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

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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. http://pubs.acs.org/doi/abs/10.1021/ac60206a048. Retrieved 2010-01-25. - ↑ Marshall AG, Rodgers RP (January 2004). "Petroleomics: the next grand challenge for chemical analysis".
*Acc. Chem. Res.***37**(1): 53–9. doi:10.1021/ar020177t. PMID 14730994. - ↑ http://www.atmos-meas-tech.net/3/1039/2010/amt-3-1039-2010.html
- ↑ Hughey CA, Hendrickson CL, Rodgers RP, Marshall AG, Qian K (October 2001). "Kendrick mass defect spectrum: a compact visual analysis for ultrahigh-resolution broadband mass spectra".
*Anal. Chem.***73**(19): 4676–81. PMID 11605846.