So we can use the equation: [tex] M_{1}V_{1}=M_{2}V_{2} [/tex]
where M is the concentration and V is the volume in liters.
We can then solve for how much of the stock solution we are going to put into the new solution:
[tex] (5M)(V_{2})=(1.5M)(0.5L) [/tex]
Then we can solve for V_{2}:
[tex] V_{2}=\frac{(1.5M)(0.5L)}{5M}=0.15L [/tex]
So now we know that we need to use 150 mL of the stock solution in the new solution - and we know that the total volume of the new solution is 500 mL. So therefore the rest of the new solution should be water:
[tex] 500-150=350 [/tex]
So the rest of the solution (350 mL) is water.
