Take relative reactivities per hydrogen for radical bromination as 1 deg : 2 deg : 3 deg = 1 : 82 : 1600. How many times faster (per molecule, same conditions) is 2-methylpropane brominated than propane?

JEE Advanced levelSingle correct optionDifficulty 3 of 3g3158

Take relative reactivities per hydrogen for radical bromination as $1^{\circ} : 2^{\circ} : 3^{\circ} = 1 : 82 : 1600$ . How many times faster (per molecule, same conditions) is 2-methylpropane brominated than propane?

Total reactivity of a molecule is the sum over its hydrogens. 2-Methylpropane:

9 \times 1 + 1 \times 1600 = 1609

. Propane:

6 \times 1 + 2 \times 82 = 170

. The ratio is

1609/170 = 9.5