Hello, Ashley,
Molar is defined as moles per liter. We want a 0.5 M solution of HCl, but we want all we can get out of 200 ml of a 3 M HCL solution. That's 3 moles/liter concentration. Therefore, we can determine how many moles of HCl we have in total to play with. Since M is moles/liter, let';s change 200 ml into liters by dividing by 1000. We have 0.200 liters of 3 M HCl.
Let's find the total moles we've been given by multiplying 0.200 liters times 3 moles/liter. Liters cancel, leaving 0.6 moles HCl total.
We want a 0.5 M solution, so let's find out how much total water, X, is needed to make 0.6 moles into the 0.5 M final concentration:
0.6 moles/X = 0.5 moles/liter
X = 1.200 liters
So the final solution is we add 1000 ml to the 200 ml of 3N HCL, to bring the total to 1.2 liters. That makes the finakl concentration 0.5 M
(0.6 mole HCl)/1.2 liters = 0.5 moles/liter or 0.5 M
Bob
