For the given expression, $\mathrm{\Delta H}=\mathrm{\Delta U}+{\mathrm{\Delta n}}_{\mathrm{g}}\mathrm{RT}$, which of the following option is correct?

According to the ideal gas law,

${\mathrm{pV}}_{\mathrm{A}}={\mathrm{n}}_{\mathrm{A}}\mathrm{RT}$

${\mathrm{pV}}_{\mathrm{B}}={\mathrm{n}}_{\mathrm{B}}\mathrm{RT}$

${\mathrm{pV}}_{\mathrm{B}}-{\mathrm{pV}}_{\mathrm{A}}={\mathrm{n}}_{\mathrm{B}}\mathrm{RT}-{\mathrm{n}}_{\mathrm{A}}\mathrm{RT}=\left({\mathrm{n}}_{\mathrm{B}}-{\mathrm{n}}_{\mathrm{A}}\right)\mathrm{RT}$

$\mathrm{p}\left({\mathrm{V}}_{\mathrm{B}}-{\mathrm{V}}_{\mathrm{A}}\right)=\left({\mathrm{n}}_{\mathrm{B}}-{\mathrm{n}}_{\mathrm{A}}\right)\mathrm{RT}$

$\mathrm{p\Delta V}={\mathrm{\Delta n}}_{\mathrm{g}}\mathrm{RT}$

where, ${\mathrm{\Delta n}}_{\mathrm{g}}$ refers to the number of moles of gaseous products minus the number of moles of gaseous reactants. 

Put the value of $\mathrm{p\Delta V}$ in equation, $\mathrm{\Delta H}=\mathrm{\Delta U}+\mathrm{p\Delta V}$

                                                       $\mathrm{\Delta H}=\mathrm{\Delta U}+{\mathrm{\Delta n}}_{\mathrm{g}}\mathrm{RT}$