Question

Which reaction has the largest positive value of ΔS?

A. CO2(g) + 3H2(g) → CH3OH(g) + H2O(g)
B. 2Al(s) + 3S(s) → Al2S3(s)
C. CH4(g) + H2O(g) → 3H2(g) + CO(g)
D. 2S(s) + 3O2(g) → 2SO3(g)

Answer 1

C. Because it is the only reaction in which the number of moles increases from products to reactants. As the number of moles increases, the entropy increases, so ΔS would be positive.

Answer 2

Sorry, but why does the entropy increase when number of moles increase?

Answer 3

Because entropy is the measure of the disorder in a system. Basically, I interpret it as predictability. With a low number of moles, the arrangement and location is very predictable...low entropy. But with a high number of moles, it is not very predictable...high entropy.

Answer 4

Because there are more ways to arrange a larger number of molecules in a given volume.

For example, suppose in this reaction you begin with 1 CH4 molecule and 1 H2O molecule, and suppose they are in a very small box so there are 10,000 different locations each molecule could be in. Then there are 10,000 x 9999 = 1.0x10^7 ways to arrange those two molecules. The entropy S = k ln W, where W is the number of ways to arrange the molecules, so S = 18.42 k.

Now after the reaction you have 3 H2 molecules and 1 CO molecule. The number of ways to arrange these molecules in the same box is (10,000 x 9999 x 9998 x 9997)/6 = 1.6 x 10^15, and the entropy is 35.05 k, which is substantially larger.

The part of this that might be unfamiliar to you is the Boltzmann equation, S = k ln W, which defines entropy in terms of the "number of microstates" W of the system. A "microstate" is any state of the system that is consistent with its thermodynamic state -- which is determined (for a gas) just by its temperature, volume, and mole number. There are clearly many different ways you can arrange the molecules in a gas -- many different locations and velocities of each individual molecule -- that will end up giving you a gas at the same temperature, volume and mole number. The entropy is just a measure of how many of these there are, for a given thermodynamic state. The more ways you can arrange the molecules to give you the same thermodynamic state, the higher the entropy. The Boltzman equation gives you the exact relationship.

Also, for the more advanced student, in my analysis above I paid no attention to the velocity part of phase space, and of course the whole analysis is classical. This is in the interests of clarity, since the conclusions don't change.

Answer 5

wow...O.o thanks! :D