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The volume that is needed to react completely with 0.100 mol of lead nitrate is 0.400 L. It is because 2 moles of HCl are required for every mole of lead nitrate.
2 x 0.100 mole Pb(NO₃) = 0.200 mole HCl 
0.200 mol HCl = L x 0.500 M 

Explanation:

Molarity is defined as the number of moles present in a liter of volume.

Mathematically,      Molarity = \(\frac{\text{no. of moles}}{Volume}\)

As it is given that molarity is 0.50 M and no. of moles is 0.1 mol. Hence, we will calculate the volume of given solution as follows.

                 Molarity = \(\frac{\text{no. of moles}}{Volume}\)

                     0.5 M = \(\frac{0.1 mol}{Volume}\)

                   Volume = \(\frac{0.5 M}{0.1 mol}\)

                                 = 5 liter

Thus, we can conclude that 5 liters of 0.500M HCl (aq) are needed to react completely with 0.100 mol of \(Pb(NO_{3})_{2}\), forming a precipitate of \(PbCl_{2}(s)\).

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