# What are the steps to this basic thermodynamics equation?

## What are the steps to solving this problem? Honestly I'm not looking for the answer, I want to actually know the steps on how to solve this sort of problem. Thanks :) A 0.582-g sample of Mg reacts with excess 1.0 M HCl (60.0 mL) according to the procedure used in this experiment. The initial and final temperatures were 24°C and 68°C. What is the ∆H of the reaction per mole of magnesium? Assume that the specific heat capacity for the solution is 4.187 J/deg∙g and that the density of the 1.0 M HCl is 1.00 g/mL. (Hints: the magnesium contributes to the mass of the solution)

Jan 19, 2016

Here's what I would do:

1) Write out the reaction itself. If magnesium, a monatomic substance, reacts with hydrochloric acid, a diatomic substance, you should expect a single replacement reaction:

$\textcolor{w h i t e}{{\text{Mg"(s) + 2"HCl"(aq) -> "MgCl"_2(aq) + "H}}_{2} \left(g\right)}$
(highlight when you figure it out)

2) Look at what variables you have available. What equation do they correspond to?

You are given what you need to determine $\Delta T$ ($\text{44 K}$ or $\text{^@ "C}$), the mass of the liquid that the metal is immersed into, and you are given the specific heat capacity.

That should remind you of:

$\setminus m a t h b f \left(q = m c \Delta T\right)$

where:

• $q$ is the heat flow. Note that you are at a constant pressure (though you may not have been told this in class, it is implied).
• $m$ is the mass of the aqueous acid solution in $\text{g}$, including the magnesium (notice the hint in the question).
• $c$ is the specific heat capacity of that solution in $\text{J/g"cdot"K}$ or $\text{J/g"cdot""^@ "C}$.
• $\Delta T = {T}_{f} - {T}_{i}$ is the change in temperature (where intervals in $\text{K}$ and $\text{^@ "C}$ are the same).

3) Figure out how to find these variables based on what you were given.

• You have the equation for $q$.
• Mass can be found simply from using the density you were given, along with the volume of the solution. Assume the volume of the solution doesn't change significantly, and it'll simplify things a bit.
• The specific heat capacity and temperatures were given.

4) Find the relationship between enthalpy $H$ and heat flow $q$.

Since we are at constant pressure (now you know!), this relationship holds true:

$\setminus m a t h b f \left(\Delta H = {q}_{p}\right)$

where $\Delta H$ is the change in enthalpy and $q = {q}_{p}$ at a constant pressure.

From this, since we want the enthalpy per $\text{mol}$, let us divide both sides by the number of $\text{mol}$s, $n$:

$\setminus m a t h b f \left(\Delta \overline{H}\right) = \frac{\Delta H}{n} = \setminus m a t h b f \left({q}_{p} / n\right)$

where $\overline{H}$ is the molar enthalpy and $n$ is the number of $\text{mol}$s. (All we did was divide by $n$.)

Furthermore, we should determine what $n$ is for. We want to divide by the number of $\text{mol}$s, but of what?

Of whatever reactant gives us the maximum yield *possible. That should be the *limiting reagent (magnesium, of course, since $\text{HCl}$ is in excess).

So, to determine the molar enthalpy:

$\textcolor{b l u e}{\Delta \overline{H} = {q}_{p} / \left(\text{mols of limiting reagent}\right)}$

color(white)(DeltabarH = ((m_"Mg" + m_"soln")cDeltaT)/("mols of limiting reagent"))
In the end, $q$ should be $\textcolor{w h i t e}{\text{11.2" "kJ}}$, and the enthalpy should be $\textcolor{w h i t e}{466}$ $\text{kJ/mol}$.