3. consider the following 'experiment'. a beaker containing 1000 black beads and 1000 white beads is mixed. the beads are identical except for their c colour. the potential energy of the beads on the left is identical to those on the right and thus the change in enthalpy for the mixing is zero. explain in terms of entropy how this mixing can be spontaneous. mnong

The spontaneity of mixing black and white beads, even when the change in enthalpy is zero, can be explained by an increase in entropy. Entropy is a measure of the disorder or the number of ways the beads can be arranged. Initially, the black and white beads are separated, which means fewer possible arrangements. When mixed, the number of possible arrangements increases significantly because the beads can now be distributed in many more ways. This increase in entropy makes the mixing process spontaneous. Since the enthalpy change is zero (no energy is gained or lost in terms of heat or work), the driving force for the mixing must come from the entropy change. The process leads to a more disordered, higher entropy state, which is thermodynamically favored. Consequently, the increase in entropy provides the necessary free energy change that drives the spontaneous mixing of black and white beads.