# Chemical Sciences: A Manual for CSIR-UGC National Eligibility Test for Lectureship and JRF/Kendrick mass

The **Kendrick mass** is a mass obtained by scaling the atomic mass unit (u), or dalton (Da) to simplify the display of peak patterns in hydrocarbon mass spectra.^{[1]}^{[2]}

## Definition edit

The Kendrick mass unit is defined as
^{[3]}

- m(
^{12}CH_{2}) = 14 Ke

In words: "the group ^{12}CH_{2} has a mass of 14 Ke exactly, by definition."

- 1 Ke = 14.0156/14.000 Da = 1.00111429 Da = 1.00111429 u

## Kendrick mass defect edit

When expressing the masses of hydrocarbon molecules in Kendrick mass, all homologous molecules will have the same mass defect Δ*m* defined as:^{[4]}

- Δ
*m*=*m*- round(*m*)

or more rigorously

- Δ
*m*=*m*-*A*·Ke

where

- Δ
*m*is the Kendrick mass defect *A*is the mass number of the molecule- m is the mass of the molecule (or isotopologue) which is also referred to as exact mass
- round(
*m*) and*A*·Ke are the**integer masses**of the molecule

## Equivalence relation edit

The Kendrick mass scale was introduced to find an equivalence relation for hydrocarbons. The same relation could be expressed with modular arithmetic using the modulo operation without introducing a new mass scale.

- A ~ B (mod CH
_{2})

The above statement is read: "A is modulo CH_{2} equivalent to B."

Or, when considering the mass of the molecules A and B:

*m*(A) ~*m*(B) (mod*m*(CH_{2}))

"A has the same modulo CH_{2} mass as B."

In a computing code the Kendrick mass defect of a molecule M, *Δm*(M), would be expressed as the remainder *r*:

*Δm*(M) =*r*=*m*(M) mod*m*(CH_{2})

or, if the modulo operation nor the remainder operation are defined

*Δm*(M) =*m*(M) -*m*(CH_{2})·round(*m*(M)/*m*(CH_{2}))

Note that:

- most programming languages implement the modulo operation with
*trunc*or*floor*instead of*round* - this approach with modular arithmetic works independent of the mass units (or mass scale)
- this approach is more generalized and allows for other building blocks than CH
_{2}, e.g. in polymer chemistry - the Kendrick mass defect
*Δm*is defined different than the mass defect in nuclear physics

## Notes edit

- ↑ Kendrick, Edward (1963). "A mass scale based on CH
_{2}= 14.0000 for high resolution mass spectrometry of organic compounds".*Anal. Chem*.**35**: 2146–2154. Retrieved 2010-01-25.`{{cite journal}}`

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(help) - ↑ Marshall AG, Rodgers RP (2004). "Petroleomics: the next grand challenge for chemical analysis".
*Acc. Chem. Res*.**37**(1): 53–9. doi:10.1021/ar020177t. PMID 14730994.`{{cite journal}}`

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ignored (help) - ↑ http://www.atmos-meas-tech.net/3/1039/2010/amt-3-1039-2010.html
- ↑ Hughey CA, Hendrickson CL, Rodgers RP, Marshall AG, Qian K (2001). "Kendrick mass defect spectrum: a compact visual analysis for ultrahigh-resolution broadband mass spectra".
*Anal. Chem*.**73**(19): 4676–81. PMID 11605846.`{{cite journal}}`

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ignored (help)CS1 maint: multiple names: authors list (link)