GATE 2024 CY – Question 32

Organic Chemistry · Experimental Techniques in Organic Chemistry: Optical rotation (polarimetry). Application of various chromatographic techniques such as thin-layer, column, HPLC and GC. Applications of UV-visible, IR, NMR spectroscopy and Mass spectrometry in the structural determination of organic molecules. · 1 mark · Numerical answer

$^1$H NMR spectrum of a mixture containing $\mathrm{CH_3Br}$ ($x$ mol) and $\mathrm{(CH_3)_3CBr}$ ($y$ mol) shows two singlets at 2.7 ppm and 1.8 ppm, with the relative ratio of 3:1 (integration value), respectively. The value of $x/y$ is ____. (rounded off to the nearest integer)

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Correct answer: 9

Explanation

In a ¹H NMR spectrum the **integrated area of a signal is proportional to the number of protons giving it**.

**CH₃Br:** one methyl group, 3 equivalent H per molecule, with $x$ mol: area $\propto3x$ (singlet at 2.7 ppm).
**(CH₃)₃CBr:** three equivalent methyl groups, 9 equivalent H per molecule, with $y$ mol: area $\propto9y$ (singlet at 1.8 ppm).

**Observed ratio** of the areas, 2.7 ppm : 1.8 ppm $=3:1$:
$$\frac{3x}{9y}=3\;\Rightarrow\;\frac{x}{3y}=3\;\Rightarrow\;\frac xy=\mathbf{9}.$$