# If the temperature of a solution decreases, what is the sign of the enthalpy change?

Here is what seems to be a straightforward question: you dissolve some ammonium chloride in water at $25\ \mathrm{^\circ C}$, lowering the temperature of the solution. Is the change in enthalpy for the dissolving process positive or negative?

My reasoning: if the temperature of the solution decreases, it means heat was released into the surroundings, so the enthalpy change is negative.

Apparently the answer is the enthalpy change is positive. What am I doing wrong? Whatever it is, it must be stupid, but please forgive me for its late here.

• Identify the system and the surrounding here; I think your confusion stems from that. – John Smith Apr 27 '15 at 3:44

When I was doing enthalpy, this was one of the tricky concepts that I still sometimes get wrong. Here is how you are supposed to remember it.

1. Identify the System
• The system is where the reaction happens. You cannot physically monitor the change in heat here. The change you always measure happens in the surroundings.
2. Identify the Surroundings
• This is the surroundings where usually the change is expressed as.

Now that we got the basics cleared away, let us look at your problem.

My reasoning: if the temperature of the solution decreases, it means heat was released into the surroundings, so the enthalpy change is negative.

This is what I usually think of, but now you must understand that as I've said before the change always happens in the surroundings and is associated with the surroundings. So the temperature of the solution decreases, which means that the surroundings temperature decreased. The solution is part of the surroundings. This means that the temperature of the system increases. Thus making the $\Delta H$ positive and the reaction endothermic.

Good Question, always remember that you cannot, in most situations, physically measure the change in the system.

Thanks.

• Can you be more clear about what EXACTLY is the system and what exactly is the surroundings. Also please explain why the thermometer is measuring the surroundings and not the system. Then I will accept your answer. – Joshua Benabou Apr 28 '15 at 3:14
• There are certain cases where the boundary between the system and the surroundings is kind of blurred. System would be the aqueous ammonium chloride; surroundings would be the solution/water solvent. Energy from the surroundings (water) is being added to the system to break the ionic bonds. – John Smith Apr 28 '15 at 4:59

It might help to think about it with an example. $\ce{NH_4Cl}$ is the 'active' ingredient in cold packs (ice packs). The system in this case, consists of the individual ions that separate when placed in solution ($\ce{NH_4^{+}}$ and $\ce{Cl^{-}}$). The solution makes up the surroundings - since the temperature of the solution decreases, the surroundings lose heat, and the system gains heat. Enthalpy is defined by a loss or gain of the system's heat. Since the system gains heat, the enthalpic value is positive (endothermic).

In general, for dissolving salts in solution, this is the case.