamber lighting for plants is sometimes expressed in micromoles per square metre per second, where i mol photons = 6.02×10²³ photons.^[24]

Multiples [edit]

SI multiples of mole (mol)

Submultiples				Multiples
Value	SI symbol	Proper name		Value	SI symbol	Proper noun
10−i mol	dmol	decimole		101 mol	damol	decamole
ten−2 mol	cmol	centimole		xii mol	hmol	hectomole
x−3 mol	mmol	millimole		xthree mol	kmol	kilomole
ten−6 mol	µmol	micromole		106 mol	Mmol	megamole
10−9 mol	nmol	nanomole		109 mol	Gmol	gigamole
10−12 mol	pmol	picomole		ten12 mol	Tmol	teramole
x−15 mol	fmol	femtomole		x15 mol	Pmol	petamole
10−18 mol	amol	attomole		ten18 mol	Emol	examole
ten−21 mol	zmol	zeptomole		ten21 mol	Zmol	zettamole
10−24 mol	ymol	yoctomole		1024 mol	Ymol	yottamole
Mutual multiples are in bold face

Like other SI units, the mole can modified past adding a prefix that multiplies it past a power of 10.

Yoctomole [edit]

A yoctomole (ymol) is one septillionth of a mole ( ten⁻²⁴ mol). It is equal to 0.602214 076 elementary entities. While the metric prefix system entails the existence of this unit, in practice it would exist more convenient to only express such extremely small quantities of amount of substance past stating the number of elementary entities directly.

Zeptomole [edit]

A zeptomole (zmol) is one sextillionth of a mole ( 10⁻²¹ mol). Information technology is equal to 602.214076 elementary entities.

Attomole [edit]

An attomole (amol) is one quintillionth of a mole ( 10⁻¹⁸ mol). It is equal to 602,214.076 simple entities.

Femtomole [edit]

A femtomole (fmol) is i quadrillionth of a mole ( x^−fifteen mol). It is equal to 602,214,076 simple entities.

Picomole [edit]

A picomole (pmol) is ane trillionth of a mole ( 10⁻¹² mol). It is equal to 602,214,076,000 elementary entities.

Nanomole [edit]

A nanomole (nmol) is one billionth of a mole ( 10⁻⁹ mol). Information technology is equal to 602,214,076,000,000 or 6.022140 76 ×x¹⁴ elementary entities.

Micromole [edit]

A micromole (μmol) is one millionth of a mole ( 10^−six mol). Information technology is equal to 602,214,076,000,000,000 or 6.022140 76 ×10¹⁷ elementary entities, the gauge number of elementary charges in 0.096485 coulombs.

Millimole [edit]

A millimole (mmol) is ane one thousandth of a mole (0.001 mol or 10^−three mol). It is equal to 6.022140 76 ×x²⁰ uncomplicated entities, the approximate number of atoms in i/5 of a gram of mercury.

Centimole [edit]

A centimole (cmol) is one one hundredth of a mole (0.01 mol or 10⁻² mol). It is equal to 6.022140 76 ×10²¹ uncomplicated entities, slightly more than the number of atoms in a gram of ruthenium metal.

Decimole [edit]

A decimole (dmol) is i tenth of a mole (0.1 mol or 10⁻¹ mol). It is equal to 6.022140 76 ×x²² elementary entities, somewhat more than than the number of atoms in a gram of boron and somewhat less than the number of atoms in a gram of glucinium.

Decamole [edit]

A decamole (damol) is ten moles (ten mol or 10¹ mol). Information technology is equal to 6.022140 76 ×10²⁴ simple entities, the approximate number of molecules in a 180 ml glass of water.

Hectomole [edit]

A hectomole (hmol) is one hundred moles (100 mol or 10² mol). It is equal to 6.022140 76 ×x²⁵ elementary entities.

Kilomole [edit]

A kilomole (kmol) is one thousand moles (chiliad mol or ten³ mol). Information technology is equal to 6.022140 76 ×10²⁶ simple entities, the gauge number of molecules in an 18 litre (4.755 US gallon) tub of water.

Megamole [edit]

A megamole (Mmol) is one million moles ( ten^{half dozen} mol). It is equal to 6.022140 76 ×10²⁹ elementary entities, the approximate number of water molecules in an eighteen cubic metre swimming.

Gigamole [edit]

A gigamole (Gmol) is i billion moles ( 10^nine mol). It is equal to vi.022140 76 ×10³² unproblematic entities, the estimate number of water molecules in an 18,000 cubic metre lake.

