Question

An insulated bottle contains 1 mole of hydrogen gas at P=1 atm and T=300K. Using a magic wand, you order all covalent bonds in the H2 molecules to break instantly. Assume that the magic wand supplies precisely the amount of energy necessary to br eak the bond in every molecule and makes them chemically inert (so they cant recombine) but does not affect the hydrogen otherwise. When the new equilibrium is established,

a) What is the new temperature of the (now) monoatomic hydrogen?

b) What is the new pressure of the monoatomic hydrogen?

c) Look up the hyd rogen bond dissociation energy to determine how much energy it actually took to perform the magic step. Imagine that the “magic” force keeping the hydrogen atoms inert suddenly fails. If ALL of the molecules were to form again, what would be the new temperature of the (diatomic) gas? (Note: it is interesting to think about what would actually happen once the magic is removed and the atomic hydrogen is allowed to behave according to physicl laws, and what the final state of the system would be. Here, I am not looking for an exact solution (It is pretty clear that It would be hard to convince all hydrogen to convert back to H2, given your result.

Answer 1

a) Since the energy supplied to the system is expended only in brake H-H bonds, the result will be that the number of moles and the pressure will double. So the temperature doesn't change- (300 K). If the energy to brake the bonds would come from the system itself it will become cold, but it is not the case because it is the magic wand that supplies the energy.

b) the new pressure will be 2 atm because the bottle is isolated.

c) then enthalpy of dissociation of H-H bond is 430 kj/mol so this is the energy expended in breake the bonds. In this case, because the magic hand is removed, the atoms combine again and release exactly the same 430 Kj, but the only receptor of that energy is the gas itself ,so the temperature will increase q = Cv(T2-T1) = (5/2)R(T2-T1)

Cv for a diatomic gas is

T2-T1 = 430/2.5R