Question

The decomposition of N2O to N2 and O2 is a first-order reaction. At 730° C the half-life of the reaction is 3.58 × 103 min. If the initial pressure of N2O is 5.50 atm at 730° C, calculate the total gas pressure after one half-life. Assume that the volume remains constant.

_____atm

Answer 1

Answer :- 6.875 atm

-------------------------------------

Explanation :-

The decomposition of N2O to N2 and O2 is a first-order reaction.

At 730 °C,  the half-life of the reaction =

=

at 730 °C, initial pressure of N2O = 5.50 atm

---------------

The balanced reaction for decomposition of N2O is

....(A)

As reaction proceeds, pressure of reactant decrease while pressure of product increases.

Thus we can construct an ICE table for reaction (A)

initial pressure	5.5		0		0
change	- 2x		+ 2x		+ x
equilibrium (final) pressure	5.5 - 2x		2x		x

Final Total pressure PT is given by

.....(1)

we know that, after one half life the pressure of N2O must be half of it's initial value

i.e.

i.e. we have,   

i.e.

i.e.

i.e.  

i.e.  

thus after one half life the pressure of gasses are

Now from equation (1) the total pressure is

i.e.

Therefore, total gas pressure after one half life is 6.875 atm.

-------------------------