Explanation Given information: Suppose A and B represent two substances that can combine to form a new substance C (chemists would write A + B —> C). Hence the rate or reaction of A and B to form C is proportional to ab. The C precipitates out of the solution as soon as it is formed, and the solution is always kept well mixed. Calculation: A and B are the two substances which combines to form C. That is, A + B —> C The a(t) and b(t) represent the amount of A and B in the solution respectively. The rate of reaction of A and B to form C is proportional to a(t).b(t). The rate of reaction A and B is proportional to a(t).b(t) gives, d A d t ∝ a ( t ) . b ( t ) d B d t ∝ a ( t ) . b ( t ) d A d t & d B d t ⇒ negative d A d t = − K a ( t ) . b ( t ) d B d t = − K a ( t ) . b ( t ) This is the required differential equation where K > 0 is the reaction rate parameter. A + B → C This involves the combination of molecules A and B to form another molecule C. The concentration of A decreases at twice the rate that the concentration of B decreases. − d A d t = − d B d t = d C d t = − K a ( t ) ⋅ b ( t ) Find K, K = r a t e a ( t )

4th Edition

ISBN: 9780495561989

Author: Paul Blanchard, Robert L. Devaney, Glen R. Hall

Publisher: Cengage Learning

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Chapter 2.1, Problem 26E

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Chapter 2.1, Problem 25E

Chapter 2.1, Problem 27E

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Chapter 2 Solutions

Differential Equations

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an approximate value for the parameters of the system being developed.

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