BTW if I had to bet my money I think you are of Indian origin (Since you know about Ayurvedic and "Being 26 makes you the old guy"
I think the answer is: C. the particles have the same kinetic energy, so the molecule with the largest mass (CO2) will be going slower than the other particles. I imagine the limiting case where there's a particle so massive that is barely moves at all. Other particles will ram into it before it has gotten very far. So in the less extreme case of CO2, the same principle should apply.
" which MUST be correct" statement III does not need to be true depending on the temperature of the reaction
I think there was a section and an example in TBR about this
My answer is: (b) II only. You stated in the problem that as contraction occurs, dS is positive thus making dH positive due to the statements. Positive dH means the reaction is endothermic so the heat is being absorbed by the rubber band. I was about to choose both II and III until I reread your statements
For me it would have to be this answer: A. In my mind, B and D make no sense as choices. I feel that C is the distractor as you would think large molecules = slower velocity. However, shortest mean free path is the distance between collisions. I think Helium with its higher velocity would encounter collisions at a faster rate and a shorter distance.
C is the answer
Loveanswers reasoning was correct. Mean free path is the distance a molecule will travel before colliding with another molecule. The velocity is irrelevant to how far it will travel before colliding with another, it would only tell us that helium would collide with another object sooner but not necessarily in a shorter distance.
Mathematical explanation is that mean free path is proportional to V/n and inversely proportional to the cross sectional area of the molecule. Since PV = nRT we have, mean free path = RT / P. The quantity is the same for all the gases so the only factor that remains is the cross sectional area. CO2 is the largest molecule out of our choices and is the correct answer.
velocity is irrelevant when all particles are the same mass, but I think it should matter when they're going different speeds.
Imagine if there's a particle, of the same size as CO2, that's extremely massive, so massive that it takes the particle 1 billion years to move infinitesimal distance dR. Over the course of 1 billion years, the particle will have gone tiny distance dR, and surely would have encountered many collisions in that time. It would encounter collisions if it didn't move at all. So the massive particle's average distance is dR ÷ (number of times it gets hit every billion years). The average distance the other particles go before collisions is obviously greater than dR.
Another example. Imaging there are only two particles in your volume. Every collision that occurs is clearly between the two particles. Let's call the average time between collisions t. If the particles have the same mass, they will be going the same speed v, and thus have the same distance vt between collisions. But if one particle is massive with smaller velocity v than a less massive particle with velocity V, the big particle will go vt and the small paorticle will go Vt. V>v, so small particle goes larger distance.
EDIT: I initially interpreted this question as implying the gases will be mixed together. Rereading, I guess the problem intended for the gases to be kept separate? In that case, mass doesn't matter. That's MCAT style ambiguity true and true, good job
I actually disagree, I think the problem is clearly intending the gases to be mixed together in the same previously evacuated container.velocity is irrelevant when all particles are the same mass, but I think it should matter when they're going different speeds.
Imagine if there's a particle, of the same size as CO2, that's extremely massive, so massive that it takes the particle 1 billion years to move infinitesimal distance dR. Over the course of 1 billion years, the particle will have gone tiny distance dR, and surely would have encountered many collisions in that time. It would encounter collisions if it didn't move at all. So the massive particle's average distance is dR ÷ (number of times it gets hit every billion years). The average distance the other particles go before collisions is obviously greater than dR.
Another example. Imaging there are only two particles in your volume. Every collision that occurs is clearly between the two particles. Let's call the average time between collisions t. If the particles have the same mass, they will be going the same speed v, and thus have the same distance vt between collisions. But if one particle is massive with smaller velocity v than a less massive particle with velocity V, the big particle will go vt and the small paorticle will go Vt. V>v, so small particle goes larger distance.
EDIT: I initially interpreted this question as implying the gases will be mixed together. Rereading, I guess the problem intended for the gases to be kept separate? In that case, mass doesn't matter. That's MCAT style ambiguity true and true, good job
The question was very good, and pedagogical. I haven't encountered the answer to it in my studies. All questions of this type that I have seen involved uniform gases, not gases of different particles. I am 99% sure that my reasoning is correct, because the limiting cases described seem undeniable. But GTLO wants to hear the correct answer from an authority in the subject. I have never seen this question answered, though. Might take some digging to find it.
