What is the balanced equation of Zn+Pb(NO3)2---Pb+Zn(NO3)2?

The balanced equation is ##"Zn" + "Pb"("NO"_3)_2 → "Pb" + "Zn"("NO"_3)_2##

You follow a systematic procedure to balance the equation.

Start with the given equation:

##"Zn" + "Pb(NO"_3)_2 → "Pb" + "Zn(NO"_3)_2##

A method that often works is to balance everything other than ##"O"## and ##"H"## first, then balance ##"O"##, and finally balance ##"H"##.

Another useful procedure is to start with what looks like the most complicated formula.

The most complicated formula looks like ##"Pb(NO"_3)_2## or ##"Zn(NO"_3)_2##.

Let's choose ##"Pb(NO"_3)_2##. We put a 1 in front of it to remind ourselves that the coefficient is now fixed.

We start with

##"Zn" + color(red)(1) "Pb(NO"_3)_2 → "Pb" + "Zn(NO"_3)_2##

Balance ##"Pb"##:

We have fixed 1 ##"Pb"## on the left, so we need 1 ##"Pb"## on the right. We put a 1 in front of the ##"Pb"##.

##"Zn" + color(red)(1) "Pb(NO"_3)_2 → color(green)(1) "Pb" + "Zn(NO"_3)_2##

Balance ##"N"##:

We have fixed 2 ##"N"## on the left, so we need 2 ##"N"## on the right. We put a 1 in front of the ##"Zn(NO"_3)_2##.

##"Zn" + color(red)(1) "Pb(NO"_3)_2 → color(green)(1) "Pb" + color(orange)(1) "Zn(NO"_3)_2##

Balance ##"Zn"##:

We have fixed 1 ##"Zn"## atom on the right so we need 1 ##"Zn"## atom on the left. We put a 1 in front of the ##"Zn"##.

##color(blue)(1)"Zn" + color(red)(1) "Pb(NO"_3)_2 → color(green)(1) "Pb" + color(orange)(1) "Zn(NO"_3)_2##

Every formula now has a fixed coefficient. We should have a balanced equation.

Let’s check:

##"Element"color(white)(m)"Left-hand side"color(white)(m)"Right-hand side"## ##color(white)(ml)"Zn"color(white)(mmmmmll)1color(white)(mmmmmmmll)1## ##color(white)(ml)"Pb"color(white)(mmmmmll)1color(white)(mmmmmmmll)1## ##color(white)(ml)"N"color(white)(mmmmmml)2color(white)(mmmmmmmll)2## ##color(white)(ml)"O"color(white)(mmmmmml)6color(white)(mmmmmmmll)6##

All atoms balance. The balanced equation is

##color(red)("Zn" + "Pb"("NO"_3)_2 → "Pb" + "Zn"("NO"_3)_2##

Surprise! The original equation was already balanced.