**How is soap made?**

The manufacture of soap requires a number of chemistry techniques. One necessary piece of information is the saponification number. This is the amount of base needed to hydrolyze a certain amount of fat to produce the free fatty acids that are an essential part of the final product. The fat is heated with a known amount of base (usually NaOH or KOH). After hydrolysis is complete, the left-over base is titrated to determine how much was needed to hydrolyze the fat sample.

### Titration Calculations

At the equivalence point in a neutralization, the moles of acid are equal to the moles of base.

\begin{align*}\text{moles acid} = \text{moles base}\end{align*}

Recall that the molarity \begin{align*}(M)\end{align*} of a solution is defined as the moles of the solute divided by the liters of solution \begin{align*}(L)\end{align*}. So the moles of solute are therefore equal to the molarity of a solution multiplied by the volume in liters.

\begin{align*}\text{moles solute} = M \times L\end{align*}

We can then set the moles of acid equal to the moles of base.

\begin{align*}M_A \times V_A=M_B \times V_B\end{align*}

\begin{align*}M_A\end{align*} is the molarity of the acid, while \begin{align*}M_B\end{align*} is the molarity of the base. \begin{align*}V_A\end{align*} and \begin{align*}V_B\end{align*} are the volumes of the acid and base, respectively.

Suppose that a titration is performed and 20.70 mL of 0.500 M NaOH is required to reach the end point when titrated against 15.00 mL of HCl of unknown concentration. The above equation can be used to solve for the molarity of the acid.

\begin{align*}M_A=\frac{M_B \times V_B}{V_A}=\frac{0.500 \ \text{M} \times 20.70 \ \text{mL}}{15.00 \ \text{mL}}=0.690 \ \text{M}\end{align*}

The higher molarity of the acid compared to the base in this case means that a smaller volume of the acid is required to reach the equivalence point.

The above equation works only for neutralizations in which there is a 1:1 ratio between the acid and the base. The sample problem below demonstrates the technique to solve a titration problem for a titration of sulfuric acid with sodium hydroxide.

#### Sample Problem: Titration

In a titration of sulfuric acid against sodium hydroxide, 32.20 mL of 0.250 M NaOH is required to neutralize 26.60 mL of H_{2}SO_{4}. Calculate the molarity of the sulfuric acid.

*Step 1: List the known values and plan the problem.*

Known

- molarity NaOH = 0.250 M
- volume NaOH = 32.20 mL
- volume H
_{2}SO_{4}= 26.60 mL

Unkonwn

- molarity H
_{2}SO_{4}= ?

\begin{align*}\text{equation} \qquad \text{H}_2 \text{SO}_4(aq)+2\text{NaOH}(aq) \rightarrow \text{Na}_2\text{SO}_4(aq)+2\text{H}_2\text{O}(l) \end{align*}

First determine the moles of NaOH in the reaction. From the mole ratio, calculate the moles of H_{2}SO_{4} that reacted. Finally, divide the moles H_{2}SO_{4} by its volume to get the molarity.

*Step 2: Solve.*

\begin{align*}& \text{mol NaOH}=M \times L=0.250 \ \text{M} \times 0.03220 \ \text{L}=8.05 \times 10^{-3} \ \text{mol} \ NaOH \\ & 8.05 \times 10^{-3} \ \text{mol NaOH} \times \frac{1 \ \text{mol H}_2\text{SO}_4}{2 \ \text{mol NaOH}}=4.03 \times 10^{-3} \ \text{mol H}_2\text{SO}_4 \\ & \frac{4.03 \times 10^{-3} \ \text{mol H}_2\text{SO}_4}{0.02660 \ \text{L}}=0.151 \ \text{M H}_2\text{SO}_4 \end{align*}

*Step 3: Think about your result.*

The volume of H_{2}SO_{4} required is smaller than the volume of NaOH because of the two hydrogen ions contributed by each molecule.

### Review

- What assumption is made about the amounts of materials at the neutral point?
- What is different about the calculation using sulfuric acid?
- Why is the mole ratio important?