Find the pH of the equivalence point(s) and the volume (mL) of 0.0372 M NaOH needed to reach the

Find the pH of the equivalence point(s) and the volume (mL)...

Key Concepts

pH Calculation at Equivalence

At the equivalence point in a weak acid-strong base titration, the solution contains the conjugate base, which reacts with water in a hydrolysis reaction to produce hydroxide ions. The resulting pH is determined by the equilibrium established by this reaction, where the base dissociation constant (Kb) is calculated from the known acid dissociation constant (Ka) and the ion-product constant of water (Kw). This concept is central to finding the actual pH value at the equivalence point.

Reaction Stoichiometry

Reaction stoichiometry involves using the measured volumes and concentrations to calculate the number of moles of reactants and products. In titration problems, the stoichiometric relationship allows determination of the volume of titrant required for complete neutralization, which is crucial for locating the equivalence point(s) and subsequent calculations like pH determination.

Polyprotic Acid Titration

A polyprotic acid, such as a weak diprotic acid, donates more than one proton and therefore exhibits multiple equivalence points during titration. Each equivalence point corresponds to the neutralization of one of the acid’s protons, and the pH at each point can be calculated separately based on the nature and strength of the acid and its conjugate bases. Understanding this concept is essential for analyzing titrations involving acids that can donate multiple protons.

Acid?Base Titration

Acid?base titration is an analytical procedure in which a solution of known concentration (titrant) is gradually added to a solution of unknown concentration until the chemical reaction between the two is complete. In these problems, a strong base (NaOH) is used to titrate a weak acid or a weak diprotic acid, thereby allowing calculation of both the equivalence point’s pH and the volume of titrant required based on stoichiometric relationships.

Equivalence Point

The equivalence point in a titration is the stage at which the moles of titrant added are exactly sufficient to completely react with the moles of analyte present in the solution. For a weak acid titrated by a strong base, the solution at the equivalence point consists chiefly of the conjugate base, whose hydrolysis affects the overall pH. In the case of a diprotic acid, two equivalence points exist corresponding to the successive neutralization of each acidic proton.

Transcript

00:02 Question number 58 includes two problems of a weak acid being titrated with a strong base.

00:11 For the first weak acid, it's monoprotic, and there's only one equivalence point, but for the second weak acid, it's diprotic, and there are two equivalence points.

00:22 We're asked to calculate the volume of sodium hydroxide required to reach each equivalence point, 1 in part a and 2 in part b.

00:34 Then we are asked to calculate the ph at each equivalence point.

00:41 For part a, we have 42 .2 milliliters of acetic acid at 0 .052 molar.

00:50 So if we were to take the 0 .0 4 to 2 liters, which corresponds to 42 .2 milliliters, multiply it by the concentration, we will get moles of acety.

01:03 Acetic acid we are starting with.

01:05 One mole of acetic acid reacts with one mole of base sodium hydroxide because all acid -based titration reactions to reach an equivalence point, just one equivalence point, is a one -to -one stoichiometry.

01:21 Once we have moles of base required, we can divide by the molarity of the base solution, 0 .0372 molar, and we will get the liters of base required.

01:33 To neutralize this volume of acid, and we can multiply by a thousand to get milliliters, 58 .99 milliliters.

01:44 Then we are asked to calculate the ph of the solution at the equivalence point.

01:51 Ph is always equal to the negative log of the hydronium concentration.

01:55 So how are we going to calculate the hydronium concentration? well, at the equivalence point, all of the acetic acid has turned into acetate.

02:04 So we have the weak conjugate base of acetic acid.

02:09 So we need to carry out a weak base kb calculation in order to get the hydroxide concentration, which we can then use to get the hydronium concentration.

02:22 So if then ph is equal to the negative log of the hydrogenium concentration, and we are calculating the hydroxide concentration first, then we need to divide the hydroxide concentration into kw, 1 .0 times 10 to negative 14, to get our ph.

02:42 So, ph is equal to negative log of the hydronium concentration, which is the hydroxide concentration, divided into kw.

02:50 So how do we get the hydroxide concentration? remember if we have a weak base, the hydroxide concentration is equal to the square root of the kb, value.

03:03 We don't have the kb value for acetate, but we do have the ka value.

03:08 The kb value will be the ka value, 1 .8 times 10 to negative 5, divided into kw.

03:15 So the hydrogenium concentration is the square root of kb multiplied by the weak base concentration.

03:23 Well, all of the weak acid, acetic acid, has turned into the weak base.

03:28 So if we take the volume times the molarity of acetic acid, we will get the moles of acetic acid we are starting with, which is now the moles of weak base acetate that we have.

03:42 If we divide that by the new volume, then here what's in parentheses is the molarity of the weak base at the equivalence point.

03:54 The new volume being the 42 .2 milliliters or 0 .04 to 2 liters plus the equivalence point volume, 58 .99 milliliters or .05989.

04:07 So this is the weak base concentration.

04:10 This is kb...

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