Since the gas expands in a well-insulated container, there is no heat exchange with the surroundings, meaning the process is adiabatic ($q = 0$). According to the First Law of Thermodynamics, the change in internal energy is given by: $\Delta U = q + w$ Since $q = 0$, $\Delta U = w$. For an expansion against a constant external pressure, the work done ($w$) is: $w = -P_{ext} \Delta V = -P_{ext}(V_f - V_i)$ Given: $P_{ext} = 2.5 \text{ atm}$ $V_i = 2.50 \text{ L}$ $V_f = 4.50 \text{ L}$ Substituting the values: $w = -2.5 \text{ atm} \times (4.50 \text{ L} - 2.50 \text{ L}) = -2.5 \times 2.0 = -5.0 \text{ L atm}$ To convert L atm to Joules, we use the conversion factor $1 \text{ L atm} = 101.325 \text{ J}$ : $w = -5.0 \times 101.325 \text{ J} = -506.625 \text{ J}$ Rounding to the closest given option, we get approximately $-505 \text{ J}$.