There are several different species of the black widow spider. While I did not manage to find chromosomal information on the Lartrodectus Variolus (northern black widow), I did manage to find a study on the Latrodectus Hesperus (western black widow), and the Latrodectus Geometricus (brown widow spider).
This figure is depicting the karyotype of both a male (B), and female (A) black widow spider. The L. Hesperus has 24 autosomal chromosomes and two sex chromosomes. According to the study done by Yonghui Zhao, Nadia A. Ayoub, and Cheryl Y. Hayashi, "The autosome pairs in the L. hesperus karyotypes are numbered according to descending size (Figure 1). The largest autosome pair of L. hesperus (LH-1) has a secondary constriction and a satellite chromosome at the end of the long arm (Figures 1, S1A, S1B). One or two additional, small, telocentric chromosomes are infrequently found in the metaphase spreads (Figure S2). These small elements could be supernumerary chromosomes (e.g., B-chromosomes), which are known from eukaryotes such as grasshoppers, wasps and plants . Because supernumerary chromosomes are often not stably transmitted, this could explain the variable number (zero, one, or two) of these small elements among L. hesperus karyotypes. The significance of the satellite and supernumerary chromosomal elements, and their polymorphic distribution among L. hesperus individuals, is an area for future inquiry."
This figure is showing the karyotype of both a male (B), and female (A) L. Geometricus. The L. Geometricus has 18 total chromosomes, 9 of which are autosomal, and the final two being sex chromosomes. In the same study that I have previously quoted, the scientists found that, "for L. geometricus (LG), ~50 high-quality metaphase spreads were derived from 20 developing eggs. There were primarily two types of cells, those with a diploid chromosome number of 17 and those with 18 (Figures 2, S1C, S1D). All chromosomes were telo/acrocentric and no supernumerary chromosomes were observed. As with the L. hesperus karyotype, L. geometricus autosome pairs were numbered by descending size (Figure 2).