# What are the steps to this basic thermodynamics equation?

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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)

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)

##### 1 Answer

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:

#color(white)("Mg"(s) + 2"HCl"(aq) -> "MgCl"_2(aq) + "H"_2(g))#

(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

That should remind you of:

#\mathbf(q = mcDeltaT)# where:

#q# is theheat flow. Note that you are at a constant pressure (though you may not have been told this in class, it is implied).#m# is themassof the aqueous acid solution in#"g"# ,the magnesium (notice the hint in the question).including#c# is thespecific heat capacityof that solution in#"J/g"cdot"K"# or#"J/g"cdot""^@ "C"# .#DeltaT = T_f - T_i# is thechange in temperature(where intervals in#"K"# and#""^@ "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

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

#\mathbf(DeltaH = q_p)# where

#DeltaH# is the change in enthalpy and#q = q_p# at a constant pressure.

From this, since we want the enthalpy per

#\mathbf(DeltabarH) = (DeltaH)/n = \mathbf(q_p/n)# where

#barH# is the molar enthalpy and#n# is the number of#"mol"# s. (All we did was divide by#n# .)

Furthermore, we should determine what ** what**?

Of whatever reactant gives us the *maximum yield **possible** . That should be the *limiting reagent** (magnesium, of course, since

So, to determine the molar enthalpy:

#color(blue)(DeltabarH = q_p/("mols of limiting reagent"))#

**5)** Determine your final equation:

#color(white)(DeltabarH = ((m_"Mg" + m_"soln")cDeltaT)/("mols of limiting reagent"))#

(highlight when you figure it out)

In the end,