Question

Choose the system with the greater entropy in each case: (a) 1 mol of H21g2 at STP or 1 mol of SO21g2 at STP, (b) 1 mol of N2O41g2 at STP or 2 mol of NO21g2 at STP. Please explain.

Answer 1

Above question can be answered by using Boltzmann entropy formula:

Where K is Boltzmann constant. W is possible orientation or possible locations, gas molecules can achieve.

To compare above systems, following points may be noted:

1. entropy of a substance whose molecules contain many atoms is greater than that of a substance composed of smaller molecules. It is obvious as higher the number of atoms, higher the possible orientations.
2. entropy of a substance with a high molecular weight is greater than that of substance with a low molecular weight. This arises from distribution of momenta of molecules.
3. Also consider the fact that since entropy is extensive property, so higher the number of moles of gas in given system, higher is its entropy.

Answer of A: 1 mole of SO₂ is answer. Since, both are 1 mole in quantity.

Answer of B: 2 moles of NO₂ is answer.In this system, 2 moles of gases is there while in only 1moles of N₂O₄.