The conversion of natural gas, which is mostly methane, into products that contain two or more carbon atoms, such as ethane (C₂H₆), is a very important industrial chemical process. In principle, methane can be converted into ethane and hydrogen: 2 CH₄(g) → C₂H₆(g) + H₂(g) In practice, this reaction is carried out in the presence of oxygen: 2 CH₄(g) + 12 O₂(g) → C₂H₆(g) + H₂O(g) (b) Is the difference in ΔG° for the two reactions due primarily to the enthalpy term (ΔH) or the entropy term (-TΔS)?

Video transcript

Hello everyone. So in this video we're given a bunch of entropy and entropy values and we're trying to see if the entropy value or the entropy value or term is going to give us a greater difference on our delta G. S. And were given two different reactions which is going to be this one and this one. So let's see what plays a bigger factor here in the comparison of these two reactions. So I'm just gonna scroll down because we don't have too much space here. Alright so the main reaction that we're going to be focusing on will be I'll write it to the right here will be that delta G is equal to delta H minus temperature multiplied by delta us. So for our delta H that is equal to the delta age of the products minus the delta H. Of our reactant and the same thing for a delta us. Okay so this is the main reaction that we're focusing on and then these two are just the components of our delta H and delta s. Okay so we're gonna go ahead and determine the delta H. And delta us. For each reaction giving these values here. So for our first reaction We have 2 C2 H six to go ahead, decompose to c. four h. 10 and H. Two. So first we'll go ahead and use or find our delta H. Let's see here. So again we're just using the values given to us in the table here. So for our delta h of our products we see that we have let's see we have negative 200 or negative 100 25. -2 times. So we have let's see 84.68. Bringing that into my calculator, we can get the value of 43.66 killer jewels. Then for my delta us again using the products or the given information to us in the table We have a seat 3 10 plus 130.7. And then we'll subtract that With the values for our reactant, which is going to be two times 2-9.21. So putting all this into my calculator, I will get the value of -17.7 and the units is going to be jewels per kelvin. And moving on to my second reaction, The second reaction is four C. To age six Reacting with 02 to go ahead and make two moles of C four H And two moles of H 20. So again, something for our delta H. First We have two times the negative 125.7 plus two times negative 2 41.8. And we're going to subtract that with four times. Let's see here we have negative 84.68 plus zero. So put all those values into your calculator. I get the value of -3 96.28. Kill Jules. Now for my delta us again it's of the products minus of the reactant. So we have two times 310.0 plus two times 88.8. And we're going to subtract this with four times 2 to 9.2 plus 205.2. Again I'll go ahead and put these values into my calculator and what I do. So I get the numeric value of 1 24.4 units being jewels per kelvin. So we can see here that both reactions have a negative delta S. Value. So we have negative here and negative here. But for the delta H values we see for our first reaction we have a positive delta H. Meaning that this reaction is going to be endo thermic. And for our second reaction we see that our delta H. Is negative. If we have a negative delta H. This means that the reaction is going to be X. A thermic. So we see now that if we compare the two different values or our terms of comparing our entropy term or the entropy term, we see that our delta H has a greater effect. So then our answer is that the delta H has a greater effect. So then this part right here is going to be our final answer for this problem. Thank you all so much for watching