Titration Setup: Analyte, Titrant, and Buret

This lesson takes a conceptual look at titrations and titration curves, focusing on curve shape and key features rather than numerical pH calculations (those come in the next lessons). Three types of titration curves are covered: strong acid–strong base, weak acid–strong base, and weak base–strong acid. Weak acid–weak base titrations are not considered here — they are rarely encountered in a general chemistry course.

In practice, the most common reason to run a titration is to determine the concentration of an unknown acidic or basic solution. Consider a classic example: you have a solution of HCl and you need to find its concentration. You place the HCl solution in an Erlenmeyer flask. Whatever species you are trying to characterize — in this case the acid — is called the analyte.

You then set up a buret filled with a solution of known, exact concentration. This solution is called the titrant. Because the analyte here is an acid, the titrant is a base — NaOH in this example. The relationship can be reversed: if you are determining the concentration of an unknown base, the base becomes the analyte and an acid serves as the titrant.

What Is the Equivalence Point on a Titration Curve?

The Shape of the pH Curve

When a strong acid like HCl is titrated with NaOH, the solution starts at a low pH. As base is added, the pH rises gradually at first. Then, over the addition of just a drop or two, the pH rockets upward through a nearly vertical region before leveling off again. The midpoint of that steep rise is called the inflection point — the point where the slope of the curve transitions from increasing to decreasing. If you think in calculus terms, the second derivative of pH with respect to volume changes sign at this point. That inflection point is the equivalence point.

Defining the Equivalence Point

For HCl and NaOH, which react in a 1:1 molar ratio, the equivalence point is reached when the moles of NaOH added exactly equal the moles of HCl originally present. At no other point in the titration is this true.

Using the Equivalence Point to Determine Molarity

Here is why this matters practically. You choose how much HCl to place in the flask — say 25.00 mL. The concentration of the NaOH titrant is known precisely, and you read from the buret exactly how much NaOH was required to reach the equivalence point. Plugging those three known values into the equation above lets you solve for the one unknown: the molarity of the HCl. Reaching the equivalence point is the entire objective of the titration.

How Do Indicators Signal the End Point?

In routine titrations, chemists do not pause to measure pH after every addition of titrant. Instead, they use a chemical indicator — a substance that changes color over a specific pH range — to signal when the equivalence point has been reached. The moment the color change is observed is called the end point, which serves as the best practical approximation of the true equivalence point.

Why the Equivalence Point Is pH 7 for Strong Acid–Strong Base Titrations

In a strong acid–strong base titration, the equivalence point occurs at exactly pH 7. The chemistry explains why. Starting with 10 moles of HCl and adding 10 moles of NaOH, both strong species react completely to completion:

Phenolphthalein as an Indicator

Phenolphthalein is the classic indicator for strong acid–strong base titrations. It is itself a weak acid: in its acidic form it is colorless, but its conjugate base form is pink-purple. As the pH surges through the equivalence point — over just a drop or two of added NaOH — the solution transitions from colorless to pink-purple. That color change marks the end point of the titration.

How to Choose the Right Indicator

Each indicator changes color across a range of roughly 2 pH units, centered near its own pK_a. Because the pH jumps so sharply through the equivalence point, the indicator's color change is effectively instantaneous regardless of exactly where within that 2-unit range the transition occurs. The key rule for selecting an indicator is straightforward:

3 Types of Titration Curves and Their Equivalence Point pH

A common misconception is that all equivalence points occur at pH 7 because "equal amounts of acid and base have been added." This is only true when both the acid and the base are strong. When one participant is weak, the equivalence point pH shifts away from 7.

A useful memory aid: whichever species is strong determines which side of 7 the pH falls on at the equivalence point.

• Strong acid–strong base titration: pH = 7 at the equivalence point (neutral salt produced)
• Weak acid–strong base titration: pH > 7 at the equivalence point (basic salt produced; typically pH 7–10)
• Weak base–strong acid titration: pH < 7 at the equivalence point (acidic salt produced; typically pH 4–7)

The deeper reason — as explored in the next two sections — lies in the nature of the salt produced at the equivalence point and whether it undergoes hydrolysis.

