How to Calculate the Degree of Unsaturation

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The degree of unsaturation of a molecule is the total number of rings, double bonds and triple bonds in the molecule. Chemists typically use this number to predict the molecule's structure, which is then verified by some means of observation such as spectroscopy. The degree of unsaturation may be calculated when the number of each type of atom in the molecule is known. This formula may also be simplified for molecules that contain only certain atoms.

    Provide the formula for the degree of unsaturation as 1 + [? ni(vi -2)]/2, where ni is the number of atoms in the molecule with a valence of vi. This equation can be used to calculate the degree of saturation for any molecular formula.

    Identify the valences for carbon, nitrogen, oxygen, hydrogen and other halogens. Carbon has a valence of 4, nitrogen has a valence of 3, oxygen has valence of 2, and hydrogen and other halogens have a valence of 1.

    Evaluate the term ni(vi-2)/2 in the equation 1 + [? ni(vi - 2)]/2 for carbon, nitrogen, oxygen and hydrogen. For carbon, n4(v4 - 2)/2 = n4 (4 - 2)/2 = n4. For nitrogen, n3(v3 - 2)/2 = n3 (3 - 2)/2 = n3/2. For oxygen, n2(v2 - 2)/2 = n2 (2-2)/2 = 0. For hydrogen, n1(v1 - 2)/2 = n1 (1 - 2)/2 = -n1/2.

    Expand the formula 1 + [? ni(vi - 2)]/2 for four terms. We now have 1 + n1(v1 - 2)/2 + n2(v2 - 2)/2 + n3(v3 - 2)/2 + n4(v4 - 2)/2. Now substitute the values for these terms that we found in step 3. We then have 1 - n1/2 + 0n2 + n3/2 + n4 = 1 - n1/2 + n3/2 + n4, where n1 is for hydrogen and other halogens, n2 is for oxygen, n3 is for nitrogen and n4 is for carbon.

    Simplify the equation 1 - n1/2 + n3/2 + n4 = 1 - X/2 + N/2 + C, where n1 is for hydrogen and other halogens, n2 is for oxygen, n3 is for nitrogen and n4 is for carbon. We now have the degree of saturation for molecules that contain only these atoms as 1 + C + (N - X)/2.

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