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How can we determine if the enthalpy of solution of a compound is positive or negative?

In order to make a clear idea about what I mean, take the following problem:

A 3.5 g sample of $\ce{NH4NO3}$ was added to 80. mL of water in a coffee cup calorimeter of negligible heat capacity. As a result, the temperature of solution decreased from $21.6 \ ^\circ\text{C}$ to $18.1\ ^\circ\text{C}$. Calculate the enthalpy change of the solution ($\Delta H_{\text{sol}}$ ). (specific heat of the solution = $4.18 \frac{\text{J}}{\text{g}\cdot ^\circ\text{C}}$; density of water $1.00 \frac{\text{g}}{\text{mL}}$)

Answer: $+28 \frac{\text{kJ}}{\text{mol}}$

Why it is positive despite there is a decrease in temperature?

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  • $\begingroup$ Possible duplicate of chemistry.stackexchange.com/questions/27159/… $\endgroup$
    – M.A.R.
    Apr 12, 2015 at 16:16
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    $\begingroup$ This question is not actually about enthalpy of formation (not a duplicate). It is about enthalpy of solution and the calorimetry experiment one might do to determine said enthalpy. I have edited the question to make it clearer. $\endgroup$
    – Ben Norris
    Apr 12, 2015 at 16:59

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The sample takes in the heat from the water, so it takes in energy to "form" the solution and the water thereby loses it, becoming a lower temperature. You need to realize the reference point is not the water, but rather the sample in this case. The heat transferred (lost) by the water is to the sample, so it is the negative of the heat lost by water, making it positive.

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