What is the volume of a 1.5 molar HCl solution that is required to prepare 1.0 liters of a 0.06 molar HCl solution? A) 10 milliliters, B) 20 milliliters, C) 40 milliliters, D) 100 milliliters, or E) 200 milliliters.
In this question, a diluted solution of HCl is being prepared from a more concentrated HCl solution. If we were doing this in a lab, we would take some volume of the concentrated HCl solution, preferably with some accurate piece of glassware such as the volumetric pipette, and then transfer that volume of concentrated HCl to a new container. We would then add water to the new container so that we had a total of one liter of solution.
Since this problem is a dilution problem, we can use this formula to solve for the volume that we need to take from the original solution. This formula tells us that the concentration of the original solution times the volume that you take from the original solution will be equal to the concentration of your new solution times the total volume of the new solution.
Before we use this formula, it’s worth understanding why it makes sense. Since concentration is given in units of moles per liter and volume is given in units of liters, liters here cancel. So this formula tells us that the moles that we take from the original solution, in this case moles of HCl, will be equal to the moles of HCl that end up in the diluted solution, which makes sense intuitively. The amount of HCl that we take from the original solution has to be equal to the amount of HCl that ends up in the diluted solution.
In this question, we need to solve for the volume of the original solution that we need to take to create the diluted solution. We can create an expression that we can use to solve for this volume by dividing both sides of our dilution expression by the original concentration of the stock solution. This original concentration is 1.5 molar. The question tells us that we’re preparing one liter of our diluted solution, so 𝑣 two is one liter. And the concentration of the diluted solution is 0.06 molar. The units of the concentration here cancel, leaving us with units of volume, which is what we’re going for.
But the units in the answer are all expressed in milliliters, and right now, we’re in liters. So let’s go ahead and do that conversion now. There are 1000 liters in one milliliter, so our 𝑣 two is equal to 1000 milliliters. Multiplying by 1000 shifts the decimal place three places to the right, so 0.06 times 1000 is equal to 60. Dividing 60 by 1.5 might be a little tricky to do in our heads. But 1.5 expressed as a fraction is three-halves. Dividing by a fraction is the same thing as multiplying by the reciprocal of that fraction. So 60 divided by three-halves is the same thing as 60 times two-thirds. 60 times two gives us 120, and 120 divided by three gives us 40.
This matches answer choice C. It would take 40 milliliters of a 1.5 molar HCl solution to prepare one liter of a 0.06 molar HCl solution.