Weak Acid–Strong Base Titration Curve

How the Curve Shape Differs from Strong-Strong Titrations

When a weak acid (here, HF) is titrated with a strong base (NaOH), the shape of the titration curve differs noticeably from the strong-strong case. In the strong acid case, adding base from the very beginning produces a long, nearly linear increase in pH. In the weak-strong case, however, there is a pronounced jump in pH right at the start — before the curve flattens into a gradual rise. This initial jump is a hallmark of weak acid–strong base titration curves.

The reaction still goes 100% to completion because one participant (the base) is strong. The equivalence point is still the inflection point of the curve, and the same governing equation applies: at the equivalence point, moles of HF = moles of NaOH, or equivalently:

M_HF × V_HF = M_NaOH × V_NaOH

Why Is the Equivalence Point pH Basic in a Weak Acid–Strong Base Titration?

Starting with 10 moles of HF and adding 10 moles of NaOH, the reaction goes to completion and produces 10 moles of sodium fluoride, NaF. Unlike NaCl, sodium fluoride is not a neutral salt.

If asked on an exam why the pH exceeds 7 at the equivalence point in a weak acid–strong base titration, you can say: the salt produced is a basic salt, or more precisely, the anion of that salt undergoes base hydrolysis to produce hydroxide ions.

The Half-Equivalence Point and the Buffer Region

Why Does the Half-Equivalence Point Matter?

Weak-strong titration curves contain 2 important landmarks, not 1. The second landmark is the half-equivalence point (also called the half-neutralization point) — the point at which exactly half the amount of titrant required to reach the equivalence point has been added. This point is unique to weak acid or weak base titrations, because strong acids do not have meaningful pK_a values.

What Happens Chemically at the Half-Equivalence Point

Suppose it takes 10 moles of NaOH to fully neutralize 10 moles of HF. At the halfway point, only 5 moles of NaOH have been added. That NaOH is entirely consumed, neutralizing 5 moles of HF and producing 5 moles of F⁻. The result is a solution containing equal moles of HF (5 mol) and its conjugate base F⁻ (5 mol).

A 1:1 mixture of a weak acid and its conjugate base is, by definition, a buffer. This is why the pH curve is notably flat in the region surrounding the half-equivalence point — the solution resists pH change, just as any buffer does.

How to Find pK_a from a Titration Curve Using pH = pK_a

Applying the Henderson-Hasselbalch equation when acid and conjugate base concentrations are equal:

It is equally true at the half-equivalence point that pOH = pK_b of the conjugate base. In practice, we focus on pK_a when the analyte is an acid, but both relationships hold simultaneously.

2 Points Students Confuse: Equivalence Point vs Half-Equivalence Point

Students often confuse these two points because both can be described as "the point where moles of acid equal moles of base." The critical distinction is which acid and which base are being compared:

Weak Base–Strong Acid Titration Curve

Curve Shape and Why the Equivalence Point pH Is Below 7

In a weak base–strong acid titration, the roles are reversed: the analyte is a weak base (such as NH₃) and the titrant is a strong acid (such as HCl). The pH therefore starts high and decreases as acid is added, with the same characteristic initial sharp drop followed by a gradual decline that is typical of weak-strong titration curves. The equivalence point is again the inflection point of the curve.

The equivalence point pH is less than 7 — typically in the range of 4 to 7. The reason parallels the weak acid case, but now the salt produced is an acidic salt.

The Half-Equivalence Point in a Weak Base–Strong Acid Titration

The same logic from the weak acid case applies here. If 10 moles of HCl are required to reach the equivalence point, then at the 5-mole mark you are at the half-equivalence point. Those 5 moles of HCl convert 5 moles of NH₃ into 5 moles of NH₄⁺, leaving 5 moles of NH₃ unreacted. The solution now contains equal concentrations of the conjugate acid (NH₄⁺) and the conjugate base (NH₃).

Applying Henderson-Hasselbalch, pH = pK_a of NH₄⁺ at this point. It is equally true that pOH = pK_b of NH₃. If your goal is the pK_b of the weak base, read the pOH at the half-equivalence point rather than the pH.

As with the weak acid titration, the flat region surrounding the half-equivalence point is a buffer zone — the solution resists pH changes within roughly one pH unit above and below pK_a. Outside that range, the buffering capacity is exhausted and the pH changes steeply.