CHEMISTRY 133

Spring, 2015 Homework Additional Problems Set 3.1

SOLUTIONS

Additional Problems:

1. In a 2.35 Tesla field, the magnetogyric ratios (g) for ³¹P is 1.08 x 10⁸ T^-1 s^-1.

a)  At what frequency does ³¹P absorb light?

n =  (g/2p)H = (1.08 x 10⁸ T^-1 s^-1/2p)(2.35 T) = 40.4 MHz

b)  If a sample has 1.000000 x 10⁶ nuclei in the ground state, how many nuclei will be in the excited state?  T needs to be given, so assume T = 298 K

N*/N₀ = e^-E/kT = e^-hn/kT = e^{-[(6.626 x 10^-34Js)(4.04 x 10^7 s^-1)]/(1.38 x 10^-23J/K)(298 K)]} = e^{-6.51 x 10^-6}

N*/N₀ = 0.999993 or 999,993 in excited state

How could the number of excited nuclei be decreased?

A more negative exponent will lead to a decrease.  This could be done by switching to a field with a greater strength or by going to a lower temperature.

2.  1,2-dichloropropane (CH₃CH(Cl)CH₂Cl) is analyzed by ¹H NMR.  It is observed to have a jumbled multiplet (unclear number of split peaks) at 4.1 ppm, and simpler peaks at 3.6 and 1.6 ppm.  (12 pts)

a) Indicate which protons are giving the signals at each peak.

The 1.6 ppm is for the CH₃ Hs. The 4.1 ppm peak must before the CH(Cl) H due to the fact that its splitting was unclear (it is split by Hs on both sides) and the 3.6 ppm peak is due to the CH₂Cl Hs.

b) Predict the splitting pattern (e.g. triplet) observed at 3.6 and 1.6 ppm.

Both are doublets