Explanation Given Information: A biomolecular chemical reaction is one in which two chemical reacts to form another substance. The one molecule of each of the two chemical reacts to form two molecule of a new substance. If x represent the number of molecule of the new substance at time t , then the rate of change of x is proportional to the product of the number of molecule of the original chemicals available to be converted. If the each of chemically initially contained A molecules, then d x d t = k ( A − x ) 2 Where k is constant, if 40 % of the initially amount A is converted after 1 hours. Formula used: The differential equation can be equivalently expressed in the form g ( y ) d y = f ( x ) d x Then the equation is separable. The solution of a separable differential is obtained by integrating both sides of the equation after the variable have been separated. Calculation: Consider a biomolecular chemical reaction is one in which two chemical reacts to form another substance. The one molecule of each of the two chemical reacts to form two molecule of a new substance. If x represent the number of molecule of the new substance at time t , then the rate of change of x is proportional to the product of the number of molecule of the original chemicals available to be converted. If the each of chemically initially contained A molecules, then d x d t = k ( A − x ) 2 Where k is constant, if 40 % of the initially amount A is converted after 1 hours. Firstly, separate the above differential equation as: d x ( A − x ) 2 = k d t Integrate the provided function as: ∫ d x ( A − x ) 2 = ∫ k d t − ( A − x ) − 1 − 1 = k t + C 1 ( A − x ) 1 = k t + C At the given condition t = 0

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ISBN: 9781305713864

Author: HARSHBARGER

Publisher: CENGAGE L

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Chapter 12.5, Problem 38E

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To calculate: The time that will it be before 90% is converted, if 40% of the initially amount A is converted after 1 hours.

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Chapter 12.5, Problem 37E

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MATHEMATICAL APPLICATIONS FOR PKG

Ch. 12.1 - 1. True or false: (a) (b) Ch. 12.1 - Prob. 2CP Ch. 12.1 - 1. If what is Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - Prob. 4E Ch. 12.1 - Prob. 5E Ch. 12.1 - Evaluate the integrals in Problems 5-28. Check...Ch. 12.1 - Prob. 7E Ch. 12.1 - Evaluate the integrals in Problems 5-28. Check...

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The time that will it be before 90 % is converted, if 40 % of the initially amount A is converted after 1 hours.

Solution Summary: The author explains that a biomolecular chemical reaction is one in which two chemical reacts to form another substance. The rate of change of x is proportional to the number of molecule of the original chemicals available

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To calculate: The time that will it be before 90% is converted, if 40% of the initially amount A is converted after 1 hours.

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Chapter 12 Solutions