How many grams of CaO should be dissolved in sufficient water to make 1.00 L of a solution with a pH of 10.50?

Video transcript

Hi everyone for this problem. It reads calculate the mass of lithium oxide required to be dissolved in a 1.55 liter of water to prepare a solution with a ph of 11.5. So our goal here is to calculate the mass of lithium oxide. Okay, and in the problem we're given volume of the solution, which is 1.55 liters and were also given the P. H. So let's go ahead and get started by looking at what we have, which is lithium oxide. And this is a group one oxide that will react with water to form lithium hydroxide. Okay, so let's go ahead and write out that equation. Or that reaction we have lithium oxide which is a group one oxide is going to react with water to form lithium hydroxide and lithium hydroxide is the compound that will make the solution basic. Okay, so there should be a two here to make that balanced. Okay, so what we're going to do then is because we have a basic solution, we will solve this problem by first converting ph two P O H. Okay, so we're gonna take P. H and convert it to P O. H. And to do that, we need to know the equation and that is P H plus P O H. Is equal to 14. So, since we want to solve for P O. H, we need to isolate this. So this becomes P O H is equal to 14 minus P H. And then the problem we were given the ph so we have minus 11.50. So that gives us a P. O. H. Equal to 2.50. Okay so now that we know what the P. O. H. Is, the second thing that we can do is we can find the concentration of hydroxide using the P. O. H. Okay so let's go ahead and do that. The way that we're going to do that is P. O. H. Is equal to the negative log of hydroxide concentration. Okay so that means that if we're trying to find the concentration of hydroxide it's going to equal 10 to the negative P. O. H. And we know what the P. O. H. Is. So we just need to plug that value in. So we have our concentration of hydroxide is going to equal 10 to the negative 2.50. That we just calculated up above. So our concentration of hydroxide is equal to zero . - three Moller. Alright. And we know that lithium hydroxide is a strong base. So let's just take a note of that. So lithium hydroxide is a strong base. And what this means is it is going to dissociate completely. Okay and so when we have our lithium hydroxide, this breaks down into the lithium ion plus the hydroxide. And ion. Alright, so with lithium hydroxide being a strong base. This means that the concentration of hydroxide is going to equal the concentration of lithium hydroxide. So we know what our concentration of hydroxide is. And it is What we just calculated 0.00316-3 moller. So this is the same. Our concentration for hydroxide and lithium hydroxide are the same. So now we just have the last step to do and or the third step was what we just did right now, which was let's move this down. So this third step that we just did was we we found the malaria t of lithium hydroxide. We found the milan city of lithium hydroxide using the value of the concentration of hydroxide. Okay, so now we just have one last step to do. And that is we're going to use stoke Eom a tree to find the mass of lithium oxide. Okay, and let's just take a look here. Yes, So we're gonna use stoke eom a tree to find the mass of lithium Oxide. And we're gonna do that by first. Starting with what was given in this problem which is we have a volume and that volume is going to be our starting point. So we have 1.55 L of solution. Okay, now we want to go from leaders of solution. Two moles. Okay, and we'll do that using the malaria T that we just found for our lithium hydroxide. Okay, So we have 0. moles of lithium hydroxide per one liter of solution. That is the value right here the concentration of lithium hydroxide is moles over leader. Okay, so we have 10.31 point 0031623 moles per one liter of solution. So now we want to go from, we want to know how many moles we need to use the multiple ratio now to go from lithium hydroxide to lithium oxide. And we do that using our equation our reaction. Okay, so let's go back up to our reaction. So we're gonna compare our multiple of lithium hydroxide to lithium oxide. So we have one mole of lithium oxide for every two moles of lithium hydroxide. That's our multiple ratio. And that's how we're going to go from moles of lithium oxide, two moles of lithium. How we're gonna go from most of lithium hydroxide to most of lithium oxide. So let's do that right here. So based off of our stoke Yama Tree, there's two moles of lithium hydroxide For every one mole of lithium oxide. Okay, so let's just take a look at our units that cancel so far our volume of solution, cancels our moles of lithium hydroxide cancel. And now we have moles of lithium oxide. The question asks us for the mass of lithium oxide. So we have one more step to go, which is we want to go from moles of lithium oxide two g of lithium oxide. So we need the molar mass. We'll need the periodic table for this and one mole of lithium oxide. There is 29. g of lithium oxide. Alright, so most cancel. And we're left with g, which is what we're looking for. We're looking for mass. So our final answer here is once we do the calculation are mass of lithium oxide is going to equal 0.073g. And this is our final answer. That is it for this problem. I hope this was helpful.