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What volume (mL) of a concentrated solution of sodium hydroxide (6.00 M) must be diluted to 406 mL to make a 1.64 M solution of sodium hydroxide?

A. 0.104
B. 0.0100
C. 3600
D. 287
E. 99.9

Answer :

Approximately 111 mL of a 6.00 M NaOH solution is required to be diluted to 406 mL to make a 1.64 M solution, with option e. 99.9 being the closest answer choice provided. The correct option is E

To determine the volume of a concentrated sodium hydroxide (NaOH) solution that must be diluted to make a new solution of a specific concentration, we can use the dilution formula which is: C1 imes V1 = C2 imes V2, where C1 and V1 are the concentration and volume of the original solution, respectively, and C2 and V2 are the concentration and volume of the final solution, respectively.

We have a concentrated NaOH solution with a concentration of 6.00 M (C1) and we want to make a 406 mL (0.406 L) solution of NaOH at a concentration of 1.64 M (C2). Using the formula, we calculate V1 as follows:

(6.00 M) imes V1= (1.64 M) imes (0.406 L)

To find V1, divide both sides of the equation by the initial concentration (C1):

V1= (1.64 M imes 0.406 L) / 6.00 M

Simplifying, we find that:

V1= (0.66584 L) / 6.00 M

V1 = 0.11097 L or 110.97 mL

Therefore, approximately 111 mL (option e. 99.9, rounded to the closest listed choice) of a 6.00 M NaOH solution must be diluted to 406 mL to achieve a 1.64 M solution.

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