  We study theoretically the quantum dynamics of nitrogen molecules (N$_2$)
exposed to intense and ultrafast x-rays at a wavelength of 1.1 nm (1100 eV
photon energy) from the Linac Coherent Light Source (LCLS) free electron laser.
Molecular rate equations are derived to describe the intertwined
photoionization, decay, and dissociation processes occurring for N$_2$. This
model complements our earlier phenomenological approaches, the single-atom,
symmetric-sharing, and fragmentation-matrix models of J. Chem. Phys.
$\mathbf{136}$, 214310 (2012). Our rate-equations are used to obtain the
effective pulse energy at the sample and the time scale for the dissociation of
the metastable dication N$_2^{2+}$. This leads to a very good agreement between
the theoretically and experimentally obtained ion yields and, consequently, the
average charge states. The effective pulse energy is found to decrease with
shortening pulse duration. This variation together with a change in the
molecular fragmentation pattern and frustrated absorption---an effect that
reduces absorption of x-rays due to (double) core hole formation---are the
causes for the drop of the average charge state with shortening LCLS pulse
duration discovered previously.
