I am reacting different masses of Magnesium with hydrochloric acid to find the temperature change. I need 2 explanations: First of all why is the reaction exothermic? Secondly, why does the difference in temperature increase as the mass of magnesium increases?



The reaction I think you're talking about is regarding magnesium solid and (concentrated?) HCl:

$Mg(s) + 2HCl(l) \rightarrow H_2(g) + MgCl_2(aq)$

The following are approximate bond enthalpies from this site and this site.

The bonds that would be broken are:

  • H-Cl single bond (x 2), $\Delta{H_{break}} = \text{+431 kJ/mol}$

The bonds that would be made are:

  • Mg-Cl single bond (x 2), $\Delta{H_{make}} = \text{-406 kJ/mol}$

  • H-H single bond (x 1), $\Delta{H_{make}} = \text{-436 kJ/mol}$

Approximately, $\Delta{H_{rxn}} = \sum{|\Delta{H_{break}}|} - \sum{|\Delta{H_{make}}|} = \text{-386 kJ/mol}$.

The reaction is exothermic because the energy absorbed in breaking bonds is smaller overall than the energy released in making bonds (and exothermic by definition is a negative enthalpy). Even though these numbers are approximate, they are clearly different enough to make such a conclusion.


The difference in temperature is related to the enthalpy. In "lab bench conditions", otherwise known as constant pressure conditions, when one performs a (coffee-cup-) calorimeter experiment to determine the change in temperature, the heat flow $q$ is essentially equal to the enthalpy $\Delta{H}$.

Recall that $q$ is often reported in $J$, joules. $q$ is an extensive property, so the more substance (in terms of mass) the process involves, the higher the magnitude of $q$ involved. Since $q$ $\alpha$ $\Delta{T}$, the more heat involved, the greater the change in temperature.

For an exothermic process, heat flows out from the reaction into the calorimeter solution, so $\Delta{T_{sys}} > 0$, i.e. the reaction releases heat into the solution, and the solution gets hotter. Note that $q_{cal} = -q_{rxn}$.

As a result, although $q_{cal} > 0$, $[q_{rxn} = \Delta{H_{rxn}}] < 0$, which has been established from (1) for this exothermic process, and when there is more $Mg(s)$ (assuming excess $HCl$), $q_{rxn}$ is larger, which corresponds to a larger $\Delta{T_{sys}}$.

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