# 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

The Kendrick mass unit is defined as [3]

m(12CH2) = 14 Ke

In words: "the group 12CH2 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

When expressing the masses of hydrocarbon molecules in Kendrick mass, all homologous molecules will have the same mass defect Δm defined as:[4]

Δm = m - round(m)

or more rigorously

Δm = m - A·Ke

where

• Δm 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

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 CH2)

The above statement is read: "A is modulo CH2 equivalent to B."

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

m(A) ~ m(B) (mod m(CH2))

"A has the same modulo CH2 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(CH2)

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

Δm(M) = m(M) - m(CH2)·round(m(M)/m(CH2))

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 CH2, e.g. in polymer chemistry
• the Kendrick mass defect Δm is defined different than the mass defect in nuclear physics

## Notes

1. Kendrick, Edward (1963). "A mass scale based on CH2 = 14.0000 for high resolution mass spectrometry of organic compounds". Anal. Chem. 35: 2146–2154. Retrieved 2010-01-25.
2. 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.
3. http://www.atmos-meas-tech.net/3/1039/2010/amt-3-1039-2010.html
4. 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.