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Questions & Answers about Ich erklärte gestern den Zweck des Projekts vor der Klasse.
Why is den Zweck in the accusative case?
den Zweck is the direct object of the verb erklären. In German, whatever you “explain” is the thing you explain to someone, and that thing takes the accusative case. Zweck is a masculine noun, so its accusative singular article is den (rather than der).
Why is des Projekts in the genitive, and can I say des Projektes or vom Projekt instead?
des Projekts shows possession: the purpose of the project. Both des Projekts and des Projektes are grammatically correct genitive forms of das Projekt; the shorter -s ending is more common in modern usage. You can also use the more colloquial construction vom Projekt (a contraction of von dem Projekt), but genitive is often preferred in formal or written German.
Why is vor der Klasse used here, and why is der Klasse dative?
vor is a two-way preposition. When it indicates a static location (“in front of”), it requires the dative case. Klasse is feminine, so its dative singular article is der. Here vor der Klasse means “in front of the class” (physically addressing the students).
Could I instead say Ich erklärte der Klasse den Zweck des Projekts?