Consider the reactions:H2 2H (I)H H+ + e- (II)The ionization energy of H is 13.53 eV and the degeneracies of the electron and H are 2, while that of the proton is 1. It is suggested that the dissociation of H2 is essentially completebefore the ionization of atomic H begins.Verify this following these steps:a. At a total P = 1atm, find T at which [H+]/[H] = 0.01b. At this temperature T show that [H]>>[H2]

and the equilibrium constants for both reactions are

where the volume, V, is

At equilibrium

Combining the last equations and assuming that the initial number of molecules for H2 is equal to Avogadro’s number

we get a system of three equations and three unknown variables

From the last equation, it can be seen that, at that temperature, the reactions do not occur simultaneously. Then, to find the temperature at which

we only need to consider the second reaction and assume that

Solving these equations, we obtain that

.

part b

Now, to check if the assumption of independent reactions is correct, it is required to solve the equilibrium for the first reaction at the found temperature.

Assuming that the initial number of molecules for H2 is Nav, we have

Solving this equation we obtain that the number of atoms of hydrogen with respect to the initial number of molecules of hydrogen tends to 2, which means

and