# Quantitative Analysis of Acids and Bases

### Gravimetric Analysis

Gravimetric analysis uses the mass of the precipitate of the ions being analyzed to determine concentration.
Quantitative analysis of acid-base solutions is the process of determining concentrations of H+ or OH ions. Gravimetric analysis uses the mass of a precipitate formed by a reaction to determine the starting concentration of an analyte, or the solution being measured. A solution of unknown concentration is combined with another substance that will cause the formation of a precipitate, a solid that falls out of solution. The mass of that precipitate can then be determined experimentally, and the molar quantities of one or more analyte ions present in the initial solution can be determined.

For example, start with a solution of NaOH. Adding a measured amount (mass) of magnesium sulfate, MgSO4, to the solution will immediately precipitate Mg(OH)2, which has a very low solubility relative to the starting materials. The mass of precipitate Mg(OH)2, an insoluble hydroxide, can then be used to determine the starting concentration of OH.

Step-By-Step Example
Using Gravimetric Analysis
A 225-mL volume of 1.0 M MgSO4 in water is added to an aqueous 135 mL solution of unknown NaOH concentration. The addition of the MgSO4 causes 10.0 grams of solid Mg(OH)2 to form. What is the original concentration of OH in the initial solution?
Step 1
Write the balanced reaction.
$2{\rm{NaOH}}(aq)+{\rm{MgSO}}_{4}(aq)\rightarrow{\rm{Mg}({OH}})_{2}(s)+{\rm{Na}}_{2}{\rm{SO}_{4}}(aq)$
Step 2
Determine the number of moles of Mg(OH)2 formed.
\begin{aligned}\text{moles of}\;{\rm{ Mg(OH)}}_2&=\left(\text{mass of}\;{\rm Mg(OH)}_{2}\right)\left(\text{molar mass of}\;{\rm Mg(OH)}_2\right)\\&=\left(10.0\;\rm{g\; Mg(OH)}_2\right)(58.32\;\rm{g/mol \;Mg(OH)}_{2})\\&=0.1715\;\rm{mol\;Mg(OH)}_2\end{aligned}
Step 3
Each mole of solid Mg(OH)2 formed requires 2 moles of hydroxide, OH, so the total number of moles of hydroxide in the resulting precipitate is twice that of the concentration of Mg2+ present:
$\left(\frac{2\;\rm{mol\;OH}^{-}}{1\;\rm{mol}\;\rm{Mg(OH)}_{2}}\right)\!(0.1715\;\rm{mol}\;\rm{Mg(OH)}_{2})=0.3430\;\rm{mol}\;\rm{OH}^{-}$
Solution
To find the original molarity, divide by the original volume of NaOH, in liters.
$\left(\frac{2\;\rm{mol\;OH}^{-}}{1\;\rm{mol\;Mg(OH)}_{2}}\right)\!(0.1715\;\rm{mol \;Mg(OH)}_{2})=0.3430\;\rm{mol\;OH}^{-}$
Therefore, the original solution of NaOH contained 2.54 M OH.

### Titration

Titration analysis is a method of determining the concentration of a solution by neutralizing it with a measured amount of solution of known concentration.
Acid-base titration is a quantitative method that relies on measuring the volume of a solution of a known concentration necessary to neutralize a given volume of acid or base. Often, acid-base titration involves an indicator, a chemical that undergoes a color change near or at the equivalence point in a titration. In the case of a titration, use an indicator that changes color at the equivalence point, the pH at which all of acid or base molecules in an acidic or basic solution have been neutralized.

Steps in performing titration analysis:

1. Obtain a measured amount of the analyte, which is the solution being analyzed (titrated) to determine its concentration, or dissolve a known amount of solute, add a few drops of indicator, and add water to a measured amount. Either of these techniques will result in a solution of known volume but unknown concentration of the analyte, the species being analyzed (often H+ or OH).

2. Create a solution of known concentration, called the titrant, that is used to neutralize a solution of unknown concentration (the analyte) in order to determine its concentration.

3. Pour some of the titrant into a buret, a type of graduated tube with a stopcock at the end that allows fine control of the release of the titrant. Note the amount of solution in the buret.

4. Slowly add titrant to the analyte solution until the color change occurs.

5. Note the volume of titrant used, and use this datum to calculate the molarity of the analyte solution.

Step-By-Step Example
Using Titration to Determine the Concentration of an Acid
A titration is performed using 1.0 M NaOH to titrate 430 mL of an H2SO4 solution of unknown concentration. The neutralization requires 48 mL of NaOH. Find the concentration of the acid solution.
Step 1
Write the balanced equation.
${\rm{H}_{2}{SO}_{4}}(aq)+2{\rm{NaOH}}(aq)\rightarrow{\rm{Na_{2}}\rm{SO}_{4}}(aq)+2{\rm{H}_{2}{O}}(aq)$
Step 2
Use the volume of NaOH used and its molarity to determine the number of moles of NaOH used in the titration.
\begin{aligned}\text{moles of }\rm{NaOH}\text{ used}&=(\text{volume of }\rm{NaOH})(\text{molarity of }\rm{NaOH})\\&=\left( {0.048{\;\rm{L}}} \right)\left( {1.0{\;\rm{M}\;\rm{NaOH}}} \right)\\&= 0.048{\;\rm{ mol\;NaOH}}\end{aligned}
Solution
It takes two moles of NaOH to neutralize one mole of H2SO4, so multiply by the mole ratio.
$(0.048{\,\rm{mol\;NaOH)}}\!\left(\frac{1{\,\rm{mol\;H}}_{2}{\rm{SO_{4}}}}{2{\,\rm{ mol\;NaOH}}}\right)=0.024\;{\rm{mol}}{\,\rm{H_{2}}}{\rm{SO_{4}}}\text{ neutralized}$