CEM 832: MASS SPECTROMETRY

Spring 2008

Potentially Useful Constants

Some Constants, Concepts and Conversion Factors useful in Mass Spectrometry, for the Calculation of Forces, Fields, Charges, Velocities, Number Densities and Pressures

Charge: 1 electronic charge = 1.6 x 10^-19 Coulomb/particle

Current: 1 ion/second = 1.60 x 10^-19 Amps

Energy: 1 eV = 23.06 kcal/mol; 1 kcal/mol = 4.18 kJ/mol

Mass: 1 Dalton (atomic mass unit) = 1.66 x 10^-27 kg

Pressure: 1 Torr = 133 Pascal = 1 mm Hg = 1.33 mbar

also, 1 Torr = 3.2 x 10¹⁶ molecules/cm³

Velocity conversion factor: a particle with a mass of 1 Dalton, accelerated to a kinetic energy of 1 eV has a velocity of 1.1 x 10⁶ cm/sec

The SI unit for magnetic field is the tesla (T). One T is equal to one newton per amp meter (N/A^.m). To rationalize the units, consider the definition of magnetic field. It is an area of influence around a moving charge. The size of the field is related to the amount of magnetic force experienced by the moving charge when it is at a given location in the field. Thus magnetic field = (force)/(charge)(speed) or B = F/qv.

Coulomb’s Law: Two charged objects attract each other with a force that is proportional to the charge on the objects and inversely proportional to the square of the distance between them. Using a constant k, the electrostatic constant, with a value of k = 9.0 x 10⁹ Nm²/C², Coulomb’s law takes the form:

electrostatic force = k(charge 1)(charge 2)/(distance)²

F = kq(1)q(2)/d²

An Electric Field is an area of influence around a charged object. The magnitude of the field is proportional to the amount of electrical force exerted on a positive test charge placed at a given point in the field.

electric field = electric force/test charge

E = F/q

The SI unit for electric field is the newton per coulomb (N/C).

m/z:  The x axis of a mass spectrum is labeled m/z.  m/z is an abbreviation used to denote the dimensionless quantity formed by dividing the mass number (mass in Daltons) of an ion by the number of charges carried by the ion.  It has long been called the mass-to-charge ratio, although m is not the actual ionic mass, nor is z the actual electronic charge.  The abbreviation m/e is not recommended.  When doing calculations, one must use the actual mass (kg) and charge (Coulombs) of an ionic species to calculate velocities, momenta, etc.  If we know that C atoms weigh 12 Daltons and H atoms weigh 1 Dalton, then simple addition identifies a CH³⁺ cation as having an m/z value of 15.

A warning on units:  When doing calculations, it is very important to keep track of units.  They will tell you if the quantities that you combined in an equation could possibly be giving you the answer that you desired.  However, complete units are not always written down - some are assumed.

For example, to calculate the kinetic energy of a single particle characterized by a temperature T, one can use the equation K.E. = 3/2 k T, where k is the Boltzmann constant.  If one would like to know the kinetic energy of a mole of these particles, one could use K.E. = 2/3 R T, where R is the molar gas constant.  R has a value of 8.314 J per K per mole.  If you divide R by Avagadro's number, you get k.  So, R is a molar value and k is a molecular value.  However, k is reported as 1.38 x 10^-23 J per K.  Shouldn't that be Joules per Kelvin per molecule?  The units of per molecule are assumed and are not specifically designated.  If you were not aware of this, look through the inside cover of any Physical Chemistry book.  The atomic mass constant is 1.66 x 10^-27 kg.  That is kg per what?  Wouldn't you write the rest mass of an electron as 9.1 x 10^-31 kg/electron, just to make certain that your calculations are yielding the appropriate answer?  The mass is only written in kg, and you must understand that this is per particle.

The problem arises in Energy units as well.  What is 1 eV equal to?  A mole of particles with kinetic energies of 1 eV have a total energy of 96.48 kJ per mole.  1 eV is also defined as 1.6 x 10^-19 Joule.  The correct interpretation is 1.6 x 10^-19 Joule/molecule, but again, the units of per molecule or per particle are assumed when not indicated.

Before using definitions of constants or conversion factors from a text book, you might want to consult introductory sections of the book to see if they have any comments on the values provided, and how they are presented.

****When using this page, or any web source of constants or conversion factors, always confirm them with a second source.****