The order of ionization enthalpy of elements of 2nd period in long form of periodic table is $\mathrm{Li}<\mathrm{B}<\mathrm{Be}<\mathrm{C}<\mathrm{O}<\mathrm{N}<\mathrm{F}<\mathrm{Ne}$.

Generally, on going left to right in a period, ionization energy increases, but there are some exceptions to this. For example, Be has more ionization energy than B, due to fulfilled s-orbital. And N has more ionization energy than O due to half filled p-subshell. 

So,In second period of the long form of the periodic table, the element $\mathrm{B}$ has second lowest first ionization enthalpy and element $\mathrm{F}$ has second highest first ionization enthalpy values.