Teramole [edit]

A teramole (Tmol) is one trillion moles ( 10¹² mol). It is equal to 6.022140 76 ×x³⁵ simple entities, the guess number of water molecules in Blithfield Reservoir in Staffordshire, U.k., when total to capacity.

Petamole [edit]

A petamole (Pmol) is 1 quadrillion moles ( 10^fifteen mol). It is equal to 6.022140 76 ×10³⁸ elementary entities, a trivial less than the number of h2o molecules in Crater Lake, Oregon, the deepest lake in the U.s..

Examole [edit]

An examole (Emol) is ane quintillion moles ( x^eighteen mol). It is equal to 6.022140 76 ×10⁴¹ unproblematic entities, a piddling less than the number of water molecules in Lake Tanganyika, the largest lake in Africa and the 3rd largest in the world by volume.

Zettamole [edit]

A zettamole (Zmol) is ane sextillion moles ( 10²¹ mol). It is equal to half-dozen.022140 76 ×10⁴⁴ elementary entities, a little less than the number of water molecules in the Arctic Sea.^[25]

Yottamole [edit]

A yottamole (Ymol) is i septillion moles ( x²⁴ mol). Information technology is equal to 6.022140 76 ×10⁴⁷ elementary entities, approximately 13.5 times the number of water molecules in all oceans on Earth.^[25]

Mole Day [edit]

October 23, denoted 10/23 in the United states of america, is recognized by some every bit Mole Day.^[26] It is an informal holiday in laurels of the unit among chemists. The appointment is derived from the Avogadro number, which is approximately 6.022×10²³ . It starts at 6:02 a.yard. and ends at 6:02 p.m. Alternatively, some chemists celebrate June 2 (06/02), June 22 (6/22), or vi Feb (06.02), a reference to the half dozen.02 or 6.022 role of the constant.^{[27] [28] [29]}

Come across as well [edit]

• Einstein (unit)
• Element-reactant-production tabular array
• Faraday (unit)
• Mole fraction – Proportion of a constituent to the full amount of all constituents in a mixture, expressed in mol/mol
• Dalton (unit) – Standard unit of mass for atomic-scale chemical species
• Molecular mass – Mass of a given molecule in daltons
• Molar mass – Mass per corporeality of substance

References [edit]

