An ideal gaseous reaction which is a hypothetical gaseous re

An ideal gaseous reaction (which is a hypothetical gaseous reaction that conforms to the laws governing gas behavior) occurs at a constant pressure of 40.0 atm and releases 74.8 kJ of heat. Before the reaction, the volume of the system was 7.60 L . After the reaction, the volume of the system was 2.40 L . Calculate the total internal energy change, E , in kilojoules

Solution

Since the process occurs at constant pressure, the heat transferred to the system equals its change in enthalpy. That means the amount of heat released equals the decrease of the system\'s enthalpy:
H = - 74.8 kJ

Enthalpy is defined in terms of internal energy U, pressure and volume:
H = U + PV
<=>
U = H + PV

So the changes are related as:
U = H - (PV)
Since P is constant you can rewrite
U = H - PV = H - P(V_final _ V_initial)

To compute the PV in kilojoules you need to covert pressure to kilopascals and volume to cubic meters.
Note that 1 kJ = 1 kPam³

Hence,
U = - 74.8 kJ - 40*101.325 kPa * (2.4×10³ m³ - 7.6×10³ m³) = -53.72 kJ