# 14.7 Acid-base titrations

 Page 1 / 8
By the end of this section, you will be able to:
• Interpret titration curves for strong and weak acid-base systems
• Compute sample pH at important stages of a titration
• Explain the function of acid-base indicators

As seen in the chapter on the stoichiometry of chemical reactions, titrations can be used to quantitatively analyze solutions for their acid or base concentrations. In this section, we will explore the changes in the concentrations of the acidic and basic species present in a solution during the process of a titration.

## Titration curve

Previously, when we studied acid-base reactions in solution, we focused only on the point at which the acid and base were stoichiometrically equivalent. No consideration was given to the pH of the solution before, during, or after the neutralization.

## Calculating ph for titration solutions: strong acid/strong base

A titration is carried out for 25.00 mL of 0.100 M HCl (strong acid) with 0.100 M of a strong base NaOH the titration curve is shown in [link] . Calculate the pH at these volumes of added base solution:

(a) 0.00 mL

(b) 12.50 mL

(c) 25.00 mL

(d) 37.50 mL

## Solution

Since HCl is a strong acid, we can assume that all of it dissociates. The initial concentration of H 3 O + is ${\left[{\text{H}}_{3}{\text{O}}^{\text{+}}\right]}_{0}=0.100\phantom{\rule{0.4em}{0ex}}M.$ When the base solution is added, it also dissociates completely, providing OH ions. The H 3 O + and OH ions neutralize each other, so only those of the two that were in excess remain, and their concentration determines the pH. Thus, the solution is initially acidic (pH<7), but eventually all the hydronium ions present from the original acid are neutralized, and the solution becomes neutral. As more base is added, the solution turns basic.

The total initial amount of the hydronium ions is:

$\text{n}{\left({\text{H}}^{\text{+}}\right)}_{0}={\left[{\text{H}}_{3}{\text{O}}^{\text{+}}\right]}_{0}\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}\text{0.02500 L}=\text{0.002500 mol}$

Once X mL of the 0.100- M base solution is added, the number of moles of the OH ions introduced is:

$\text{n}{\left({\text{OH}}^{\text{−}}\right)}_{0}=0.100\phantom{\rule{0.4em}{0ex}}M\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}\text{X mL}\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}\left(\phantom{\rule{0.2em}{0ex}}\frac{\text{1 L}}{\text{1000 mL}}\right)\phantom{\rule{0.2em}{0ex}}$

The total volume becomes: $V=\left(\text{25.00 mL}+\text{X mL}\right)\left(\phantom{\rule{0.2em}{0ex}}\frac{\text{1 L}}{\text{1000 mL}}\right)\phantom{\rule{0.2em}{0ex}}$

The number of moles of H 3 O + becomes:

$\text{n}\left({\text{H}}^{\text{+}}\right)=\text{n}{\left({\text{H}}^{\text{+}}\right)}_{0}-\text{n}{\left({\text{OH}}^{\text{−}}\right)}_{0}=\text{0.002500 mol}-0.100\phantom{\rule{0.4em}{0ex}}M\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}\text{X mL}\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}\left(\phantom{\rule{0.2em}{0ex}}\frac{\text{1 L}}{\text{1000 mL}}\right)\phantom{\rule{0.2em}{0ex}}$

The concentration of H 3 O + is:

$\begin{array}{}\\ \\ \left[{\text{H}}_{3}{\text{O}}^{\text{+}}\right]=\phantom{\rule{0.2em}{0ex}}\frac{\text{n}\left({\text{H}}^{\text{+}}\right)}{V}\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}\frac{\text{0.002500 mol}-0.100\phantom{\rule{0.4em}{0ex}}M\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}\text{X mL}\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}\left(\phantom{\rule{0.2em}{0ex}}\frac{\text{1 L}}{\text{1000 mL}}\right)\phantom{\rule{0.2em}{0ex}}}{\left(\text{25.00 mL}+\text{X mL}\right)\left(\phantom{\rule{0.2em}{0ex}}\frac{\text{1 L}}{\text{1000 mL}}\right)\phantom{\rule{0.2em}{0ex}}}\phantom{\rule{0.2em}{0ex}}\\ =\phantom{\rule{0.2em}{0ex}}\frac{\text{0.002500 mol}\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}\left(\phantom{\rule{0.2em}{0ex}}\frac{\text{1000 mL}}{\text{1 L}}\right)\phantom{\rule{0.2em}{0ex}}-0.100\phantom{\rule{0.4em}{0ex}}M\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}\text{X mL}}{\text{25.00 mL}+\text{X mL}}\phantom{\rule{0.2em}{0ex}}\end{array}$
$\text{pH}=\text{−log}\left(\left[{\text{H}}_{3}{\text{O}}^{\text{+}}\right]\right)$

