Serial Dilution Question?
A flask initially contains 240ml of alcohol. The alcohol is then diluted by removing 60ml from the flask, replacing it with pure water until the volume again is 240mils, and mixing the contents together, if this process was repeated 5 times what would be the final volume of alcohol in the flask???
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Let initial volume of alcohol be XmL before a process, total volume is 240 mL so in 60mL we have X/4 mL alcohol then we use process:
step 1: remove 60 ml mixture => remove X/4 mL alcohol: 3X/4 mL left
step 2: fill with water => still 3X/4 mL alcohol left
So after 1 process, we multiply the amount by 3/4
After 5 processes, we multiply the amount by (3/4)^5
Thus final volume = 240 x (3/4)^5
..........................= 56.95mL (2dp)
Ist time you took away 60 ml alcohol, 2nd time 75% of 60 = 45 ml, 3rd time 75% of 45 = 33.75ml, 4th time 75% of 33.75 = 25.32 ml, 5th time 75% of 25.32 = 18.99 ml 6th and final time being one initial with 5 repeats = 14.24 ml.
60+ 45+ 33.75+ 25.32+ 18.99+ 14.24 = 197.3 ml.
240.0 - 197.3
= 42.7 ml alcohol final volume.
[Initial + 4 repeats
= 56.94 ml alcohol final volume].