When a stock solution is diluted, the number of moles of solute (NaNO3 in this case) remains constant. Therefore, we can use the following equation to find the final molarity of the diluted solution:
M1V1 = M2V2
where M1 is the initial molarity (0.275 M), V1 is the initial volume (15.00 mL), M2 is the final molarity (what we want to find), and V2 is the final volume (100.0 mL).
First, we need to convert the initial volume from milliliters to liters:
V1 = 15.00 mL = 0.01500 L
Next, we can substitute the given values into the equation:
(0.275 M) × (0.01500 L) = M2 × (0.1000 L)
Solving for M2, we get:
M2 = (0.275 M × 0.01500 L) ÷ 0.1000 L
M2 = 0.04125 M
Therefore, the final molarity of the NaNO3 solution is 0.04125 M.