The number of moles of AgNO3 needed to prepare 0.50 L of a 4.0 M solution can be calculated using the formula:

Molarity (M) = Moles of Solute (mol) / Volume of Solution (L)

Rearranging the formula to solve for moles of solute, we get:

Moles of Solute (mol) = Molarity (M) x Volume of Solution (L)

Substituting the given values into the formula, we have:

Moles of AgNO3 = 4.0 M x 0.50 L = 2.0 moles

Therefore, 2.0 moles of AgNO3 are needed to prepare 0.50 L of a 4.0 M solution.