Rearranging this equation to solve for solubility (S) gives:

Plugging the value for Ksp into the equation gives:

The equivalence point is when enough titrant has been added so that the number of moles of titrant equals the number of moles of analyte. We must first determine the number of moles of silver ions at the equivalence point.

At the equivalence point the following occurs in solution:

The number of moles of silver ions at equivalence point is calculated as follows:

Plugging these values into the equation gives:

Recall that the solubility product constant is given by the equation below, for a reaction in the following format.

Using our balanced reaction, we can find the solubility product equation for the dissociation of lead (II) fluoride.

For each molecule of lead (II) fluoride that dissolves, it produces one lead ion and two fluoride ions. We can conclude that the concentration of fluoride ions in solution will be twice the concentration of lead ions.

Use these variables in the solubility product equation, along with the given value from the question.

Now we can solve for the value of .

Remember that this value is equal to the concentration of lead ions in solution and half the concentration of fluoride ions in solution.

The molecular ion peak is determined using mass spectrometry. The parent peak is formed when a mystery molecule does not fragment, and simply loses an electron. This means that the mass to charge ratio of this peak will allow us to determine the molecular weight of the compound.

IR spectroscopy allows you to identify what functional groups are present in a compound. The IR spectrum is created by recording the frequencies at which a polar bond's vibration frequency is equal to the infrared light's frequency.

The fingerprint region is separate from the function group region, and generally corresponds to carbon-carbon or carbon-hydrogen interactions. While the spectrum can show what groups are present in a compound, it cannot be used to find the position of these groups or provide a carbon skeleton.

IR spectroscopy is most commonly used to determine the functional groups found in the molecule being observed. This is done by observing the vibration frequencies between atoms in the molecule. It does not easily reveal the size or shape of the molecule's carbon skeleton. Although the fingerprint region is unique for every molecule, it is very difficult to read when attempting to determine the molecule's functional groups. Most functional group peaks are observed in the functional group region adjacent to the fingerprint region.

Infrared (IR) spectroscopy takes advantage of the electrical difference between atoms in a polar bond. These dipole moments, when exposed to infrared radiation, stretch and contract in what appears to be a vibrating motion between the atoms. The different vibrational frequencies in the molecule allow for the compound to be "read" using IR spectroscopy.

An alcohol (-ROH) exhibits a strong, broad absorbance peak at about 3500cm^-1. A nitrile's (-RCN) characteristic absorbance peak is at about 2200cm^-1. Carbonyl groups have strong, sharp peaks from 1700cm^-1 to 1750cm^-1, depending on the type of carbonyl group. For instance, an ester (-RCO₂R'-) has an absorbance at about 1750cm^-1, while a ketone (-ROR'-) has an absorbance at around 1710cm^-1.