The preceding calculations work if $\text{n}{\left({\text{H}}^{\text{+}}\right)}_{0}-\text{n}{\left({\text{OH}}^{\text{−}}\right)}_{0}>0$ and so n(H + )>0. When $\text{n}{\left({\text{H}}^{\text{+}}\right)}_{0}=\text{n}{\left({\text{OH}}^{\text{−}}\right)}_{0},$ the H 3 O + ions from the acid and the OH ions from the base mutually neutralize. At this point, the only hydronium ions left are those from the autoionization of water, and there are no OH particles to neutralize them. Therefore, in this case:

$\left[{\text{H}}_{3}{\text{O}}^{\text{+}}\right]=\left[{\text{OH}}^{\text{−}}\right],\phantom{\rule{0.2em}{0ex}}\left[{\text{H}}_{3}{\text{O}}^{\text{+}}\right]={K}_{\text{w}}=1.0\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{\text{−14}};\phantom{\rule{0.2em}{0ex}}\left[{\text{H}}_{3}{\text{O}}^{\text{+}}\right]=1.0\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{\text{−7}}$
$\text{pH}=\text{−log}\left(1.0\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{\text{−7}}\right)=7.00$

Finally, when $\text{n}{\left({\text{OH}}^{\text{−}}\right)}_{0}>\text{n}{\left({\text{H}}^{\text{+}}\right)}_{0},$ there are not enough H 3 O + ions to neutralize all the OH ions, and instead of $\text{n}\left({\text{H}}^{\text{+}}\right)=\text{n}{\left({\text{H}}^{\text{+}}\right)}_{0}-\text{n}{\left({\text{OH}}^{\text{−}}\right)}_{0},$ we calculate: $\text{n}\left({\text{OH}}^{\text{−}}\right)=\text{n}{\left({\text{OH}}^{\text{−}}\right)}_{0}-\text{n}{\left({\text{H}}^{\text{+}}\right)}_{0}$

In this case:

$\begin{array}{}\\ \\ \left[{\text{OH}}^{\text{−}}\right]=\phantom{\rule{0.2em}{0ex}}\frac{\text{n}\left({\text{OH}}^{\text{−}}\right)}{V}\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}\frac{0.100\phantom{\rule{0.4em}{0ex}}M\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}\text{X mL}\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}\left(\phantom{\rule{0.2em}{0ex}}\frac{\text{1 L}}{\text{1000 mL}}\right)\phantom{\rule{0.2em}{0ex}}-\text{0.002500 mol}}{\left(\text{25.00 mL}+\text{X mL}\right)\left(\phantom{\rule{0.2em}{0ex}}\frac{\text{1 L}}{\text{1000 mL}}\right)\phantom{\rule{0.2em}{0ex}}}\phantom{\rule{0.2em}{0ex}}\\ =\phantom{\rule{0.2em}{0ex}}\frac{0.100\phantom{\rule{0.4em}{0ex}}M\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}\text{X mL}-\text{0.002500 mol}\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}\left(\phantom{\rule{0.2em}{0ex}}\frac{\text{1000 mL}}{\text{1 L}}\right)\phantom{\rule{0.2em}{0ex}}}{\text{25.00 mL}+\text{X mL}}\phantom{\rule{0.2em}{0ex}}\end{array}$
$\text{pH}=14-\text{pOH}=14+\text{log}\left(\left[{\text{OH}}^{\text{−}}\right]\right)$

Let us now consider the four specific cases presented in this problem:

(a) X = 0 mL

$\left[{\text{H}}_{3}{\text{O}}^{\text{+}}\right]=\phantom{\rule{0.2em}{0ex}}\frac{\text{n}\left({\text{H}}^{\text{+}}\right)}{V}\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}\frac{\text{0.002500 mol}\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}\left(\phantom{\rule{0.2em}{0ex}}\frac{\text{1000 mL}}{\text{1 L}}\right)\phantom{\rule{0.2em}{0ex}}}{\text{25.00 mL}}\phantom{\rule{0.2em}{0ex}}=0.1\phantom{\rule{0.4em}{0ex}}M$

