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

May 26, 2014

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

#### Explanation:

You follow a systematic procedure to balance the equation.

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

A method that often works is to balance everything other than $\text{O}$ and $\text{H}$ first, then balance $\text{O}$, and finally balance $\text{H}$.

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.

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

Balance $\text{Pb}$:

We have fixed 1 $\text{Pb}$ on the left, so we need 1 $\text{Pb}$ on the right. We put a 1 in front of the $\text{Pb}$.

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

Balance $\text{N}$:

We have fixed 2 $\text{N}$ on the left, so we need 2 $\text{N}$ 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 $\text{Zn}$:

We have fixed 1 $\text{Zn}$ atom on the right so we need 1 $\text{Zn}$ atom on the left. We put a 1 in front of the $\text{Zn}$.

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:

$\text{Element"color(white)(m)"Left-hand side"color(white)(m)"Right-hand side}$
$\textcolor{w h i t e}{m l} \text{Zn} \textcolor{w h i t e}{m m m m m l l} 1 \textcolor{w h i t e}{m m m m m m m l l} 1$
$\textcolor{w h i t e}{m l} \text{Pb} \textcolor{w h i t e}{m m m m m l l} 1 \textcolor{w h i t e}{m m m m m m m l l} 1$
$\textcolor{w h i t e}{m l} \text{N} \textcolor{w h i t e}{m m m m m m l} 2 \textcolor{w h i t e}{m m m m m m m l l} 2$
$\textcolor{w h i t e}{m l} \text{O} \textcolor{w h i t e}{m m m m m m l} 6 \textcolor{w h i t e}{m m m m m m m l l} 6$

All atoms balance. The balanced equation is

${\textcolor{red}{{\text{Zn" + "Pb"("NO"_3)_2 → "Pb" + "Zn"("NO}}_{3}}}_{2}$

Surprise! The original equation was already balanced.