Two chemicals A and B are combined to form a chemical C. the reaction rate is pr

Question

Two chemicals A and B are combined to form a chemical C. the reaction rate is proportional to the product of the amounts of A and B not yet converted to chemical C. Initially, the re are 60 grams of A and 40 grams of B. Each gram of C created consumes 1 gram of B and 3 grams of A. It is observed that 10 grams of C is formed in 5 minutes. Write an autonomous differential equation which gives the amount x of chemical C created in t minutes. Solve the differential equation. As time increases, how much chemical C is created? Which and how much of chemical A and B is left?

Explanation / Answer

a.) 3A +B ----> C

at time t let x gram C be formed so unused A = 60-3x and unused B = 40-x

dx/dt = (60-3x)*(40-x)

b)

dx/dt = (60-3x)*(40-x)

so, 1/(60-3x)*(40-x) dx=dt

integrate both side

[(60-3x)^3]/(40-x)=exp(60t)

c)

As A is 60 grams

as time increases total C formed will be 60/3=20 grams

B left = 40-20=20 g

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.