Question

Find ΔErxn for the reaction in kJ/mol hexane. The heat capacity of the bomb calorimeter, determined in a separate experiment is 5.79 kJ/∘C ?

Answer 1

I got `-3.99 xx 10^(3)` `"kJ/mol"`.

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Bomb calorimeters are constant-volume calorimeters, which implies that the heat flow `q` is equal to the change in internal energy, `DeltaE`, i.e.

`q_V = DeltaE`

We know that the heat flow is given by:

`q_V = C_VDeltaT`

where you were given that the constant-volume heat capacity is `C_V = "5.79 kJ/"^@ "C"` (rather than the specific heat capacity in `"kJ/g"^@ "C"`).

So, we can first calculate `q_V` to be:

`q_V = "5.79 kJ/"^@ "C" cdot (38.22^@ "C" - 25.74^@ "C")`

`=` `72.2_(592)` `"kJ"`

We then use the definition of `q_V = DeltaE`, dividing by the mols of limiting reagent (hexane) to get:

`q_V/n_(LR) = DeltabarE_(sol n)`,

where `n_(LR)` is the mols of limiting reagent and `DeltabarE_(sol n) -= (DeltaE_(sol n))/n_(LR)` is the change in molar internal energy of the solution.

The heat `q_V` transferred out from the product into the calorimeter is about `"72.26 kJ"`. With respect to the system, `q_V < 0`.

From here, we just need the mols of hexane:

`1.560 cancel"g hexane" xx ("1 mol hexane")/(6cdot12.011 + 14cdot1.0079 cancel"g")`

`= 0.0181_(02)` `"mols hexane combusted"`

Therefore, the change in molar internal energy for the reaction, which is EXOTHERMIC with respect to the system, is:

`color(blue)(DeltabarE_(rxn)) = -DeltabarE_(sol n) = color(red)(-)(q_V)/n_(LR) = color(red)(-)"72.2592 kJ"/"0.018102 mols hexane"`

`=` `color(blue)(-3.99 xx 10^(3))` `color(blue)("kJ/mol hexane")`

to three sig figs.