A titration curve is a plot of pH (y-axis) versus volume of added titrant in milliliters (x-axis). To make one, you calculate the pH at several key points during the titration, then plot those values to reveal the characteristic S-shaped curve. The process differs depending on whether you’re working with strong or weak acids and bases, but the underlying logic is the same: figure out what’s in the solution after each addition of titrant, then calculate the pH from that composition.
What You Need Before You Start
Whether you’re building a titration curve from calculations or from lab data, you need a few pieces of information: the concentration of your acid (or base) in the flask, the concentration of the titrant in the burette, and the volume of solution you started with. For calculated curves, you also need the acid dissociation constant (Ka) if you’re working with a weak acid. For lab-generated curves, you need a pH meter or indicator and a burette, which is accurate to ±0.05 mL per reading.
A standard lab setup includes a burette clamped above a conical flask, a white tile underneath to help you spot color changes, a volumetric pipette to measure your starting solution precisely, and a wash bottle of distilled water to rinse the flask walls so no reactant gets stranded above the liquid line.
The Four Zones of a Titration Curve
Every acid-base titration curve has four distinct zones, and you calculate the pH differently in each one. Understanding these zones is the key to building the entire curve.
Initial point: Before any titrant is added. For a strong acid like HCl at 0.100 M, the pH is simply the negative log of the concentration, giving you pH 1.00. For a weak acid like acetic acid, you need to use the Ka expression to solve for the hydrogen ion concentration, which gives a higher starting pH (less acidic) than a strong acid at the same concentration.
Before the equivalence point: You’ve added some base, but acid is still in excess. For a strong acid/strong base titration, calculate the leftover acid concentration by subtracting the moles of base added from the moles of acid you started with, then dividing by the total volume. For a weak acid/strong base titration, this region creates a buffer, and you use the Henderson-Hasselbalch equation: pH = pKa + log([conjugate base] / [weak acid]).
At the equivalence point: The moles of acid and base are exactly equal. For strong acid/strong base, the pH is 7.00 because only water’s self-ionization determines the hydrogen ion concentration. For weak acid/strong base, the equivalence point pH is above 7 because the conjugate base of the weak acid makes the solution slightly basic.
After the equivalence point: Base is now in excess. Calculate the excess hydroxide ion concentration by subtracting the original acid moles from the total base moles added, divide by total volume, then convert to pH using the relationship between hydroxide concentration and the water dissociation constant (Kw = 1.00 × 10⁻¹⁴).
Step-by-Step: Strong Acid With Strong Base
Let’s walk through the most common example: titrating 25.0 mL of 0.100 M HCl with 0.100 M NaOH. You’ll calculate pH at about 10 to 15 different volumes to get a smooth curve.
Start with 0 mL NaOH added. You have pure 0.100 M HCl, so pH = -log(0.100) = 1.00. Next, pick a volume like 5.0 mL NaOH. The moles of HCl remaining are (0.100 × 25.0) – (0.100 × 5.0) = 2.00 mmol. The total volume is now 30.0 mL. So the HCl concentration is 2.00/30.0 = 0.0667 M, and pH = -log(0.0667) = 1.18.
Repeat this for 10.0, 15.0, 20.0, 24.0, 24.9, and 24.99 mL. You’ll notice the pH climbs slowly at first, then starts accelerating as you approach the equivalence point. At exactly 25.0 mL (the equivalence point), the moles are equal and pH = 7.00. For 25.01, 25.1, 26.0, and 30.0 mL, switch to calculating the excess hydroxide concentration, convert to pOH, then subtract from 14 to get pH. The pH jumps rapidly right after the equivalence point, then levels off in the high range.
Calculating several points very close to the equivalence point (24.9, 24.99, 25.01, 25.1 mL) is essential. This is where the curve is steepest, and skipping these points will make your curve look like a gradual slope instead of the dramatic vertical jump that defines a titration curve.
