The answer is #7.65*10^(-3)# #"moles"# of #Pb^(2+)# ions were present in the sample.
The balanced chemical equation is:
#PbCl_(2(aq)) + Zn_((s)) -> ZnCl_(2(aq)) + Pb_((s))#
Notice the #1:1# mole ratio between #Zn# and #PbCl_2#; this means that one mole #Zn# will react with 1 mole of #PbCl_2#.
You know that #7.65*10^(-3)# moles of #Zn# had reacted after one day, which automatically means that the exact number of #PbCl_2# moles had reacted as well. The number of #PbCl_2# moles is equal to the number of moles of #Pb^(2+)# ions, since
#PbCl_(2(aq)) -> Pb_((aq))^(2+) + 2Cl_((aq))^(-)#
The complete ionic equation looks like this:
#Pb_((aq))^(2+) + 2Cl_((aq))^(-) + Zn_((s)) -> Zn_((aq))^(2+) + 2Cl_((aq))^(-) + Pb_((s))#
The net ionic equation is
#Pb_((aq))^(2+) + Zn_((s)) -> Zn_((aq))^(2+) + Pb_((s))#
This is a single replacement reaction. Since #Zn# is more reactive metal than #Pb#, the #Zn# ions will completely replace the #Pb# ions present in the solution.
