Which state in each of the following pairs has the higher entropy per mole of substance? (b) N₂ at STP or N₂ at 0 °C and 10 atm

Video transcript

well. Everyone in this video, we're being asked to identify which one has a higher entropy per mole between helium at zero degrees Celsius and at 58 E. M. And helium at standard temperature and pressure at zero degrees Celsius 1 80 M. And 22.4 liters. So let's go ahead and recall what entropy is. Entropy is. A measure of disorder or randomness. Alright, so between helium at STP and helium as their degree Celsius and 50 M. The former has the higher entropy per mom. So the factors that we can compare this with of course is from the given information that's just pressure and volume. So for helium at S. T. P we have a pressure being at one A. T. M. And the volume equal to 22.4 liters. Now for helium at zero degrees Celsius and 50 A. T. M. Of course the pressure is at 58 E. M. But the volume is unknown. So assuming a mole of helium gas, which is an ideal gas, Its volume can be calculated using the equation PV equals N. R. T. So calculate for volume that should ve going to N. R. T. Overpay I isolated V by dividing both sides by P. So if we do so putting in the numbers here. So for the molds we have, we just said assuming one mole and for my art, my gas constant that 0.8 to 06 units being leader times A T. M. Over mole times kelvin. And then we're multiplying this with temperature and temperature. What we said to be 0°C to convert C into Kelvin's. We're adding to 73.15 is divided by pressure. Were established that the pressure is 58 E. M. So putting everything into my calculator, I get my volume TB 0.448294 liters. So the volume at S. T. P is 22.4 liters. Actually write this out. So again the volume of helium at S. T. P. Is 22.4 and this is going to be greater than the helium at zero degrees Celsius and 50 80 M, which has a volume of 0.448 liters. So since helium at STP has a greater volume, there's going to be more room or space or freedom whatever you wanna call it, for the same amount of atoms, a bump into each other and into the walls of the container, which means there's more mobility and means that we have greater randomness and disorder, therefore meaning that we have a higher entropy. So our answers to this question is that the one with the higher entry paper mole is the helium at centered temperature and pressure at zero degree Celsius 1 80 M and 22. liters. So this right here is going to be my final answer for this problem