Potassium nitrate has a lattice energy of -163.8 kcal/mol and a heat of hydration of -155.5 kcal/mol. How much potassium nitrate has to dissolve in water to absorb 1.00⨉10² kJ of heat?

Video transcript

Hey everyone in this example we're told that the lattice energy of sodium hydroxide is negative 887 kg joules per mole and its hydration entropy is negative 931.5 kg joules per mole. We're told that the solution releases 165 kg joules of heat but how much sodium hydroxide is going to be dissolved. So what we want to do is recall the following setup we have our entropy of our solution is going to equal the change in entropy of our salute added to the change in entropy of our hydration. And we should recall that the entropy of our salute is going to equal negative one times our lattice entropy which is going to equal negative one times according to the problem. The lattice entropy is given as negative 8 87 point oh kayla jewels per And so we can go ahead And multiply this by negative one so that we have a value of positive 87.0 Kayla jewels per mole. Now we're also given our entropy of hydration from the prompt which has a value Of -9 31.5 kg per mole. So we'll also plug that in. And so now we're going to find our entropy of our solution equal to The entropy of our salute which above the stated it's 887.0 Kayla Jules Permal. This is then going to be added to the entropy of our hydration which from the prompt is given as negative 9 31.5 kg jewels per mole. So this gives us a result equal to a value of -44.5, sorry, 44. kayla jewels per mole. So now that we have the change in entropy of our solution, we want to go ahead and use this info to find our mass of sodium hydroxide. So we would find this by taking the heat that is released according to the prompt from the solution as 165.0 Kayla Jules of heat which we will multiply by the entropy of our solution, which above we just found as negative 45 kg joules per mole. But we want to go ahead and write this in as a positive value since we know that that was A release of entropy. So this would be positive 44.5 kg jewels for one mole of solution. And so last we want to go ahead and end up with mass as our final unit. So we're going to plug in for one mole Of our solution of sodium hydroxide. The molar mass which from the periodic table is equal to a value of 40 graham's Permal. And so now we can go ahead and cancel out our units. We can get rid of moles as well as kill a jules leaving us with grams of sodium hydroxide as our final unit. And this is going to give us our mass of sodium hydroxide equal to a value Of 148.3 g of sodium hydroxide. And this would be our final answer for our mass of sodium hydroxide ingram's that was dissolved. So I hope that everything I reviewed was clear. If you have any questions, please, leave them down below and I will see everyone in the next practice video.