Why do aqueous solutions of sodium chloride and silver nitrate swap ions?

Question

So, we know that:

$$ \ce{NaCl(aq) + AgNO3(aq) -> NaNO3(aq) + AgCl(s)}$$

(In other words, the ions swap and a precipitate forms).

However, both of those compounds seem pretty stable, since $\ce{Ag}$ and $\ce{Na}$ cations both have a 1+ charge, and $\ce{Cl}$ and $\ce{NO3}$ both have a 1- charge. Since they are stable, I would assume no reaction would take place since both ions are happy with the ions they are currently bonded to (sodium and silver, respectively).

However, $\ce{Na}$ is higher on the activity series than $\ce{Ag}$, and we know that these aqueous solutions actually contain dissociated ions, so I assume this has something to do with the double-replacement. But why is this? Why does this reaction take place, even though the original compounds appear stable at first glance?

Edit

I read this question, and it says

Le Châtelier's principle only states that a system previously at equilibrium will want to stay at equilibrium - that is, if we perturb it, it will try to go back to equilibrium.

The above compounds of sodium chloride and silver nitrate appear to be at an initial equilibrium, do they not?

Edit 2

The question isn't why silver chloride is a solid, but rather, why does this reaction take place if the initial two compounds are stable to begin with?

Answer 1

While solutions of silver nitrate and sodium chloride are in stable equilibrium on their own, once mixed the equilibrium is changed. When the salts are dissolved, you no longer have silver and nitrate or sodium and chloride ions associated with each other, you have a mixture of individual ions in solution.

But silver chloride has very low solubility, about 1 mg can dissolve in 1 L of water. So when a silver ion and chloride ion meet, they quickly fall out of solution. So if we had an equilibrium between the dissolved ions and the small amount of "soluble" silver chloride, that equilibrium would be driven toward the silver chloride by the precipitation. When compounds escape the solution by precipitating or evaporating, they are removed from the equilibrium, so trying to replace them to restore equilibrium requires converting more free ions into silver chloride and pushes the reaction to completion.

Answer 2

So, we know that:

$$\ce{NaCl (aq) + AgNO3 (aq) -> NaNO3 (aq) + AgCl (s) v}$$

(In other words, the ions swap and a precipitate forms).

Ah yes, that is how it is always written on the blackboard. But remember that the label (aq) actually carries a meaning. It means that upon dissolution, it is wrong to talk about associated sodium and chloride ions in any way, rather they are separated and go diffusing through the solution on their own.

$$\ce{NaCl (s) + H2O -> Na+ (aq) + Cl- (aq)}$$

If you took one pair of $\ce{NaCl}$ ions and coloured them both pink, you would realise that the two pink ions move through the solution entirely individually. The same thing goes for $\ce{AgNO3}$. Sometimes a sodium ion may meet a chloride ion (or a silver ion a nitrate ion) but they’ll just greet and move on.

Now we mix the two solutions. All of a sudden in this chaos of ions diffusing everywhere, silver ions can meet chloride ions. They won’t just greet but they’ll hug each other because they like to hold tight together. And thus they shall precipitate. The reaction is much better written as:

$$\ce{Cl- (aq) + Ag+ (aq) -> AgCl (s) v + H2O}$$

Think about it a different way. Mix a solution of sodium chloride and potassium bromide and then evaporate the water. You will obtain a mixture of $\ce{NaCl, NaBr, KCl}$ and $\ce{KBr}$. Why? Because all ions are equally distributed and upon removal of the solvent, they will all fall together. All salts will form in an entirely statistical distribution.