compound C is formed when two chemicals A and B are combined. The rate of the re

Question

compound C is formed when two chemicals A and B are combined. The rate of the reaction is proportional to the amounts of A and B remaining. For every 3 grams of A used, 4 grams of B are used, producing 7 grams of C. It is observed that 21 grams of C are formed in 10 minutes. Initially there are 60 grams of A, 70 grams of B, and O grams of C. (See pp. 96-97 for a similar example.) a) Determine the amount of C at any time e of round-off error. c) Determine how many grams of A, B, and C are present as t 00, -k(grams ofA remaining)(grams of Bremaining.whereX= grams of C produced. dt a dX Hint:

Explanation / Answer

Let x=gram of C produced

U(t)=gram of A remaining

V(t)=gram of B remianing

a)So, The equation to show the amount of C produced at any time is given as :

dX/dt = k (U) (V) .......(1) where k=propotinal contant.

Applying the integration condition over equation(1), we get

X(t) = k(UV)t + M ............(2) where M is integrating constant.

Initial condition is given as at time, t=0 , x(t=0) -0 so, M =0

so, the general solution becomes:

X(t) =k(UV) t .....(3)

Observed at t=10 mins, x(t=10) = 21 grams , so, k(UV=2.1 grams per minute is formed.

Hence , amount of C chemical formed at any time is defined as:

x(t) = 2.1 t ....(4)

b) A t tmine, t=20 mins , amount of C formed :

x(t=20 mins) = 2.1*(20)= 42 grams

c) When t is going to be infinite then,

Amount of A and B remianing becomes limited with C.

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