Which area received the most damage in the Civil War

Ca^2+ is smaller than Mg^2+ hence it has a greater heat of formation or lattice energy.

When a crystal lattice is formed, the energy that is released if the component ions of the compound are brought together from infinity is called the lattice energy. It is the energy released when a crystal lattice is formed from its component ions.

The question lets us know that the heat released by the compounds depends on the energy released upon formation of the compound. Hence, the higher the energy released upon formation, the higher the magnitude of heat released upon dissolution of the compound.

Recall that lattice energy depends on the size of the ions. Thus, the smaller the ions, the higher the lattice energy.

Ca^2+ is smaller than Mg^2+ hence more energy is given off when CaCl2  is formed than when MgCl2  is formed.

As stated above, the greater the lattice energy, the greater the heat released when the lattice dissolves and the higher the rise in temperature.

Putting all these together, Sample A must be CaCl2 while sample B must be MgCl2.