We are ready to begin our 7th learning objective in which way to learn to calculate the Delta S of the system. Se have previously learned to calculate the Delta S of the the surroundings from Delta H. Here we are going to do it for the system. We have led up to this by learning about the third law of thermodynamics. We were, actually, in this section going to be talking about doing it in standard state conditions. Here's our equation. The Delta s for a reaction is going to be the sum of the entropies of products minus the sum the entropies of the reactants. This equation we very, very similar to one that you saw when you dealt with thermochemistry and learn to calculate the Delta H of a reaction using the sum of the Delta H of formation of products minus the sum of the Delta H of formation of reactants. So we went to tables we were able to obtain those values and we always had to look at delta H but now that we know about the third law of thermodynamics we know we can talk about just entropy. We don't have to look at Delta S but just entropies of the products and reactants. But the process is so very very similar to what you did with Delta H of a reaction. Because of that similarity I will let you just go ahead and work a problem. In this problem you are going to determine the Delta S of the reaction that you see here. Go ahead and work it and then we will comment. Did you get 4 as your answer? Number 4 is your answer which is, 20 joules per Kelvin. If so then you work the question correctly. If not I'll go through some common mistakes. One common mistake is that students do not to incorporate that 2. They forget about the coefficients. So to get the Delta S we need to go 2 moles times the entropy of HCl. So that is one mistake that students make. Another common mistake as we continue on to this equation, is they forget to subtract the sum of these two things. So it is the S of the H_2 and you need to add that together with the s of the Cl_2. We have those that we would add together and then subtract. A common mistake is student will subtract the first and then add the second but you cannot. Subtract the first and then add the second. You will not want to do that. You want to subtract the sum both the those Now in that previous problem. and we'll look back at it here, we had 2 moles of gas on the left and we have 2 moles and gas on the right. What would happen if we had a reaction in which the number of moles and gas is increasing from reactants to products? So maybe we start with 1 mole of gas in the left and we have 3 moles of gas on the right. That would lead to an increased number moles of gas. What would you expect to be the sign of delta S in that case? Well, if you said positive you'd be correct because we know entropy of gases far higher than entropies of solid and liquids. So if you're increasing how much gas you have in your reaction chamber then you would have an increase in entropy. Now in their previous example we have the same number of moles of gas but we are seeing an increase in entropy. It is not a big increase, twenty joules per mole, but it is an increase. What do you think would lead to that increase in entropy? Well. its molecular complexity. We have 2 moles of gas that are elements. Then we have two moles of gas that are compounds. So we have increased the molecular complexity so we should see an increase in the entropy. Now let's go back to consider what would happen if we had a decrease in the number of moles a gas. Maybe your reaction had 4 moles of gas on the left hand side of the equation. The reaction sign and you are producing 2 moles on the right. What would you expect? Well in this case it would be a negative change because the moles of gas is decreasing. One more problem for you to work and here we are going to calculate the Delta G of a reaction by going back to thinking of a equation that you learned. That the Delta G over a reaction would be the Delta H at the reaction minus T, the temperature, delta S of the other reaction. Now that we have learned how to calculate the delta S of the reaction and if we are given the Delta H of a reaction. We are forced to calculate it, we can get the Delta G of a reaction and then determine whether a reaction is spontaneous or not. So calculate it. Did you come up with a -190.6 kilojoules? If so you did it correctly. If not here are some other common mistakes. Did you remember to work in Kelvin? I gave it to you in Celsius but you have to be working in Kelvin, in that equation. If you didn't work in Kelvin then you probably answered B. Did you watch your units? Another very common mistake of students'. Here is kilojoules our delta S is in joules, you have to make sure if we are going to have our answer in kilojoules that you've converted the entropy to kilojoules before you put it into the equation. The last choice of you selected D maybe you didn't watch sign here we have got a negative sign. A minus there and if you add instead of subtract you may have come up with an answer D. So this is the end of the learning objective number 7 in which we learned to calculate the delta S of a reaction by knowing the entropies of the products and the reactants. We also learned to predict the Delta s sign just by looking at the moles of gas and whether it's increasing or decreasing. Lastly we incorporated the Delta s for reaction into the equation that we see on this slide and obtain a value for the Delta G of a reaction. We know that if the Delta G is negative as it is in this case the reaction would be spontaneous in the forward direction.
