Sample Question Not Seen On Test

I anticipated a problem on determining the number or protons giving rise to an NMR signal. The example listed in chapter 14 on page 505 is a good example of this type of problem. The problem and solution are listed below.

Question:
A compound of molecular formula C9H10O2 gives the following integrated 1H NMR spectrum. How many protons give rise to each signal?

(The spectrum is shown in the book on page 505 at the bottom of the page.)

Answer:
Step 1: Determine the number of integration units per proton by dividing the total number of integration units by the total number of protons.

• Total number of integration units: 54+23+33=110 units
• Total number of protons = 10
• Divide: 110 units/10 protons = 11 units per proton

Step 2: Determine the number of protons giving rise to each signal.

• To determine the number of H atoms giving rise to each signal, divide each integration value by the answer of Step 1 and round to the nearest whole number. 

                      Solution: Signal A - 54/11 = 4.9 = 5 H
                                    Signal B - 23/11 = 2.1 = 2 H
                                    Signal C - 33/11 = 3H

The area under an NMR signal is proportional to the number or absorbing protons. The height of each step is proportional to the area under the peak, which is in turn proportional to the number of absorbing protons. Knowing the molecular formula of a compound and integration values from its 1H NMR spectrum gives the actual number of protons responsible for a particular signal.