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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 [ H 3 O + ] 0 = 0.100 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:

n ( H + ) 0 = [ H 3 O + ] 0 × 0.02500 L = 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:

n ( OH ) 0 = 0.100 M × X mL × ( 1 L 1000 mL )

The total volume becomes: V = ( 25.00 mL + X mL ) ( 1 L 1000 mL )

The number of moles of H 3 O + becomes:

n ( H + ) = n ( H + ) 0 n ( OH ) 0 = 0.002500 mol 0.100 M × X mL × ( 1 L 1000 mL )

The concentration of H 3 O + is:

[ H 3 O + ] = n ( H + ) V = 0.002500 mol 0.100 M × X mL × ( 1 L 1000 mL ) ( 25.00 mL + X mL ) ( 1 L 1000 mL ) = 0.002500 mol × ( 1000 mL 1 L ) 0.100 M × X mL 25.00 mL + X mL
pH = −log ( [ H 3 O + ] )

The preceding calculations work if n ( H + ) 0 n ( OH ) 0 > 0 and so n(H + )>0. When n ( H + ) 0 = n ( OH ) 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:

[ H 3 O + ] = [ OH ] , [ H 3 O + ] = K w = 1.0 × 10 −14 ; [ H 3 O + ] = 1.0 × 10 −7
pH = −log ( 1.0 × 10 −7 ) = 7.00

Finally, when n ( OH ) 0 > n ( H + ) 0 , there are not enough H 3 O + ions to neutralize all the OH ions, and instead of n ( H + ) = n ( H + ) 0 n ( OH ) 0 , we calculate: n ( OH ) = n ( OH ) 0 n ( H + ) 0

In this case:

[ OH ] = n ( OH ) V = 0.100 M × X mL × ( 1 L 1000 mL ) 0.002500 mol ( 25.00 mL + X mL ) ( 1 L 1000 mL ) = 0.100 M × X mL 0.002500 mol × ( 1000 mL 1 L ) 25.00 mL + X mL
pH = 14 pOH = 14 + log ( [ OH ] )

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

(a) X = 0 mL

[ H 3 O + ] = n ( H + ) V = 0.002500 mol × ( 1000 mL 1 L ) 25.00 mL = 0.1 M

Questions & Answers

mention some examples of ester
Chinenye Reply
do you mean ether?
Megan
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Rozzi Reply
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Bulus
oi
Amargo
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Bassidi
similarities between elements in the same group and period
legend Reply
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Nadeen
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Nadeen
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Amarachi Reply
please what is the chemical configuration of sodium
Sharon
2.8.1
david
1s²2s²2p⁶3s¹
Haile
2, 6, 2, 1
Salman
1s2, 2s2, 2px2, 2py2, 2pz2, 3s1
Justice
1s2,2s2,2py2,2
Maryify
1s2,2s2,2p6,
Francis
1s2,2s2,2px2,2py2,2pz2,3s1
Nnyila
what is criteria purity
Austin Reply
cathode is a negative ion why is it that u said is negative
Michael Reply
cathode is a negative electrode while cation is a positive ion. cation move towards cathode plate.
king
CH3COOH +NaOH ,complete the equation
david Reply
compare and contrast the electrical conductivity of HCl and CH3cooH
Sa Reply
The must be in dissolved in water (aqueous). Electrical conductivity is measured in Siemens (s). HCl (aq) has higher conductivity, as it fully ionises (small portion of CH3COOH (aq) ionises) when dissolved in water. Thus, more free ions to carry charge.
Abdelkarim
HCl being an strong acid will fully ionize in water thus producing more mobile ions for electrical conduction than the carboxylic acid
Valentine
differiante between a weak and a strong acid
david
how can I tell when an acid is weak or Strong
Amarachi
an aqueous solution of copper sulphate was electrolysed between graphite electrodes. state what was observed at the cathode
Bakanya Reply
write the equation for the reaction that took place at the anode
Bakanya
what is enthalpy of combustion
Bakanya
Enthalpy change of combustion: It is the enthalpy change when 1 mole of substance is combusted with excess oxygen under standard conditions. Elements are in their standard states. Conditions: pressure = 1 atm Temperature =25°C
Abdelkarim
Observation at Cathode: Cu metal deposit (pink/red solid).
Abdelkarim
Equation at Anode: (SO4)^2- + 4H^+ + 2e^- __> SO2 + 2H2O
Abdelkarim
Equation : CuSO4 -> Cu^2+ + SO4^2- equation at katode: 2Cu^2+ + 4e -> 2Cu equation at anode: 2H2O -> 4H+ + O2 +4e at the anode which reacts is water because SO4 ^ 2- cannot be electrolyzed in the anode
Niken
what is the electrolysis of sulphuric acid
Bakanya Reply
why is electrolysis difficult using solid lead chloride
Bakanya
what is heat formation
Biefon Reply
what are atoms
Happy Reply
this are small substances that form together and complained one
Belvine
okay gud
Bol
what's covalent bonding
Basil Reply
Covalent bonds are characterized by the sharing of electrons between two or more atoms. These bonds mostly occur between nonmetals or between two of the same (or similar) elements.
Haile
covalent bonding is the mutual sharing of electrons between two element in a molecule, usually it involves non metals as they are less ionic and more electronegative than metals( ionic). and these bonds have high enthalpy of formation. and are strong bonds than most of the bond.
Chiranjeev
covalent bonding involves both nonmetals where there is complete sharing of electrons on the outermost energy level
david
I don't understand
Belvine
Practice Key Terms 3

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Source:  OpenStax, Chemistry. OpenStax CNX. May 20, 2015 Download for free at http://legacy.cnx.org/content/col11760/1.9
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