## Introduction

In chemistry, precipitation reactions are commonly used to form a solid precipitate from two aqueous solutions. One example of a precipitation reaction is the reaction between lead(II) nitrate and potassium iodide, which forms lead iodide as the precipitate. To properly understand and study this reaction, it is important to balance its chemical equation.

## Word Equation

The word equation for the precipitation reaction between lead(II) nitrate and potassium iodide is:

*Lead(II) nitrate + potassium iodide → potassium nitrate + lead iodide*

## Input Interpretation

The word equation can be translated into a chemical equation, which is as follows:

*Pb(NO3)2 + KI → KNO3 + PbI2*

## Balanced Equation

To balance the chemical equation, we must add stoichiometric coefficients to the reactants and products until the number of atoms on both sides of the equation is equal. This can be achieved by following the steps below:

**Step 1 **

Write the unbalanced chemical equation.

**Pb(NO3)2 + KI → KNO3 + PbI2**

**Step 2 **

Assign variables to the stoichiometric coefficients of each compound.

**c1Pb(NO3)2 + c2KI → c3KNO3 + c4PbI2**

**Step 3 **

Create a system of equations by setting the number of atoms of each element in the reactants equal to the number of atoms of each element in the products.

*N: 2c1= c3*

*O: 6c1 = 3c3*

*Pb: c1= c4*

*I: c2=2 c4*

*K: c2= c3*

**Step 4**

Choose an arbitrary value for one of the coefficients and solve the system of equations for the remaining coefficients.

Since the coefficients are relative quantities and underdetermined, we can choose a coefficient to set arbitrarily. To keep the coefficients small, we will choose c1 = 1 and solve for the remaining coefficients.

*c1 = 1*

*c2=2*

*c3=2*

*c4 = 1*

**Step 5 **

Substitute the coefficients into the chemical reaction to obtain the balanced equation.

*Pb(NO3)2 + 2KI → 2KNO3 + PbI2*