"Khartoum is the capital of Sudan."
Translation:اَلْخَرطوم عاصِمة الْسّودان.
In Arabic it is so. Many capital names in Arabic are defined with AL, specially if the name is purely of Arabic origin. There are many of course without (AL), but Sudan's capital is defined. As well as many country names.
Because here, عاصمة is added to another noun: السودان. This is addition of nouns (or as they call it in Western grammar books: Genitive case).
In such compound of nouns, in Arabic, the "AL" is attached to the SECOND noun and not the first. However, if the second noun is a proper name, AL might not be added at all. Example: the capital of Turkey would be عاصمة تركيا (3ácimatu Turkyá). No "AL" was added to تركيا.
"C" here is for ص - I just like to type it that way instead of "ss" or "S".