At 5000 K and 1.000 atm, 83.00% of the oxygen molecules in a sample have dissociated to atomic oxygen. At what pressure will 95.0% of the molecules dissociate at this temperature

At ; 95.0% of the molecules will dissociate at this temperature

Explanation:

The chemical  reaction of this dissociation is:

The ICE table is as follows:

Initial               100                        0

Change            -83                      +166

Equilibrium          17                      166

The mole fractions of each  constituent is now calculated as:

= 0.9071

= 0.0929

Given that the total pressure = 1.000 atm ; the partial pressure of each gas is calculated by using Raoult's Law.

Now; we proceed to determine the equilibrium constant ; which is illustrated as:

Let assume that the partial pressure of be x ;&

the change in pressure of   be y ; then

we can write that the following as the changes in concentration of species :

Initial                    x                         0

Change              -y                          +2 y

Equilibrium         x - y                    2 y

From above; we can rewrite our equilibrium constant as:

From the question; we are told that provided that 95% of the molecules dissociate at this temperature. Therefore, we have:

%   -------- equation (2)

Solving and equating equation 1 and 2 ;

x = 0.123 atm

y = 0.117 atm

Thus, the pressure required can be calculated as :