Titration Calculations
From UCDavis Chemwiki
Before we get into titration calculations, let us use what we know about reaction stoichiometry to determine the concentration of a standard solutions.
EXAMPLE 1 Calculate the molarity of a solution of H2SO4 if 30 mL of the solution neutralizes 0.465 g of Na2CO3.
As stated previously, the object of a titration (wether it be acid-base titration or another type which will be discussed in later sections) is always to add just the amount of titrant needed to consume exactly the amount of substance being titrated. In the NaOH—CH3COOH reaction the equivalence point occurs when an equal molar amount of NaOH has been added from the graduated cylinder for every mole of CH3COOH originally in the titration flask. That is, at the equivalence point the ratio of the amount of NaOH, added to the amount of CH3COOH consumed must equal the stoichiometric ratio:
`CH_3COOH (aq) + NaOH (aq) -> Na^(+) (aq) + CH_3COO^(-) (aq) + H_2O(l)`
`(n_(NaOH) ("added from graduated cylinder"))/(n_(CH_3 COOH) ("initially in flash")) = S((NaOH)/(CH_3 COOH))`
`= ( 1 "mol " NaOH "/" 1 "mol " CH_3COOH)`
EXAMPLE 2 How many liters of 3.4 M HI will be required to reach the equivalence point with 2.1 L of 2.0 M KOH?
Titration is often used to determine the concentration of a solution. In many cases it is not a simple matter to obtain a pure substance, weigh it accurately, and dissolve it in a volumetric flask as was done in Example 1 of Solution Concentrations. NaOH, for example, combines rapidly with H2O and CO2 from the air, and so even a freshly prepared sample of solid NaOH will not be pure. Its weight would change continuously as CO2(g) and H2O(g) were absorbed. Hydrogen chloride (HCl) is a gas at ordinary temperatures and pressures, making it very difficult to handle or weigh. Aqueous solutions of both of these substances must be standardized; that is, their concentrations must be determined by titration.
EXAMPLE 3 A sample of pure Acetic acid weighing 0.3421 g is dissolved in distilled water. Titration of the sample requires 27.03 ml NaOH(aq). The titration reaction is
`NaOH(aq) + CH_3 COOH (aq) -> NaCH_3 COO(aq) + H_2O`
What is the concentration of NaOH(aq)?
By far the most common use of titrations is in determining unknowns, that is, in determining the concentration or amount of substance in a sample about which we initially knew nothing. The next example involves an unknown that many persons encounter every day.
EXAMPLE 4 Vitamin C tablets contain ascorbic acid (C6H8O6) and a starch “filler” which holds them together. To determine how much vitamin C is present, a tablet can be dissolved in water and sodium hydroxide solution, NaOH(aq). The equation is
`C_6 H_8 O_6 (aq) + NaOH(aq) -> Na C_6 H_7 O_6 (aq) + H_2 O(l)`
If titration of a dissolved vitamin C tablet requires 16.85 cm³ of 0.1038 M NaOH, how accurate is the claim on the label of the bottle that each tablet contains 300 mg of vitamin C?
The 308.0 mg obtained in this example is in reasonably close agreement with the manufacturer’s claim of 300 mg. The tablets are stamped out by machines, not weighed individually, and so some variation is expected.
