- (a) Thompson KC, Crittenden DL, Jordan mJT (2005) J Am Chem Soc 127:4954. (b) Schreiner
PR (2000) Angew Chem Int Ed Engl 39:3239. (c) Marx D, Parrinello M (1999) Science 284:59;
White ET, Tiang J, Oka T (1999) Science 284:135
Chapter 2, Harder Questions, Answers
Q2
How high would you have to lift a mole of water for its gravitational potential
energy to be equivalent to the energy needed to dissociate it completely into
hydroxyl radical and hydrogen atoms? The strength of the O–H bond is about
400 kJ mol#^1 ; the gravitational accelerationgat the Earth’s surface (and out to
hundreds of kilometres) is about 10 m s#^2. What does this indicate about the role of
gravity in chemistry?
This was put in the “Harder Questions” category because the answer can’t be
found just be reading the chapter, but actually the solution comes from a straight-
forward application of simple physics.
The energy needed to homolytically dissociate a mole of water into HO.And H.
is ca. 400 kJ. We want to calculate how high 18 g of water must be lifted for its
gravitational potential energy to be 400 kJ. Working in SI units:
Pot E¼force%distance¼mgh,energy in J, mass in kg, g in m s#^2 , h in m
h¼Pot E=mg¼ 400 ; 000 = 0 : 018 %10 m¼ 2 % 106 m or 2,000 kmActually the height is the same regardless of the mass of water, since, e.g.
doubling the mass doubles both the energy needed for dissociation, and m in the
denominator. The calculation is flawed somewhat by the fact that the force of
gravity is considerably smaller 2,000 km above the surface of the Earth (radius¼
6,000 km) (by a factor of (8,000)^2 /(6,000)^2 ¼1.8). A more realistic calculation
would express the force as a function of h and integrate with respect to h. This
calculation does however show that if all the potential energy were somehow
directed into dissociating the H–O bond, a fall from a great height would be needed!
Chapter 2, Harder Questions, Answers
Q3
If gravity plays no role in chemistry, why are vibrational frequencies different for,
say, C–H and C–D bonds?
Answers 595