$$Cu + 4HNO_3 \rightarrow Cu(NO_3)_2 + 2NO_2 + 2H_2O$$
From the stoichiometry of the equation, we can see that 1 mol of Cu reacts with 4 mol of HNO3. Therefore, to react with 2.0 mol of HNO3, we need:
$$2.0 \text{ mol HNO}_3 \times \frac{1 \text{ mol Cu}}{4 \text{ mol HNO}_3} = 0.50 \text{ mol Cu}$$
The molar mass of Cu is 63.55 g/mol. Therefore, the mass of Cu needed is:
$$0.50 \text{ mol Cu} \times 63.55 \text{ g/mol} = \boxed{31.78 \text{ g Cu}}$$
