Question

List these in order of increasing entropy: (a) 0.01 mol of \(\mathrm{N}_{2}\) gas in a \(1-\mathrm{L}\) container at \(0^{\circ} \mathrm{C} ;\) (b) 0.01 mol of \(\mathrm{N}_{2}\) gas in a 2 -L container at \(0^{\circ} \mathrm{C} ;\) (c) 0.01 mol of liquid \(\mathrm{N}_{2}\).

Short answer

Question: Arrange the following conditions in order of increasing entropy: (a) nitrogen gas in a 1-L container, (b) nitrogen gas in a 2-L container, and (c) liquid nitrogen in a 1-L container. Answer: The order of increasing entropy is (c) < (a) < (b).

Step-by-step solution

Compare the physical state of the substance

In this exercise, we have two cases with nitrogen gas and one case with liquid nitrogen. As a general rule, gases have higher entropy than liquids because the particles in gases have greater freedom of motion and are more randomly distributed than in liquids. So, the order of entropy based on the state of the substance would be (c) < (a) or (b)

Compare the size of the container

Next, let's consider the size of the container. We have two cases with nitrogen gas: one in 1-L container (a) and another in a 2-L container (b). Since larger volumes provide more room for the gas particles to move around and create more disorder, we can conclude that the entropy of the system increases when the volume of the container increases. So, the order of entropy based on the volume of the container is (a) < (b).

Combine the factors

Now, let's put together the findings from step 1 and step 2. Comparing the cases considering the differences in physical state and volume, we arrive at the final order of increasing entropy: (c) < (a) < (b).