How many total absorptions would appear on proton -NMR spectrum for this molecule?
To answer this question properly one must understand that the field of the instrument is important. At 400 MHz, ibuprofen displays 7 distinct carbon-bound proton signals. Below is the spectrum from the SDBS website. Although the two methyls of the isobutyl chain are recorded [G] as a "singlet" at &delta; 0.889, they are diastereotopic and inherently different no matter how far they are removed from the asymmetry on the other side of the ring. If this spectrum were recorded on a 1,020 MHz 1H NMR, perhaps separation of the two methyl signals would occur. That the two methyls are different, imagine that one of them is a perdeutero methyl group. This compound is a diastereomer of the compound having the other methyl group as the perdeutero group. So there are actually 9 total distinct types of hydrogens (including the carboxyl hydrogen) that, given the right spectrometer, could appear in a spectrum of ibuprofen. It is a matter of resolution. [As a case in point, see the 1H NMR of cholesterol at the SDBS website and note that the two methyl groups at the end of the side chain have different chemical shifts even though the are separated from the nearest center of asymmetry by three methylene groups.]
Acknowledgment: http://sdbs.db.aist.go.jp/sdbs/cgi-bin/direct_frame_top.cgi