Step-by-Step: Weak Acid With Strong Base
Titrating a weak acid like acetic acid (Ka = 1.8 × 10⁻⁵) with NaOH produces a curve with the same general S-shape but three important differences: the starting pH is higher, the equivalence point pH is above 7, and there’s a flat buffer region in the middle.
At the start (0 mL NaOH), set up an equilibrium calculation using Ka. Acetic acid partially dissociates, so you solve Ka = x²/(initial concentration – x) for x, which gives you the hydrogen ion concentration.
Once you start adding NaOH, the reaction converts some acetic acid into its conjugate base (acetate). This creates a buffer solution, and the Henderson-Hasselbalch equation becomes your main tool. The conjugate base concentration equals the moles of NaOH added divided by total volume. The remaining weak acid concentration equals the original acid moles minus the NaOH moles, divided by total volume. Plug both into pH = pKa + log([A⁻]/[HA]).
There’s an especially useful point halfway to equivalence: when you’ve added exactly half the volume needed to reach the equivalence point, the moles of weak acid and conjugate base are equal. The log term becomes log(1) = 0, so pH = pKa. For acetic acid, that’s pH 4.74. This is the center of the buffer region, where the solution most effectively resists pH changes, and the curve appears flattest. The solution acts as an effective buffer within about one pH unit above and below the pKa.
At the equivalence point, all the weak acid has been converted to its conjugate base. You now solve a base equilibrium problem using Kb (which equals Kw/Ka) to find the hydroxide concentration, then convert to pH. The result is always above 7 for a weak acid/strong base titration.
Polyprotic Acids Have Multiple Curves
Acids that can donate more than one proton, like carbonic acid (H₂CO₃), produce titration curves with multiple equivalence points and multiple plateaus. Each proton comes off in a separate stage. The first proton is easier to remove, so its equivalence point appears first. The second proton, now being pulled from a negatively charged species, requires more base to remove, producing a second, higher equivalence point.
For a diprotic acid, you essentially see two stacked S-curves. A triprotic acid like phosphoric acid shows three. Each plateau between equivalence points represents a buffer region with its own pKa value. You calculate pH in each region using the Ka that corresponds to that particular proton loss, applying the same Henderson-Hasselbalch approach within each buffer zone.
Plotting the Curve by Hand or in a Spreadsheet
Once you’ve calculated pH values at 10 to 15 volumes, plot them with volume of titrant (mL) on the x-axis and pH on the y-axis. Connect the points with a smooth curve, not straight line segments. The result should show a gradual rise, a steep nearly vertical section around the equivalence point, then a leveling off.
If you’re working in a spreadsheet with lab data, enter your volume readings in one column and pH readings in another. Select both columns and create a scatter plot with smooth lines. To pinpoint the equivalence point precisely, calculate the first derivative of your data. In a new column, compute the absolute value of the change in pH divided by the change in volume for each pair of consecutive data points: |ΔpH/ΔV|. In another column, calculate the average volume for each pair. Plot this first derivative on the same chart or a separate one. The sharp peak in the derivative plot marks the equivalence point volume. Drop a vertical line from that peak to the x-axis to read the exact volume.
For even more precision, you can calculate a second derivative (the change in the first derivative divided by the change in volume). The equivalence point is where the second derivative crosses zero.
Choosing an Indicator From the Curve
The steep vertical section of your titration curve tells you which pH indicator will work for a given titration. An indicator changes color over a range of about two pH units. For it to signal the endpoint accurately, that color-change range needs to fall within the steep portion of the curve, where the pH swings dramatically with a single drop of titrant.
For a strong acid/strong base titration, the steep region spans roughly pH 4 to 10, so almost any common indicator works. For a weak acid/strong base titration, the equivalence point is above pH 7 and the steep section is narrower, sitting in the basic range. Phenolphthalein, which changes color between about pH 8 and 10, is a good match. For a strong acid/weak base titration, the equivalence point falls below 7, so you’d want an indicator like methyl orange that changes in the acidic range (pH 3 to 4.5). The titration curve itself is your guide: if the indicator’s transition range doesn’t overlap the steep part, it won’t give you a sharp color change and your results will be imprecise.