Dinitrogen pentoxide decomposes in the gas phase to form nitrogen dioxide and oxygen gas. The reaction is first order in dinitrogen pentoxide and has a half-life of 2.81 h at 25 ∘C. If a 1.7 −L reaction vessel initially contains 755 torr of N2O5 at 25 ∘C, what partial pressure of O2 will be present in the vessel after 215 minutes?

Answer : The partial pressure of is, 222.93 torr

Explanation :  

Half-life = 2.81 hr = 168.6 min

First we have to calculate the rate constant, we use the formula :

Now we have to calculate the partial pressure of

The balanced chemical reaction is:

Initial pressure   760                0             0

At eqm.             (760-2x)            4x            x

Expression for rate law for first order kinetics is given by:

where,

k = rate constant

t = time passed by the sample  = 215 min

a = initial pressure of  = 760 torr

a - x = pressure of  at equilibrium = (760-2x) torr

Now put all the given values in above equation, we get:

The partial pressure of = x = 222.93 torr