Two chemicals A and B are combined to form a chemical C. The rate, or velocity, of the reaction is proportional to the product of the instantaneous amounts of A and B not converted to chemical C. Initially, there are 40 grams of A and 50 grams of B, and for each gram of B, 2 grams of A is used. It is observed that 15 grams of C is formed in 7 minutes. How much is formed in 14 minutes? What is the limiting amount of C after a long time? How much of chemicals A and B remains after a long time?

25.35 grams of C  is formed in 14 minutes

after a long time , the limiting amount of C = 60g ,

A = 0 gram

and  B = 30 grams;           will remain.

Step-by-step explanation:

From the information given;

Let consider x(t) to represent the number of grams of compound C present at time (t)

It is  obvious that x(0) = 0 and x(5) = 10 g;

And for x gram of C;

  grams of A is used ;

also   grams of B is used

Similarly; The amounts of A and B remaining at time (t) are;

  and

Therefore ; rate of formation of compound C can be said to be illustrated as ;

=

where;

k = proportionality constant.

=

By applying the  separation of variable;

Solving by applying partial fraction method; we have:

Taking the integral of both sides ; we have:

Applying the initial condition x(0) =0  to determine the value of P

Replace x= 0 and t =0 in the above equation.

Thus;

Thus;

Applying the initial condition for x(7) = 15 , to find the value of k

Replace t = 7 into

k = 0.0013

Thus;

The amount of C formed in 14 minutes is ;

x(14) = 25.35 grams

Thus 25.35 grams of C  is formed in 14 minutes

NOW; The limiting amount of C after a long time is:

As;

⇒

= 60 grams

Therefore  as t → ;   x = 60

and the amount of A that remain =

=

= 40 -40

=0 grams

The amount of B that remains =

=

= 50 - 20

= 30 grams

Hence; after a long time ; the limiting amount of C = 60g , and 0 g of A , and 30 grams of B will remain.

I Hope That Helps You Alot!.

step-by-step explanation:

the answer is b