Final answer:
20 mL of concentrated nitric acid (15.0 M) is required to prepare 100 mL of a 3.0 M diluted solution by using the dilution formula M1V1 = M2V2.
Step-by-step explanation:
To calculate the volume of concentrated nitric acid (15.0 M) needed to make 100 mL of a 3.0 M solution, we use the dilution equation which is M1V1 = M2V2, where M1 is the molarity of the concentrated solution, V1 is the volume of the concentrated solution needed, M2 is the molarity of the diluted solution, and V2 is the volume of the diluted solution. Using the given data:
- M1 = 15.0 M (concentrated nitric acid)
- M2 = 3.0 M (diluted solution)
- V2 = 100 mL (diluted solution volume)
We need to rearrange the formula to solve for V1: V1 = (M2 * V2) / M1
Now, plug in the numbers: V1 = (3.0 M * 100 mL) / 15.0 M = 300 mL / 15 = 20 mL. So, 20 mL of concentrated nitric acid is required to make 100 mL of a 3.0 M solution.
Remember, in this calculation we did not need to convert volumes to liters because the mL units cancel out, giving us a volume in mL directly. However, if the units were different, you would need to use a conversion factor.