A solution is tested and found to have a concentration of 0.50 M. If you measure 0.50 L of the solution, how many moles of solute are known to be...

Molarity is equal to the number of moles of solute divided by volume in liters.

   Molarity (M) = moles (mol)/liters (L)

If you have a 0.50 M solution, this means that there are 0.50 moles dissolved in 1 L of solution.

Notice that your question asks you about 0.5 L of the 0.50 M solution. Often in word problems, the word "of" is a clue to multiply. So, let's try multiplying 0.5 L times 0.50 M.

   (0.5 L)(0.50 M) = 0.25 unit?

When we set up our calculation as shown above, it's hard to tell what the unit in our answer is.

Let's try setting it up by writing the molarity value in terms of moles/liter.

   (0.5 L)(0.50 moles/1 L) = 0.25 mole

Now we can see that the unit of liters (L) cancels out leaving us in moles, which is what we want! So, 0.25 moles of solute are dissolved in the solution.