The existence of vacancies in crystals is explained thermodynamically because vacancies:

• A. Decrease the entropy of the crystal.
• B. Do not affect the entropy.
• C. Increase the entropy of the crystal.
• D. Only appear at high temperatures.

Answer: (C)

The key idea is that defects like vacancies raise the configurational entropy of a crystal. Creating a missing atom adds more ways to arrange the remaining atoms, increasing disorder. Thermodynamically, a crystal minimizes its free energy F = E − TS. While forming a vacancy costs energy, it also increases entropy; at any finite temperature, if the entropy gain is large enough to compensate the energy cost (ΔG = ΔH − TΔS becomes negative), vacancies become favorable and thus exist in equilibrium. This is why vacancies are thermodynamically explained as an entropy-driven feature: they increase the crystal’s entropy, helping to lower the free energy at nonzero temperatures. They do not decrease entropy, they do affect it, and they are not strictly limited to high temperatures—their concentration grows with temperature but can be present at lower temperatures too, just in smaller amounts.