Preperation and Setup
Masses of atoms are measured relative to the mass of the carbon-12 isotope, which itself is defined to have a mass of exactly 12 atomic mass units (or amu). This definition is especially useful when measuring isotope masses with a mass spectrometer. The mass spectrometer is a device used to measure the mass of an atom by reading on a detecting screen the amount of deflection their +1 ions experience in a magnetic field: the smaller the deflection the larger the mass. More specifically, the mass of an atom is measured by comparing its deflection in the mass spectrometer to the deflection of the carbon-12 mass standard. For a sample of an element one can also count the number of atoms of each isotope that hit the detecting screen to obtain the fractional abundance of each isotope. The average atomic mass of the element that appears on the periodic table is then the weighted average of the isotope masses.
Masses of molecules can also be measured using the mass spectrometer as well. In this case the molecule may also break into fragments that produce a characteristic "fingerprint" pattern for the molecule. The highest masses observed are the molecular masses for molecules containing differing isotopes. One could obtain the molecular mass experimentally from the weighted average of these highest masses, but it is usually far simpler to calculate the molecular mass by simply adding together the atomic masses of all the atoms in the molecular formula. Refer to the diagram below to learn how a mass spectrometer works.
Single atoms or molecules are far too small to work with in the laboratory and the atomic mass unit is also far too small a mass to work with conveniently in the laboratory. Instead, in the laboratory we prefer to work with masses in units of grams. So we need some means to scale the masses that we can measure with a mass spectrometer up to usful masses in grams. This is accomplished by defining a special number called the mole.
The mole is defined as the number of carbon atoms in exactly 12 grams of the carbon-12 isotope. This number is also known as Avogadro's number. Since this mass in grams is numerically equal to the mass of carbon-12 in amu (and carbon-12 is the mass standard) the mole provides a simple way to use atomic mass measurements. A mole of atoms of any element has a mass equal to its atomic mass, but expressed in grams not amu. Likewise, the mass of one mole of molecules is the molecular mass expressed in grams. The mass of one mole of a substance is called the molar mass.
The mole is a special name for a number, like a dozen is a special name for 12 and a pair is a special name for 2. Unlike the dozen or the pair, which are defined numbers, the mole is an experimentally measured number. In principle one would have to weigh out exactly 12 grams of carbon-12 and count how many atoms were in the sample to find out how many particles are in a mole (although in practice this number is determined through X-ray measurements on extremely pure silicon crystals). Since the number of particles in a mole is determined experimentally, there is some uncertainty in its value. A recent measurement of the number of particles in a mole (or Avogadro's number) to 8 significant figures is 6.0221421 x 1023.
Before mass spectrometers or other fancy pieces of apparatus existed, however, scientists measured Avogadro's number and molar masses of substances using simple equipment similar to that found in your lab drawer. In this experiment you will measure the molar mass of magnesium using simple equipment.
Experimentally the molar mass is measured as the mass of a sample of a substance divided by the number of moles in the sample. The mass of the sample is measured easily. For the magnesium ribbon we will be using we will measure the length of the ribbon and multiply this by a mass/length ratio that you will be given in class (the masses of the pieces of ribbon are too small to be measured reliably on the balances).
For the other half of the measurement you will need to determine the number of moles in the sample of ribbon. In this experiment we will assume that we do not know the atomic or molar mass of magnesium (although we can use the atomic mass of magnesium off the periodic table at the end to check our results), so we cannot simply divide the mass of the magnesium ribbon by its molar mass to get number of moles. Instead we will have to measure number of moles experimentally.
One way of measuring number of moles directly without knowing a molar mass is by using the ideal gas equation (rearranged to solve for moles: n = PV/RT) and along with pressure, temperature, and volume observations. This will work only if our sample is a gas, however, but magnesium ribbon is a solid. To get around this we will consume the magnesium metal in a single replacement reaction with HCl(aq) that will produce H2(g). Once the number of moles of H2(g) has been determined, we can find the number of moles of magnesium at the start of the reaction through a simple stoichiometry calculation using the balanced chemical equation for the reaction.