Why are ionic compounds solid at room temperature?
They are solids because the particles which make up ionic compounds are held together by very strong bonds.
Ionic compounds are formed when atoms of different charges (i.e. positive and negative ions) come together and form ionic bonds. These ionic bonds are typically very strong due to the high attractive forces holding the positively and negatively charged ions together (called electrostatic forces of attraction).
Because ionic compounds are formed by alternating positive and negative ions, and because they are all held together with these strong electrostatic forces, the oppositely charged ions pack tightly with each other and form a crystal lattice structure that is extremely hard to break. Thus, at normal room temperatures, the strength of these connections are much stronger than the kinetic energy of the ions, and so they cannot break away from each other! Instead, the ions are held rigidly together in their organized crystal lattice structure, and that is why they are a solid under normal conditions.
Examples of ionic solids are sodium chloride - NaCl (which has atomic ions), potassium nitrate -
The melting point of NaCl is 801 C. For potassium nitrate it is 304 C, because the anion is large and the negative charge dispersed over a larger volume. This weakens the attractive forces and lowers the melting point. Ammonium sulfate, where both ions are molecular, has the lowest melting point (235 C).