You want to clean a 500-ml flask that has been used to store a 0.9m solution. each time the flask is emptied, 1.00 ml of solution adheres to the walls, and thus remains in the flask. for each rinse cycle, you pour 9.00 ml of solvent into the flask (to make 10.00 ml total), swirl to mix uniformly, and then empty it. what is the minimum number of such rinses necessary to reduce the residual concentration of 0.0001 m or below?

The minimum number of rinses needed to reduce the residual concentration of 0.001 m is ;  3 rinses

Given that ;

For every rinse 1 ml of the solution adheres to the wall

For every rinse concentration drops by  1/10 ( 1 tenth times of previous conc ) because 9.0 ml of solvent is added for every rinse cycle

Initial concentration of solution =  0.9m

Determine the number of rinses ( n ) needed to reduce residual conc of 0.0001m  or below

using the relation below

Final concentration ≤ Initial concentration *  (1/10)ⁿ

0.0001m ≤  0.9m * 1/10ⁿ

0.0001m / 0.9m ≤  1/ 10ⁿ

0.00011 ≤ 1 / 10ⁿ

∴ 10ⁿ ≥  1 / 0.00011

     ≥ 9090.91

∴ n (  number of  such rinses ) ≈ 3

Hence we can conclude that the minimum number of rinses necessary to reduce the residual concentration of 0.001 m is ;  3 rinses.

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