Given the values of ΔH°_rxn, ΔS°_rxn, and T, determine ΔS_univ and predict whether or not each reaction is spontaneous. (Assume that all reactants and products are in their standard states.) a. ΔH°_rxn = -95 kJ; ΔS°_rxn = -157 J/K; T = 298 K

Video transcript

Hello everyone. So in this video we're trying to calculate for our delta as of the universe as well as predict if the reaction is going to be spontaneous or not. And of course we're given this piece of information right over here. Alright, so let's first recognize the equation to solve our delta as of universe. So the delta S of our universe is equal to the delta us of the system, plus the delta us of our surroundings. So first part we're gonna go ahead and calculate for the delta S. Of the system. So actually the delta us of our system is equal to the delta us of our reaction. And conveniently we are given that right over here. So given to us that's going to equal to negative 2 jules per kelvin. So that's one component of this equation here let's calculate for the second part which is the delta us of our surroundings. So the delta as our surroundings. That it goes to the negative delta H. Of our reaction divided by R. T. For temperature. So if I'm going to go ahead and plug that numerical value in which is given to us here and here, we're gonna get this Positive 56. Since we have a negative and negative canceling out. So we have killer jewels, we're gonna wash they want to calculate that into jewels or convert that into jewels. So 103 jewels on top, one killer jewels on the bottom And then of course all this is going to be divided by R. T. for temperature which is 206 Kelvin's. Of course you can see that the kill jewel unit will cancel out leaving us with just the jewels as we want. All right, so putting all this into my calculator when numerical value is going to be to 71.84. And of course units being jewels per kelvin. Now that we have both components of this occasion here, let's finally plug in those numerical values. So we have that the delta S of the universe is equal to negative 2 jules per kelvin. And then we're adding the delta aspect of surroundings which were found to be to 71.84. Of course, units being jewels per kelvin. So putting that into my calculator. Then my final song for the Delta S of the universe is going to be 20.8 joules per kelvin. So that's one part of my answer. The next part of course is asking us if the reaction is going to be spontaneous. So how we calculate that is by solving for our delta G, delta G. The equation for that is going to be delta H minus t. Times our delta s. Of course we have all these numerical values already. So this would be simple. Our delta H is going to be negative 56 killer jewels. And we're going to subtract R. T, Which is going to be 206 K. or Kelvin's. And then we're gonna multiply that by the Delta S. So that's negative 2 51 jewels per kelvin. We're gonna go ahead and convert the jewels back into killer jewels. So we have one killer jewel on top and 10 to the third jewels on the bottom. Of course those jewels were cast out. Okay, so then Bringing all this into my calculator, the numerical value is going to be negative 4.29 and units is going to be just killed jules. And as you can see from this part, right over here, is that our kelvin's will cancel out as well. So we'll just have killed jules and kill jules. And that's why we have this unit here. And because we have a negative delta G. What that means is that also recognized that this is negative a negative delta G. Means that the reaction will be spontaneous. All right, and that's going to be the second answer for our problem. And again, our adult SF universities 20.8 joules per kelvin. And the reaction will be spontaneous. Alright, thank you all so much for watching