Calculate ∆Stotal, and determine whether the reaction is spon-taneous or nonspontaneous under standard-state conditions. (a) -429 J/K; nonspontaneous (b) -123 J/K; spontaneous (c) +3,530 J/K; nonspontaneous (d) +184 J/K; nonspontaneous

Video transcript

Hello everyone today. We have the following problem. Consider the following reaction. What is the total entropy? What is its spontaneity under standard state conditions. So first we need to find the formula or recall the formula for the total entropy and that's going to be the entropy of the surroundings plus the entropy of the system to find the entropy of our system. That's going to require a separate formula. That's essentially going to be just the change in entropy overall. Which is going to be the difference between the entropy of the product. So the entropy of our product minus the entropy change of our reactant. So We need to solve for the entropy of our system 1st. And so how are we going to go about that? Well our products and this reaction our both this fluoride gas or flooring and then we have our iodide here so we have our one mole of flooring which we're not one ball of flooring. We're going to multiply that by its entropy value which is 202 jewels per kelvin mole. And then we're gonna add that to our two moles Of Iodide. We're gonna multiply those two moles by its entropy value which was jewels per Kelvin mole. And that's it for our products and we're going to subtract by our reactant which is two moles of our fluoride Times its entropy value which is negative 13.8 jewels per Kelvin Mole and then we're gonna add that to the one mole of iodide which has an H A P value of 1 16 .1 Jewels Per Kelvin Mole. So when we do these calculations, we end up with an entropy of the system equaling 336. jewels per kelvin. No, we need to solve for our entropy of our surroundings. So the entropy of our surroundings and this is going to be equal to negative change in entropy over our temperature. We need to solve for our change in entropy first, which is going to be equal to the change in the entropy for our product minus the change in entropy for our reactant as we did before. We're going to have our products here which was the one mole of flooring. We're going to multiply that by zero because that is its value and then we're gonna add that to the two moles of iodide, Followed by multiplying that by its entropy changes was 55 or negative 55.2 kg per mole. We're going to subtract that by the reactant which was two moles of our fluoride And its entropy change was 3 32.6 kg per mole. And then we're gonna add one mole of our iodine and multiply that by zero. When we saw for this we get an entropy change of 5: 0.8 kg joules. Now the question stated that there was under standard state conditions and that means that our temperature is equal to 273 Kelvin with this, we can solve for our change in the entropy for our surroundings, which we said was negative. The change in our entropy was said to be 554.8 kg joules And our temperature was 2 73 Kelvin. This is going to give us a value of negative 2. kilograms per kelvin. However, this has to be in terms and units of jewels And so we're going to multiply by the conversion factor that one killer jewel is equal to 1000 jewels. And when our units cancel we're left with negative 2,032. jewels per kelvin. Last but at least we can finally circle back and solve for our total entropy, which we said before was the entropy of our surroundings plus the entropy of our system. Those two values were 3 36.2 joules per kelvin and -2032. Joules Per Kelvin. And that value is going to add up to negative 1696.03 jewels per kelvin and because it is negative, this is going to be non spontaneous. And so with that we have solved this problem overall, I hope this helped and until next time