what does the term carbon-12 scale mean
what are the six types of elements
carbon,hydrogen,nitrogen,oxygen,phosphorus and sulphur....#the CHNOPS element
Amanda
👍
clement
those are the six types of elements I know
Amanda
Yea
clement
thats all
Davy
which table is flammable
I haven't gotten to tables o 😥
Rebecca
pls how can I give an IUPAC nomenclature in organic chemistry
The Akanes, Akenes, Akynes, Alkanols, Alkanals and so on. you can further bring out the structural and empirical formula which also is a good example to represent it's numenclature.
Andrew
Paul's exclusion principle
what do you mean by d block ,give more details element
d block elements are also called transition metals. It includes elements from group 3-12 and d block elements hold up to 10 electrons in their shell
Amanda
all?
Davy
they are called transition elements
Andrew
Define chemical formula
they are the mathematical representation of chemicals I guess
Uche
Bohr model of hydrogen atom
what is important of this model
nagesh
this question is not correct, it is Boyles law.
Andrew
what is the main reaction between sodium and chlorine
when a sodium atom is transferred an electron to a chloride atom forming a sodium cation and a chlorde anoin both ions are compltely valence shells and a energetically more stable this reaction is extremely more exothermic producing a bright yellow light abd a great deal of heat energy
sani
well what kind of sodium
coland
sodium chloride
coland
Tyropanoic acid and its salt sodium tyropanoate are radiocontrast agents used in cholecystography (X-ray diagnosis of gallstones). Trade names include Bilopaque, Lumopaque, Tyropaque, and Bilopac. The molecule contains three heavy iodine atoms which obstruct X-rays in the same way as the calcium in
coland
Sodium tetradecyl sulfate (STS) is a commonly used synonym for 7-ethyl-2-methyl-4-undecanyl sulfate sodium salt which is anionic surfactant that is the active component of the sclerosant drug Sotradecol. It is commonly used in the treatment of varicose and spider veins of the leg, during the procedu
coland
Sodium stibogluconate, sold under the brand name Pentostam among others, is a medication used to treat leishmaniasis. This includes leishmaniasis of the cutaneous, visceral, and mucosal types. Some combination of miltefosine, paramycin and liposomal amphotericin B; however, may be recommended due to
coland
Sodium picosulfate (INN, also known as sodium picosulphate) is a Contact stimulant laxative used as a treatment for constipation or to prepare the large bowel before colonoscopy or surgery. It is sold under the trade names Sodipic Picofast, Laxoberal, Laxoberon, Purg-Odan, Picolax, Guttalax, Namilax
coland
Ipodate sodium (sodium iopodate) is an iodine-containing radiopaque contrast media used for X-rays. The drug is given orally and the resulting contrast allows for easy resolution of the bile duct and gall bladder. Other uses Although not FDA approved, ipodate sodium has been used to treat Graves'
coland
Sodium ferric gluconate complex (brand name ferrlecit by Sanofi), is an intravenously administered iron product indicated in the treatment of iron deficiency anemia. It is frequently used in patients undergoing hemodialysis, those undergoing erythropoietin therapy, and/or patients who have chronic k
coland
Dehydrocholic acid is a synthetic bile acid, manufactured by the oxidation of cholic acid. It acts as a hydrocholeretic, increasing bile output to clear increased bile acid load.
coland
Ethylenediaminetetraacetic acid (EDTA), also known by several other names, is an aminopolycarboxylic acid and a colourless, water-soluble solid. Its conjugate base is ethylenediaminetetraacetate. It is widely used to dissolve limescale. Its usefulness arises because of its role as a hexadentate ("s
coland
Sodium aurothiomalate (INN, known in the United States as gold sodium thiomalate) is a gold compound that is used for its immunosuppressive anti-rheumatic effects. Along with an orally-administered gold salt, auranofin, it is one of only two gold compounds currently employed in modern medicine. Med
coland
Sodium ascorbate is one of a number of mineral salts of ascorbic acid (vitamin C). The molecular formula of this chemical compound is C6H7NaO6. As the sodium salt of ascorbic acid, it is known as a mineral ascorbate. It has not been demonstrated to be more bioavailable than any other form of vitamin
coland
Diatrizoic acid (or its anionic form, diatrizoate), also known as amidotrizoic acid, or 3,5-diacetamido-2,4,6-triiodobenzoic acid, is a radiocontrast agent containing iodine. Trade names include Hypaque, Gastrografin, Iothalmate and Urografin, the latter being a combination of the sodium and meglum
coland
Sodium acetrizoate (rINN, trade names Urokon, Triurol and Salpix), the sodium salt of acetrizoic acid, is a high-osmolality, water-soluble, iodine-based radiographic contrast medium no longer in clinical use. Acetrizoate was developed by V.H. Wallingford of Mallinckrodt, and introduced in 1950; it
coland
i think some was missed
coland
what chlorine L-Alpha glycerylphosphorylcholine (alpha-GPC, choline alfoscerate) is a natural choline compound found in the brain. It is also a parasympathomimetic acetylcholine precursor which may have potential for the treatment of Alzheimer's disease and other dementias. Alpha-GPC rapidly delive
coland
Choline Theophyllinate , also known as oxtriphylline, is a cough medicine derived from xanthine that acts as a bronchodilator to open up airways in the lung. Chemically, it is a salt of choline and Theophylline. It classifies as an expectorant. The drug is available under the brand names Choledyl an
coland
Choline (/ˈkoʊlin/) is a water-soluble vitamin. It is usually grouped within the B-complex vitamins. The term cholines refers to the class of quaternary ammonium salts containing the N,N,N-trimethylethanolammonium cation (X− on the right denotes an undefined counteranion). The cation appears in the
coland
thanks
sani
BABARINDE
the oxidation increases
Andrew
hydrogen reacting with water
yes
Moha
what is matter
matter is anything that has Mass and can occupy space
Moshood
apart from those device there is there any device
how many elements do we have
Modern Electronic Theory
a new way or an improvement in modern electrical products.
Andrew
find the volume of oxygen produced from the electrolysis of acidified water of a current of a 2A was passed through the electrolysis of acidified water for 2 hours
14400J
Ese
wrong question, go through it. oxygen cannot be produced.
Andrew