Rank of ideal sheaf of a curve in $\mathbb{P}^3$

Question

Let $Z$ be a closed subscheme of $\mathbb{P}^3$ with pure codimension 2. Have one an exact sequence $$0\longrightarrow\mathscr{I}_Z\longrightarrow\mathscr{O}_{\mathbb{P}^3}\longrightarrow\mathscr{O}_Z\longrightarrow0$$ over $\mathbb{P}^3$. Why is one the rank of $\mathscr{I}_Z$? Is $c_{1}(\mathscr{O}_{Z}) = 0$ ? Where $c_{1}$ denotes the First class of Chern.