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Jacob Dale

**Assuming all gases in the combustion reaction of benzoic acid (C**

_{6}H_{5}COOH) behave ideally, what is the "exact" change in internal energy?The context in which this question is being asked is after a calorimetry experiment. For all the intents and purposes of calorimetry, the change in internal energy (ΔU) can be related to the change in enthalpy (ΔH) at a 1:1 ratio because the volume of the calorimeter remains constant.

dU = dq + dw simplifies to dU = dq

However, this question asks for the "exact" ΔU. Therefore, a correction factor needs to be introduced to account for the variable thermodynamic values.

The only variables at play here are temperature and pressure. The temperature changed around 2 degrees Celsius for each trial of the combustion of benzoic acid so it's contribution to U is negligible. Pressure, however, changes drastically. Pressure can be assumed to be function of moles of gas:

2 C6H5COOH + 15 O2 => 6 H2O + 14 CO2

There is 3:4 ratio for moles of gas. So the pressure of the system increases by a factor of 4/3.

But now I am stuck. I don't know how to calculate the "exact" ΔU. Does anyone know what my lab instructor is asking for in this situation?

Thank you for your help!