Kendrick mass scale

The Kendrick mass scale defines a unit of mass kendrick (Ke) which is useful in chemistry of hydrocarbons. The kendrick is close to the atomic mass unit but it uses the group CH₂ as the basis of an integer mass.

When measuring the masses of hydrocarbon molecules in kendricks, 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
• Ke is the mass unit kendrick
• 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

This unit simplifies the interpretation of a hydrocarbon mass spectrum.

Definition

The Kendrick mass unit is defined as:

m(CH₂) = 14 Ke

In other words, "the group CH₂ has a mass of 14 Ke exactly, by definition."

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

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

History

In 1963 the chemist E. Kendrick suggested an alternative mass scale in the following publication:

Kendrick, E.: A mass scale based on CH₂ = 14.0000 for high resolution mass spectrometry of organic compounds. Anal Chem. 1963;35:2146–2154.

See also

• atomic mass unit

External links

• Petroleomics: Chemistry of the underworld
• Google books
• Atmos. Meas. Tech., 3, 1039–1053, 2010