The density of 63.7 weight percent sodium hydroxide is 0.915 grams per milliliter. How many milliliters of water should be diluted to 850 ml to create 0.425 molar sodium hydroxide? Alright. So here they're asking us how many ml of water. It's really asking how many milliliters of solution should be diluted. That's what we're looking for. What we're going to do now is to isolate all the given information and see how we can isolate those ml of solution. We're told here that we have 63.7 weight percent sodium hydroxide. So that means we have 63.7 grams of sodium hydroxide for every 100 grams of solution. We're told that the density of the solution is 0.915, so that's 0.915 grams of solution per 1 milliliter of solution.

What else are we given? We're told that we have 850 ml to create 0.425 molar sodium hydroxide. So we have 850 ml. And then remember, molarity is moles over liters, so that's just 0.425 moles of sodium hydroxide per 1 liter. We're going to start out with 850 ml first because remember that's just one unit, easier to deal with. The others have a mixture of 2 units involved, harder to control. So we have 850 ml's. This 850 ml's is attached to this molarity. If we could change those mls into liters and multiply it by the molarity, we can isolate the moles of sodium hydroxide. So we're going to change mls into liters. Remember that 1 liter is 1,000 milliliters. Now that we have liters of solution, we can cancel out the liters from the molarity given. And that'll give us moles of NaOH at the end.

But here, we got to keep going. So far, we've used this portion of the given information. What do we have left? We have left the mass or weight percent and we're left with density. We know that we need to isolate ml's of solution which are right here. Next, I see that I have moles of NaOH. So if I could change them into grams, I can cancel out these grams of NaOH. So we're going to say here for every 1 mole of NaOH, what is the mass of NaOH? Well, it's made up of 1 sodium, 1 oxygen, and 1 hydrogen. And based on the atomic masses from the periodic table, each of them is 22.98977 grams, 15.99994 grams, and 1.00794 grams. Add them all up together, gives us 39.99765 grams. So we have grams of NaOH, so bring down the weight percent, 63.7 grams of NaOH here on the bottom, 100 grams of solution on top.

Finally, I can cancel out the grams of solution by using the density of the solution given. So we put 0.915 grams of solution here on the bottom and then, 1 ml of solution here on top. So when we punch all that in, that gives me 24.79 ml of solution. And here, we have 3 significant figures, 3 significant figures, 4 significant figures, and 3 significant figures. So we can round that just to 24.8 ml's of solution would need to be diluted to 850 ml's in order to create 0.425 molar NaOH solution.

Again, the wording of some of these problems can be a bit challenging, but the best approach like I've been saying is to write down what you're looking for first, write down all the given information, try to isolate the units that you need to get the desired answer at the end. Doing that helps us to navigate through all the wording, all the crazy jumbled numbers in order to get our final answer. So hopefully, you guys were able to follow along in terms of these typical types of dilution questions, and we'll continue onward into talking more about chemical reactions as well as stoichiometric calculations that'll become a focal point in discussing concentrations of solutions.