Hello, Isabella,
We'll find this answer by first looking into how many moles of nitric acid are actually required.
Molar is defined as moles/liter. To find the moles in 200ml of 0.100 M nitric acid we need to recognize that it can be written as 0.100 moles/liter. If we multiply that by the volume we have (200ml) the volumes will cancel, leaving us moles. But the units are different - one is liters and the other ml. Let's convert the 200ml into liters: 200ml*(1 liter/1000ml) = 0.200 liter nitric acid.
Now we can find the moles required: 0.200L*(0.100moles/L) = 0.0200 moles HNO3.
The concentrated HNO3 stock solution is 6.0 moles/Liter. We only need 0.0200 moles, so we want a volume that when multiplied times the concentration, will give that amount:
(6 moles/liter)*(Liters Required) = 0.0200 moles
Liters Required = 0.00333 liters, or 3.33 ml.
Add 3.33 ml of 6.0M HNO3 to 196.7 (200 - 3.33) ml of water to produce 200 ml of a 0.100M HNO3 solution.
I hope this helps,
Bob