When to include the mass of the dissolved substance in calorimetry problems?

Question

In some calorimetry problems, in which a substance is dissolved in water and we want the heat of the reaction, the mass of the dissolved substance is included in the mass plugged into mcat but other times it isn't. When should I include the mass of the substance?

For example, in this problem the mass of $\ce{NH4NO3}$ is not added to the mass of water to find the enthalpy:

$\pu{5.44 g}$ of ammonium nitrate was added to $\pu{150.0 mL}$ of water in a coffee-cup calorimeter. The temperature changed from $\pu{18.6 °C}$ to $\ce{16.2 °C}.$ Calculate the enthalpy change for dissolving $\ce{NH4NO3(s)}$ in water in $\pu{kJ mol^-1}.$ Assume the solution has a specific heat capacity of $\pu{4.18 J g^-1 K^-1}.$

But in this problem the mass of $\ce{CaCl2}$ is added to the mass of water:

In a coffee cup calorimeter, $\pu{2.6 g}$ $\ce{CaCl2(s)}$ was dissolved in $\pu{260 g}$ of water at a combined initial temperature of $\pu{23 °C}.$ The final temperature was $\pu{26.4 °C}.$ Calculate the enthalpy change of the reaction.

I would really appreciate if someone could explain to me when to include the mass of the dissolved substance.

Answer 1

There are multiple issues here, and the answer is: it depends.

1. How much of your substance is there relative to the solution? If the mass is, say, 1% of total and the specific heat is comparable, then your answer may be off by 1%, which is probably smaller than the systematic measurement error from heat loss in the calorimeter.

2. What is the specific heat of your substance? If it's very small, then it will hardly require any heat to raise the temperature of your substance.

Frequently, you have to make assumptions. Note that in your first example, it asked you to make assumptions about the specific heat of the solution. This is the specific heat for a mixture of your substance and water. That basically addresses both (1) and (2) above. Note that in this case, since it's the total solution, you should use the total mass.

In the second question, the total mass of calcium chloride is very small, so whether or not you include it is almost irrelevant.