Final answer:
Russian troops were mobilized against Austria-Hungary as a direct response to Austria-Hungary's declaration of war on Serbia, fueled by the assassination of Archduke Franz Ferdinand and the support provided to Austria-Hungary by Germany's 'blank check'.
Step-by-step explanation:
The Russian troops were being mobilized against Austria-Hungary following an incident where a Serbian nationalist assassinated Archduke Franz Ferdinand of the Austro-Hungarian Empire on June 28, 1914. This assassination precipitated a crisis, leading to Austria-Hungary issuing an ultimatum to Serbia. When Serbia failed to comply with all demands, Austria-Hungary declared war on Serbia on July 28, 1914. Russia, which had a treaty to defend Serbia, ordered the mobilization of its troops on July 30. This sequence of events drew the major powers of Europe into war due to a complex system of alliances and promises of support, notably Germany's "blank check" assurance to Austria-Hungary, emboldening them to take military action against Serbia.