1. ^ IUPAC Golden Book. "IUPAC - mole (M03980)". International Union of Pure and Applied Chemistry.
2. ^ ^{a b} "On the revision of the International Organisation of Units - International Union of Pure and Applied Chemistry". IUPAC | International Wedlock of Pure and Practical Chemistry. xvi November 2018. Retrieved 1 March 2021.
3. ^ BIPM (20 May 2019). "Mise en pratique for the definition of the mole in the SI". BIPM.org . Retrieved 18 February 2022.
4. ^ ^{a b} International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), pp. 114–xv, ISBN92-822-2213-half-dozen, archived (PDF) from the original on 2021-06-04, retrieved 2021-12-16
5. ^ Wang, Yuxing; Bouquet, Frédéric; Sheikin, Ilya; Toulemonde, Pierre; Revaz, Bernard; Eisterer, Michael; Weber, Harald Due west.; Hinderer, Joerg; Junod, Alain; et al. (2003). "Specific heat of MgB₂ after irradiation". Periodical of Physics: Condensed Matter. xv (6): 883–893. arXiv:cond-mat/0208169. Bibcode:2003JPCM...fifteen..883W. doi:10.1088/0953-8984/15/6/315. S2CID 16981008.
6. ^ Lortz, R.; Wang, Y.; Abe, S.; Meingast, C.; Paderno, Yu.; Filippov, V.; Junod, A.; et al. (2005). "Specific heat, magnetic susceptibility, resistivity and thermal expansion of the superconductor ZrB₁₂". Phys. Rev. B. 72 (2): 024547. arXiv:cond-mat/0502193. Bibcode:2005PhRvB..72b4547L. doi:ten.1103/PhysRevB.72.024547. S2CID 38571250.
7. ^ ^{a b c} de Bièvre, Paul; Peiser, H. Steffen (1992). "'Atomic Weight' — The Proper name, Its History, Definition, and Units" (PDF). Pure and Applied Chemistry. 64 (10): 1535–43. doi:10.1351/pac199264101535.
8. ^ ^{a b c} International Agency of Weights and Measures. "Realising the mole Archived 2008-08-29 at the Wayback Machine." Retrieved 25 September 2008.
9. ^ Helm, Georg (1897). "The Principles of Mathematical Chemistry: The Energetics of Chemical Phenomena". transl. by Livingston, J.; Morgan, R. New York: Wiley: vi.
10. ^ Some sources place the appointment of first usage in English equally 1902. Merriam–Webster proposes Archived 2011-xi-02 at the Wayback Machine an etymology from Molekulärgewicht (molecular weight).
11. ^ Ostwald, Wilhelm (1893). Mitt- und Hilfsbuch zur Ausführung Physiko-Chemischer Messungen [Handbook and Auxiliary Book for Conducting Physical-Chemical Measurements]. Leipzig, Federal republic of germany: Wilhelm Engelmann. p. 119. From p. 119: "Nennen wir allgemein das Gewicht in Grammen, welches dem Molekulargewicht eines gegebenen Stoffes numerisch gleich ist, ein Mol, so ... " (If we phone call in general the weight in grams, which is numerically equal to the molecular weight of a given substance, a "mol", then ... )
12. ^ mole, n.⁸ , Oxford English Dictionary, Draft Revision Dec. 2008
13. ^ physics.nist.gov/ Archived 2015-06-29 at the Wayback Automobile Primal Concrete Constants: Avogadro Constant
14. ^ Andreas, Birk; et al. (2011). "Conclusion of the Avogadro Constant by Counting the Atoms in a ²⁸Si Crystal". Physical Review Letters. 106 (3): 30801. arXiv:1010.2317. Bibcode:2011PhRvL.106c0801A. doi:10.1103/PhysRevLett.106.030801. PMID 21405263. S2CID 18291648.
15. ^ "BIPM – Resolution three of the 14th CGPM". www.bipm.org. Archived from the original on 9 October 2017. Retrieved one May 2018.
16. ^ CIPM Report of 106th Meeting Archived 2018-01-27 at the Wayback Auto Retrieved seven April 2018
17. ^ "Redefining the Mole". NIST. NIST. 2018-ten-23. Retrieved 24 October 2018.
18. ^ Giunta, C. J. (2015) "The Mole and Corporeality of Substance in Chemistry and Education: Beyond Official Definitions" J. Chem. Educ. 92: 1593–1597.
19. ^ ^{a b} Schmidt-Rohr, K. (2020). "Analysis of Two Definitions of the Mole That Are in Simultaneous Use, and Their Surprising Consequences" J. Chem. Educ. 97: 597–602. http://dx.doi.org/10.1021/acs.jchemed.9b00467
20. ^ Price, Gary (2010). "Failures of the global measurement system. Part one: the case of chemistry". Accreditation and Quality Balls. 15 (vii): 421–427. doi:10.1007/s00769-010-0655-z. S2CID 95388009.
21. ^ Johansson, Ingvar (2010). "Metrological thinking needs the notions of parametric quantities, units, and dimensions". Metrologia. 47 (3): 219–230. Bibcode:2010Metro..47..219J. doi:10.1088/0026-1394/47/3/012.
22. ^ Cooper, G.; Humphry, S. (2010). "The ontological distinction betwixt units and entities". Synthese. 187 (2): 393–401. doi:10.1007/s11229-010-9832-one. S2CID 46532636.
23. ^ ^{a b} Himmelblau, David (1996). Bones Principles and Calculations in Chemical Engineering (6 ed.). pp. 17–xx. ISBN978-0-13-305798-0.
24. ^ "Lighting Radiation Conversion". Archived from the original on March 11, 2016. Retrieved March 10, 2016.
25. ^ ^{a b} "Volumes of the World's Oceans from ETOPO1". noaa.gov. National Oceanic and Atmospheric Assistants. Retrieved 8 March 2022.
26. ^ History of National Mole Day Foundation, Inc. Archived 2010-10-23 at the Wayback Machine.
27. ^ Happy Mole Mean solar day! Archived 2014-07-29 at the Wayback Machine, Mary Bigelow. SciLinks blog, National Science Teachers Clan. October 17, 2013.
28. ^ What Is Mole Day? – Date and How to Celebrate. Archived 2014-07-30 at Wikiwix, Anne Marie Helmenstine. Almost.com.
29. ^ The Perse Schoolhouse (February seven, 2013), The Perse School celebrates moles of the chemical variety, Cambridge Network, archived from the original on 2015-02-11, retrieved Feb 11, 2015, Equally six.02 corresponds to sixth February, the Schoolhouse has adopted the appointment as their 'Mole Day'.

External links [edit]

• ChemTeam: The Origin of the Word 'Mole' at the Wayback Machine (archived December 22, 2007)

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Source: https://en.wikipedia.org/wiki/Mole_%28unit%29

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