A solution contains the maximum amount of dissolved solute at a given temperature when it has reached its solubility limit. At that point the system is in dynamic equilibrium: dissolved molecules continually exchange with solid solute so that the amount in solution stays constant. This means you can’t dissolve any more solute under the same conditions, and adding more tends to cause excess to crystallize out. An unsaturated solution has less than this maximum and can still dissolve more solute, while a supersaturated solution temporarily holds more dissolved solute than the usual limit but is unstable and can precipitate when disturbed.

When soluble salts react in solution, the actual chemical change is the pairing of ions to form an insoluble product, while ions that stay in solution as ions are spectators. Here, Ba2+ from BaCl2 meets SO4^2− from Na2SO4. The combination Ba2+ with SO4^2− forms BaSO4, which is highly insoluble and appears as a solid precipitate. The other ions, Na+ and Cl−, remain dissolved as NaCl and do not precipitate. That makes the net ionic equation: Ba2+ + SO4^2− → BaSO4(s), and the precipitate is BaSO4. The other possible products, NaCl, Na2SO4, and BaCl2, are all soluble and do not form a solid, so they don’t appear in the net ionic equation.

Electric conduction requires mobile charge carriers. In ionic compounds, the charged particles are ions held in a rigid crystal lattice in the solid state, so they cannot move freely to carry current. When the compound is melted, the lattice breaks apart and the ions become mobile, allowing electricity to flow. Similarly, dissolving the compound in water dissociates it into ions that can move in the solution and conduct current. Therefore, ionic compounds conduct electricity only when molten or dissolved. They do not conduct in the solid state, they do not conduct in all states equally, and they do not never conduct.

The main idea here is quantization: electrons in atoms are described by specific, discrete values that come from solving the quantum mechanical description of the atom. These discrete values are called quantum numbers. They label the allowed states an electron can occupy: the principal quantum number sets the energy level and size of the orbital, the azimuthal quantum number describes the subshell’s shape, the magnetic quantum number tells how the orbital is oriented in space, and the spin quantum number indicates the electron’s intrinsic spin. An orbital, by contrast, is a region of space where there’s a high probability of finding the electron, not the discrete numbers themselves. The ground state is simply the lowest-energy state, and quantum theory is the broader framework that describes all of this. So the term that refers to those discrete values is quantum numbers.