Question About Kinetics Of Batch Reactor

Hi! I understand a lot of people come here to post their homework, just so someone else can solve it. I only have one doubt: i was trying to solve this problem, i can give it a rough translation:

 

Find the equation of first order for A on the gas fase, A → 1,6R, if the reaction volume, starting from pure A, is increased by 50% in 4 minutes. The total internal pressure is constant (1.2 atm) and the temperature is 25°C

 

The thing is that it's apparently supposed to be 0.447Ca, but i get 0.55Ca

Could someone possibily help to confirm if i'm wrong? I just started using moles, and then found the fractional conversion (5/6) from knowing that an increase of volume by 50% is the same thing as an increase in the total number of moles by 50%. Using the ideal gas law, we get that the total molar concentration is constant, and the concentration of A is the molar fraction of A times the total concentration. Then using that the change in concentration with time equals the reaction rate, i just integrate from the fractional conversion being 0 to 5/6 (but i changed the integration limits to make it easier to solve). What i don't understand is why using the equation that the change of moles of A in time equals the reaction rate times the volume yields a different result, like a friend of mine did, and found K=0.447. I would really like to know what i'm doing wrong!

I attached the original problem in portuguese, my answer (K=0.55) and my friend's answer (K=0.447)

I apologize if my question is not appropriate for the forum. Thanks!

 

 

Hi Pedro ,
As suggested in your original document , the answer is RA =- 0.447 *CA .
Hope this is helping you
Breizh

Thank you so much!! Really appreciated it! I admit i was a bit hopeful i was right hahaha, but at least now i know how it's done, thanks!