In the equation $$\Delta H = \Delta U + \Delta PV,$$ under what circumstances can we simplify it into $$\Delta H = \Delta U + P\,\Delta V + V\,\Delta P$$ by product rule?
In this article (pdf slides) it is mentioned that it isn't true. In one question I got a wrong answer using $$\Delta H = \Delta U + \Delta PV + V\,\Delta P,$$ but the correct answer using $$\Delta H = \Delta U + \Delta PV = \Delta U + P_\mathrm f V_\mathrm f -P_\mathrm i V_\mathrm i.$$
The question was:
one mole of a non ideal gas undergoes a change of state from ($\pu{2 atm}$, $\pu{3 L}$, $\pu{95 K}$) to ($\pu{4 atm}$, $\pu{5 L}$, $\pu{245 K}$) with a change in internal energy, $\Delta U = \pu{30.0 L atm}$. Calculate $\Delta H$ in the process.
Using $$\Delta H = \Delta U + P\,\Delta V + V\,\Delta P$$ you get $\Delta H = \pu{40 L atm}$, which is wrong. And using $$\Delta H = \Delta U + \Delta PV$$ you get $\Delta H = \pu{44 L atm}$, which is correct.
Is it something to do with the non ideal gas?
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