Problems with the instalaltion of arch linux in my chromebook

Hi, Im using a Lenovo 300e Chromebook 2nd Gen, and when im done installing arch, in the grub, arch doesnt apperar. What could be wrong?

These are the most important comands im using:

mount /dev/root_part /mnt

mount --mkdir /dev/efi_sys_part /mnt/boot

arch-chroot /mnt

grub-install --target=x86_64-efi --efi-directory=/boot --bootloader-id=grub --boot-directory=/boot

grub-mkconfig -o /boot/grub/grub.cfg