Alkanes do not ordinarily exhibit a molecular ion M+.M^+. in the electron ionization mass spectrum because M+.M^+. breaks into fragments. If dilute alkane vapor in HeHe is allowed to expand through a narrow orifice into a vacuum, expansion of the gas cools the molecules and reduces their vibrational energy. The molecular ion of the alkane C₇₂H₁₄₆ С₇₂Н₁₄₆ is the base peak when the molecule is sufficiently cold.

a. Find the nominal mass of the molecular ion C₇₂H₁₄₆+. С₇₂Н₁₄₆+.

b. Find the monoisotopic mass of C₇₂H146+. С₇₂Н₁₄₆+.

c. 13C¹³Chas a natural abundance of 1.07%,1.07%, whereas 2H²H has a natural abundance of 0.012%.0.012%.

Therefore, the main isotopologues of the molecular ion are 12C₇₂H₁₄₆1 ¹²C₇₂H₁₄₆ and 12C7113C1H₁₄₆. ¹²C₇₁¹³C₁H₁₄₆. As in the previous problem, we can find the relative abundance of 12C72¹²C₇₂ and 12C7113C1¹²C₇₁¹³C₁ from the first two terms of the binomial expansion (a+b)72,(a+b)⁷², where a=0.989 3 a=0.989 3 for 12C ¹²C and b=0.010 7b=0.010 7 for 13C¹³C. Predict the relative abundance of MM and M+1M+1 in the mass spectrum of C₇₂H₁₄₆.C₇₂H_146.