Determining the Empirical Formula

Hydrates are chemical compounds that have water molecules attached (but not covalently bonded) to the compound. Formulas that are hydrated are symbolized by a dot ("·") between the compound and the water molecule. Hydrates easily lose water molecules upon heating, leaving behind the anhydrous (without water) compound. In this case, it would be copper chloride, Cu_xCl_y. The difference in mass between the anhydrous and hydrated forms of the salt corresponds to the mass (and moles) of water in the chemical compound Cu_xCl_y·nH₂O. The anhydrous copper chloride is then dissolved in water, and copper is removed through a redox reaction with aluminum to form solid copper. The difference in mass between the total copper chloride hydrate and the sum of the reduced copper metal and water molecules corresponds to the mass of chloride in the sample. The mass of each component (Cu, Cl, H₂O) is converted to moles, and the mole ratio is used to determine the empirical formula of the compound. The true chemical formula of the compound cannot be determined without knowing its molecular mass, but the ratio will always remain the same.

1. Experiment
   1. Heat 1.25 g of copper chloride hydrate in a crucible. After heating and then cooling, the final mass is 0.986 g of copper chloride, Cu_xCl_y.
   2. Dissolve the Cu_xCl_y sample in 50 mL of deionized water and add 0.2 g of fine aluminum mesh to the beaker.
   3. After reacting and dissolving the excess aluminum, 0.198 g of dried copper metal is recovered.
   4. Subtract the mass of both copper and water from the initial copper chloride hydrate to yield the mass of chloride ion in the sample:
      
2. Data
   1. To determine the smallest whole-number ratio of components in the compound, convert the mass of each component to moles and then divide each by the smallest number of moles in the sample (copper in this case):

   Component	Mass (g)	Molar mass (g/mol)	Moles	Ratio	Calculated whole-number ratio
   Copper	0.479	63.55	7.53 x 10-3		1
   Chloride	0.533	35.45	1.50 x 10-2		1.99 ≈ 2
   Water	0.273	18.01	1.51 x 10-2		2.01 ≈ 2

   Table 1. Experimental results.

   2. The resulting smallest whole-number ratio yields a formula of CuCl₂·2H₂O.
      1. In the event the final ratio yields decimal values, the whole formula would be multiplied by a constant to give whole-number values. Common fractional values are 0.25, 0.333, 0.50, 0.667, and 0.75. For example, if a smallest whole-number ratio yielded the formula yielded C₇H₉NO_2.5, the entire formula would be multiplied by 2 to give the empirical formula C₁₄H₁₈N₂O₅.
   3. A molecular formula cannot be determined from the empirical formula without knowing the molecular mass of the compound. The reason for this is demonstrated in the example below:

   Name	Molecular Formula	Empirical Formula
   Acetic acid	CH3COOH	CH2O
   Formaldehyde	CH2O	CH2O
   Glucose	C6H12O6	CH2O

   Table 2. Example of a common empirical formula.

   All three compounds have the same empirical formula, but very different molecular formulas.

In one example, suppose an unknown biomolecule containing only C, H, and O is found to act well as a new fuel. One way to determine the formula of the fuel would be to combust it in air and analyze the products:

C_xH_yO_z + O₂ → mCO₂ + nH₂O

While O₂ is in excess, we would know all the carbon in CO₂ originated from the biomolecule and all the hydrogen would be present in H₂O. The difference between that total mass and the mass of initial sample would be the mass of oxygen in the molecule. We could then convert to moles and determine the empirical formula.

In another example, a hydrate sample of Mg_xCl_y·nH₂O is given. The mass of the water molecules would again be easily determined by heating. Using some solubility rules, chloride is then precipitated with silver ion, Ag⁺, to form AgCl(s). Once the mass of AgCl(s) is found, the moles of Cl^- are determined using the molar mass of AgCl(s) and then converted to grams of Cl^-. This would allow us to determine the mass of Mg in the sample followed by the empirical formula.

Determining an empirical formula is at the center of identifying the formula of the actual molecule. From pharmaceuticals to forensics, determination of a molecular formula is key to identifying an unknown compound, which means taking the empirical formula to the next step. Typically, the determination of an empirical formula is coupled with elemental analysis to obtain elemental weight percent information. From these data, the molar ratios are calculated and the empirical formula is determined. We can determine the mass of molecule using another analytical tool, like a mass spectrometer. Then, the ratio between the molecular mass and empirical mass is calculated to determine the true molecular formula.