What volume (mL) of a concentrated solution of sodium hydroxide (6.00 M) must be diluted to 187 mL to make a 1.53 M solution of sodium hydroxide

47.68 mL

Explanation:

In this case, we have a dilution problem. So, we have to start with the dilution equation:

We have to remember that in a dilution procedure we go from a higher concentration to a lower one. With this in mind, We have to identify the concentration values:

The higher concentration is C1 and the lower concentration is C2. Now, we can identify the volume values:

The V2 value has "mL" units, so V1 would have "mL" units also. Now, we can include all the values into the equation and solve for "V1", so:

So, we have to take 47.68 mL of the 6 M and add 139.31 mL of water (187-47.68) to obtain a solution with a final concentration of 1.53 M.

I hope it helps!