When Can A Reaction Happen?

In class, you saw some demonstrations.  The first one was the following reaction between aluminum metal and copper (II) chloride:

              Al (s) + CuCl₂ (aq) → AlCl₃ (aq) + Cu (s)          (1)

The reverse reaction (the same reaction in the opposite direction) is:

              Cu (s) + AlCl₃ (aq) → CuCl₂ (aq) + Al (s)          (2)

However, this didn’t happen in the demo.  Reaction (1) proceeded until all of the aluminum metal and CuCl₂ were used up, and there was only AlCl₃ and copper metal in the beaker.  Once that happened, the beaker was set for reaction (2), but reaction (2) didn’t happen.

The second demo was the reaction between sodium carbonate (Na₂CO₃) and calcium chloride (CaCl₂):

  Na₂CO₃ (aq) + CaCl₂ (aq) → NaCl (aq) + CaCO₃ (ppt)    (3)

However, once the calcium carbonate is formed, it doesn’t redissolve.  I.e., reaction (3) happens, but the reverse reaction (4), doesn’t:

   CaCO₃ (s) + NaCl (aq) → CaCl₂ (aq) + Na₂CO₃ (aq)     (4)

Why might reactions (1) and (3) happen, but not reactions (2) and (4)?