Is the reaction of silver nitrate and copper endothermic or exothermic?
You may already know that the world is not about enthalpy but about Gibbs free energy. A reaction is sponanteous if the change Gibbs free energy is negative.

$$\Delta G = \Delta H - T \cdot \Delta S$$

As you see, enthalpy and entropy play into this. Looking at your reaction, we note that we are taking two ions out of a solution to release one into solution. Compare the following, slightly different description:

$$\ce{2 Ag+ (aq) + Cu (s) &lt;=&gt;&gt; 2 Ag (s) + Cu^2+ (aq)}$$

From an entropic point of view, this is bad. Rather than having two dissolved ions, we have one on the products’ side. Therefore, we can assume $\Delta S &lt; 0$, therefore $T \cdot \Delta S &lt; 0$. Negating it gives a positive value.

But the reaction is spontaneous, so $\Delta G &lt; 0$. This can only be true if $\Delta H$ is sufficiently negative to counteract the loss of entropy. Thus we conclude that $\Delta H &lt; 0$ and the reaction is exothermic.