Question

# A zero-order reaction is 40% complete at the end of 50 minutes. What is the value...

A zero-order reaction is 40% complete at the end of 50 minutes. What is the value id the rate constant with proper units? In many minutes will the reaction be 80% complete?

Suppose the reaction is

A => B

Rate of reaction

Rate of disappearance of A (-rA)= Rate of formation of B (+rB) = k ........where k is rate constant

-dCA/dt = k

-dCA= kt

integrate the above equation in the limits CA0 to CA at t= 0 to t

So the integration within the limits wil give

CA0- CA= -kt

(CA0= initial concentartion in mol/L of A at t=0 mins, CA= concentartion of A in mol/L at t=t mins)

Now 40% of reaction went to completion in 50 mins.

Means the 40% of A is reacted to produce B in 50 mins.

So,

CA0- CA = CA0 - 0.60 CA0 = 0.40 CA0

And t= 50 mins

So, put this in above equation

0.40 CA0 = -50k

k= - (0.40/50) CA0

k= -8*10-3 CA0 mol/(L.min)

Now for 80% completion

CA0-CA = 0.80CA0

Then,

0.80CA0 = -kt

0.80CA0 = - (-8*10-3) CA0 * t

t= 100 mins

So in 100 mins reacion will be 80% complete.