So now we're going to work on Problem 72 from chapter 13 in this problem. Whereas three questions, Um, we want to prepare a solution of caesium bromide, which is Ah, zero point for morality. And we have a volume of 0.5 leaders to work with of water. So we needed first know what mask of caesium bromide ad. And then we want to know also the mole fraction and mass percent of this solution. So, first for morality, we need to calculate massive assault. So we're told that we have 0.5 leaders, so let's go ahead and see how much a mass that would be. So our density is given in milliliters, so we convert to milliliters, then we multiply by our density. And then finally we convert kilograms because that's what we need for morality. And then we see, perhaps unsurprisingly, to some of you that we have 0.500 kilograms of war. So if the density is one, than the number of leaders will equal the number of kilograms. But it's always best to make sure if you're not completely positive about the conversion. Um, so we're given the concentration that we want to have a 0.400 moral ality. CCM bride. That's what we want. And so this morality here is gonna be equal to the moles of caesium bromide divided by this mass we just calculated. So if we multiply both sides by 0.5, then we can calculate the molds of caesium bromide as being zero 0.200 moles. So the first question is, what's the Mass? So to find mass, all we need to do is multiply by the molar mass, which is 212.84 caesium reminded, and so that gives us the value of 42.6 grams. So this is the mass that we need to add to our 0.5 leaders to make this ah, solution. So that's the first answer. Second, we're asked, what is mole fraction? What is the mole fraction of the solution and then mass percent. So we know moles of caesium bromide already. We just need to calculate moles of water. So we have, um, kilograms as 0.500 for water. So we need to convert to grams and then multiply by the molar Mass. Excuse me. Divide by the molar mass to get the number of moles, which is 27.75 months. So to calculate more fraction, we just need to put the moles of caesium bromide over the whole. So we have 0.200 moles provided by 0.200 plus 27.75 models. And so when we do this calculation, we get a value of 7.1 six times 10 to the negative three unit list, of course, because of cancellation of the mole unit. So the last question is percentage of CCM bride specifically, uh, mass percent. So we calculated 42.56 grams as the amount of caesium bromide that we need. So we want to put that over the entire mass 42.56 grams, plus be 500 grams of water, which we get from the the 0.5 kilograms, and then we're calculating a percentage value. So we want to make sure we multiply by 100 and that gives a value of 7.84 percent.