  Supernova (SN) explosions enrich the intra-cluster medium (ICM) both by
creating and dispersing metals. We introduce a method to measure the number of
SNe and relative contribution of Type Ia supernovae (SNe Ia) and core-collapse
supernovae (SNe cc) by directly fitting X-ray spectral observations. The method
has been implemented as an XSPEC model called snapec. snapec utilizes a single
temperature thermal plasma code (apec) to model the spectral emission based on
metal abundances calculated using the latest SN yields from SN Ia and SN cc
explosion models. This approach provides a self-consistent single set of
uncertainties on the total number of SN explosions and relative fraction of SN
types in the ICM over the cluster lifetime by directly allowing these
parameters to be determined by SN yields provided by simulations. We apply our
approach to the XMM-Newton European Photon Imaging Camera (EPIC), Reflection
Grating Spectrometer (RGS), and 200 ks simulated Astro-H observations of a
cooling flow cluster, A3112. We find that various sets of SN yields present in
the literature produce an acceptable fit to the EPIC and RGS spectra of A3112.
We infer that 30.3% +/- 5.4% of the total SN explosions are SNe Ia, and the
total number of SN explosions required to create the observed metals is in the
order of (1.06 +/- 0.34)*10^{9}, from snapec fits to RGS spectra. These values
may be compared to the enrichment expected based on well-established
empirically-measured SN rates per star formed. The proportions of SNe Ia and
SNe cc inferred to have enriched the ICM in the inner 52 kpc of A3112 is
consistent with these specific rates, if one applies a correction for the
metals locked up in stars. At the same time, the inferred level of SN
enrichment corresponds to a star-to-gas mass ratio that is several times
greater than the 10% estimated globally for clusters in the A3112 mass range.
