Reaction Kinetics, batch reactor varying volume

[MatStrat]

NO TEMPLATE BECAUSE THREAD WAS ORIGINALLY ENTERED INTO WRONG FORUM

Hi Guys,

I have attached the question that I am struggling with (part b of the question)

I have worked out that the conversion of A is X=0.21

Using this conversion I'm trying to work out the time required for the reaction

I am trying to use this equation: dCa/dt=Ra
where Ra is the reaction rate
but if i integrate the reaction rate i can't assume its constant due to volume and concentration changes so I'm in a bit of a dilemma.

Can you guys let me know if my reasoning is wrong, or if Ra is constant

 

[Chestermiller]

What is the total molar density in the reactor? Does this change as the reaction proceeds?