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.

Definition
The Kendrick mass unit is defined as


 * 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:


 * 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