In particular chemical reaction, a grams of substance A react with b grams of substance B

Math Dec 02, 2020

In particular chemical reaction, a grams of substance A react with b grams of substance B. The number of grams of reaction product produced, x(t), at time t can be deterrnined by integrating both sides of the following relation where k is a constant for the reaction: dx (a — x)(b —)k f dt
Suppose x(0) = 0. Deterrnine x(t) if a = b = 50. (Write your numbers in the form of fractions a/b if needed.) x(t) =

Expert Solution

Since a = b is given

Integration left side becomes 1/(a-x)^2

Whose integration is 1/(a-x)

So both sides after integration become

1/(a-x) = kt + c

Since at t = 0, x =0

We have 1/(a-0) = 0+c

We get c = 1/a

Finally we get

1/(a-x) = kt + 1/a

Now at a= 50

We have 1/(50-x) = kt + 1/50

1/(50-x) = (50kt+1)/50

=> 50-x = 50/(50kt+1)

=> x = 50-50/(50kt+1)

=> x = 2500kt/(50kt+1)

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