Gas Tank (Part 2)

Algebra Level 4

Suppose you start with a full gasoline tank containing 3000 moles of gasoline molecules. You use up $\frac{3}{4}$ of the gasoline in the tank, and then add new gasoline to completely fill up the tank again.

How many use-refill cycles does it take for there to be none of the original gasoline molecules left?

Details and Assumptions:

There are $6.022 \times 10^{23}$ molecules in a mole.
Assume perfect mixing at all times.
"None of the original molecules left" means that the expected number of remaining molecules is less than one.

The answer is 46.

1 solution

X X
Aug 17, 2018

There are $1.8066\times10^{27}$ molecules.

Each time we use the gasoline, the original molecules become one fourth of the previous. So we have to calculate $\log_4 (1.8066\times10^{27})$ . It is about $45.273$ , so the first time the expected number of remaining molecules is less than one is at the 46th time.

Gas Tank (Part 2)

The answer is 46.

1 solution

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