Eggshells are made primarily of calcium carbonate. The acid in vinegar softens the calcium of the eggshell. Adding a little vinegar to the water when boiling eggs is an old cook’s trick that makes them easier to peel.
A link to this experiment is below in the comment box
The precipitation reaction of sodium nitrate and lead (II) chloride would not happen. No reaction will happen between these substances. Hope this answers the question. Have a nice day.