A chemist must dilute 54.9 ml. of 9.84 M aqueous sodium nitrate (NaNO3) solution until the concentration falls to 4.00 M. She'll do this by adding distilled water to the solution until it reaches a certain final volume.
Calculate this final volume, in liters. Be sure your answer has the correct number of significant digits.
To calculate the final volume of the solution, we can use the formula for dilution:
M1V1 = M2V2
where:
M1 = initial concentration of the solution = 9.84 M
V1 = initial volume of the solution = 54.9 ml = 0.0549 L
M2 = final concentration of the solution = 4.00 M
V2 = final volume of the solution (what we need to calculate)
Plugging in the values:
(9.84 M)(0.0549 L) = (4.00 M)(V2)
0.5416 = 4.00V2
V2 = 0.5416 / 4.00
V2 = 0.1354 L
Therefore, the final volume of the solution, when diluted to a concentration of 4.00 M, is 0.1354 liters.