Concept explainers
To find: Decomposition of Sucrose Reacting with water in an acidic solution at , sucrose (C12H22O11) decomposes into glucose (C6H12O6) and fructose (C6H12O6)* according to the law of uninhibited decay. An initial amount of mole of sucrose decomposes to mole in 30 minutes. How much sucrose will remain after 2 hours? How long will it take until mole of sucrose remains?
Answer to Problem 19AYU
So, the amount of sucrose will be mole in hours or 395 minutes.
Explanation of Solution
Given:
An initial amount of mole of sucrose decomposes to mole in 30 minutes.
Calculation:
The function represents the amount of a radioactive material present at time . where represents the time of decay.
Substitute for , for and 30 minutes or for in the equation and find .
Taking log on both sides we get
Substitute for , 2 for in the equation and
So the amount of sucrose that will remain after 2 hours is moles.
Substitute for , for in the equation and find .
Taking log on both sides we get
So, the amount of sucrose will be mole in hours or 395 minutes.
Chapter 5 Solutions
Precalculus
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