How do I evaluate the PV term when calculating a change in enthalpy?
The derivation for $\Delta H$ is 
$$H = U + PV$$
$$\Delta H = \Delta U + \Delta (PV)$$

The $\Delta (PV)$ term expands to your $P_2 V_2 - P_1 V_1$ term. However, when the pressure is constant $P_2 = P_1 = P$, and $\Delta (PV)$ term becomes $P\Delta V$. The most common situation when the latter is true is when the system is open to the atmosphere and $P$ is the external pressure. In the former case, $P$ is more likely the internal pressure, which changes during the reaction.