Step 1: Concept
"Vitriol" is an archaic name for various sulfate minerals or chemical compounds.
Step 2: Meaning
Green vitriol is the common name for the heptahydrate form of ferrous sulfate.
Step 3: Analysis
The chemical formula for ferrous sulfate heptahydrate is $FeSO_{4}\cdot 7H_{2}O$. In contrast, $CuSO_{4}\cdot 5H_{2}O$ is known as blue vitriol.
Step 4: Conclusion
Therefore, $FeSO_{4}\cdot 7H_{2}O$ is the correct molecular formula for green vitriol.
Final Answer: (C)