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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?

Respuesta :

In this question, every time you rinse the flask, 1 ml of the solution will adhere and you add it with 9ml which will result as 10ml(1ml + 9ml). So, every time you rinse the flask it concentration will drop to 1/10 times of before. If the solution initial concentration is 0.9m, then the amount needed to rinse is:


Final concentration <= initial concentration *  (1/10) ^ rinse 
0.0001m<= 0.9m * 1/10^rinse
0.001m/ 0.9m<= 1/ 10^ rinse
0.11 * 10^-3 <=1* 10 ^ - rinse
rinse= 3

it needs at least 3x rinse to get the concentration into <0.0001 m
batolisis

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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