The Molecular Mass and The Mass Spectrometer
Molecular Mass
** If
we know the atomic masses of the component atoms, we can calculate the mass of a
molecule.
** The
molecular mass: (sometimes called molecular weight) is the sum of the atomic
masses (in amu) in the molecule.
** For
example, the molecular mass of H2O is:
** In general,
we need to multiply the atomic mass of each element by the number of atoms of
that element present in the molecule and sum over all the elements.
Problem (1): Calculate
the molecular masses (in amu) of the following compounds:
(a) sulfur dioxide
(SO2)
(b) caffeine (C8H10N4O2)
Strategy:
How do atomic
masses of different elements combine to give the molecular mass of a compound?
Solution:
To calculate
molecular mass, we need to sum all the atomic masses in the molecule. For each element,
we multiply the atomic mass of the element by the number of atoms of that
element in the molecule. We find atomic masses in the periodic table (inside
front cover).
(a) There are
two O atoms and one S atom in SO2, so that:
(b) There are
eight C atoms, ten H atoms, four N atoms, and two O atoms in caffeine, so the
molecular mass of C8H10N4O2 is
given by:
Notes
** From the
molecular mass we can determine the molar mass of a molecule or compound.
** The molar
mass of a compound (in grams) is numerically equal to its molecular mass (in
amu). For example, the molecular mass of water is 18.02 amu, so its molar mass
is 18.02 g.
** Note that 1 mole
of water weighs 18.02 g and contains 6.022 × 1023 H2O molecules,
just as 1 mole of elemental carbon contains 6.022 × 1023 carbon atoms.
** As the following Examples show, a knowledge of
the molar mass enables us to calculate the numbers of moles and individual atoms
in a given quantity of a compound.
Problem (2): Methane
(CH4) is the principal component of natural gas. How many moles of
CH4 are present in 4.83 g of CH4?
Strategy:
We are given
grams of CH4 and asked to solve for moles of CH4. What
conversion factor do we need to convert between grams and moles? Arrange the appropriate
conversion factor so that grams cancel and the unit moles are obtained for your
answer.
Solution:
The conversion
factor needed to convert between grams and moles is the molar mass. First we
need to calculate the molar mass of CH4
Because
the conversion
factor we need should have grams in the denominator so that the unit g will
cancel, leaving the unit mol in the numerator:
We now write:
Thus, there is
0.301 mole of CH4 in 4.83 g of CH4.
Check:
Should 4.83 g
of CH4 equal less than 1 mole of CH4? What is the mass of
1 mole of CH4?
Problem (3): How
many hydrogen atoms are present in 43.8 g of urea [(NH2)2CO],
which is used as a fertilizer, in animal feed, and in the manufacture of
polymers? The molar mass of urea is 60.06 g?
Strategy:
We are asked to
solve for atoms of hydrogen in 43.8 g of urea. We cannot convert directly from
grams of urea to atoms of hydrogen. How should molar mass and Avogadro’s number
be used in this calculation? How many moles of H are in 1 mole of urea?
Solution:
** To
calculate the number of H atoms, we first must convert grams of urea to moles
of urea using the molar mass of urea.
** The molecular
formula of urea shows there are four moles of H atoms in one mole of urea molecule,
so the mole ratio is 4:1.
** Finally,
knowing the number of moles of H atoms, we can calculate the number of H atoms
using Avogadro’s number.
** We need two
conversion factors: molar mass and Avogadro’s number. We can combine these
conversions:
into one step:
Check:
Does the answer
look reasonable? How many atoms of H would 60.06 g of urea contain?
Notes
** For ionic
compounds like NaCl and MgO that do not contain discrete molecular units, we
use the term formula mass instead.
** The formula
unit of NaCl consists of one Na+ ion and one Cl- ion.
Thus, the formula mass of NaCl is the mass of one formula unit:
and its molar
mass is 58.44 g.
The Mass Spectrometer
** The most direct and most accurate
method for determining atomic and molecular
masses is mass spectrometry.
** The figure shows Schematic
diagram of one type of mass spectrometer
** In a mass spectrometer:
(1) a gaseous sample is bombarded by
a stream of high-energy electrons.
(2) Collisions between the
electrons and the gaseous atoms (or molecules) produce positive ions by dislodging
an electron from each atom or molecule.
(3) These positive ions (of mass m
and charge e) are accelerated by two oppositely charged plates as
they pass through the plates.
(4) The emerging ions are deflected
into a circular path by a magnet. The radius of the path depends on the
charge-to-mass ratio (that is, eym).
(5) Ions of smaller eym ratio
trace a wider curve than those having a larger eym ratio, so that
ions with equal charges but different masses are separated from one
another.
(6) The mass of each ion (and
hence its parent atom or molecule) is determined from the magnitude of its deflection.
Eventually the ions arrive at the detector, which registers a current for each
type of ion.
(7) The amount of current generated
is directly proportional to the number of ions, so it enables us to
determine the relative abundance of isotopes.
** The first mass spectrometer,
developed in the 1920s by the English physicist F. W. Aston, was crude
by today’s standards. Nevertheless, it provided indisputable evidence of
the existence of isotopes—neon-20 (atomic mass 19.9924 amu and natural abundance
90.92 percent) and neon-22 (atomic mass 21.9914 amu and natural abundance
8.82 percent).
** When more sophisticated and sensitive mass
spectrometers became available, scientists were surprised to discover
that neon has a third stable isotope with an atomic mass of 20.9940 amu
and natural abundance 0.257 percent (Figure shows The
mass spectrum of the three isotopes of neon ).
** This example illustrates how very
important experimental accuracy is to a quantitative science like
chemistry. Early experiments failed to detect neon-21 because its
natural abundance is just 0.257 percent. In other words, only 26 in 10,000 Ne
atoms are neon-21. The masses of molecules can be determined in a similar
manner by the mass spectrometer.
Reference: General Chemistry: The Essential Concepts / Raymond Chang , Jason Overby. (sixth edition).
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