Titration Curves Of Strong And Weak Acids And Bases

Setting Up A Titration Curve Experiment

The actual mechanics of running a titration are straightforward, but getting publishable data requires discipline. You start with a clean burette, calibrated at least once per session. Rinse it with the titrant before filling. Your analyte goes into an Erlenmeyer flask, not a beaker, because the swirling motion matters. A magnetic stir bar and a stir plate give you the most consistent mixing. Place the pH electrode in the analyte before you begin adding anything, let it equilibrate for about thirty seconds, then record your initial reading. From there, you add titrant in small increments, pausing after each addition to let the reading stabilize. The increments matter more than most people realize. Near the equivalence point, where the pH is about to jump, you need increments as small as 0.05 milliliters. Far from that region, 0.5 milliliters is fine. I once spent two days troubleshooting a titration curve that looked absolutely wrong. The equivalence point for a strong acid and strong base should show a vertical section spanning roughly six pH units over less than a milliliter of titrant. Mine showed a slope that was nowhere near vertical. Turns out the electrode hadn't been properly stored in KCl solution between uses. The response time had degraded, and the recorded pH values were lagging behind the actual solution pH, which rounded off the sharp corner of the equivalence point into a gentle hill. It took a full electrode reconditioning cycle and a standardization check against pH 4.00 and pH 7.00 buffers before the curve snapped back into shape. That cost me a full day of wasted titrant and calibration attempts.

Titration Curves Of Strong And Weak Acids And Bases

The core difference between strong and weak acid or base titrations shows up in three specific places on the curve: the starting pH, the shape around the equivalence point, and the pH at the equivalence point itself. A strong acid like HCl at 0.1 M starts at pH 1.0 exactly. A weak acid like acetic acid at the same concentration starts around pH 2.9 because only a fraction of the molecules are dissociated. This initial pH gap is the first signal that tells you what you are working with before you even reach the equivalence region. The equivalence point pH is where most students get tripped up. In a strong acid strong base titration, the equivalence point lands at pH 7.0. The salt that forms, NaCl, is neutral. Nothing hydrolyzes. In a weak acid strong base titration, the equivalence point sits above 7.0, typically between pH 8.5 and 9.5 for acetic acid and sodium hydroxide. That is because the conjugate base of the weak acid, acetate in this case, reacts with water to produce hydroxide ions. The reverse happens with a weak base and strong acid. Ammonia titrated with HCl gives an equivalence point around pH 5.3 because the ammonium ion donates protons to water. The shape of the curve in the buffer region is another practical detail that textbooks often gloss over. When you are titrating a weak acid, the curve flattens out before the equivalence point. That flat region is the buffer zone, and its midpoint carries a specific piece of information. At exactly half the volume needed to reach equivalence, the concentrations of the weak acid and its conjugate base are equal. The Henderson-Hasselbalch equation collapses to pH equals pKa plus log of one, and log of one is zero. So the pH at the half-equivalence point equals the pKa of the weak acid. You can determine an unknown pKa directly from the curve without any additional measurements. This is not a trick. It is a reliable experimental method. I use it routinely when I need the pKa of a new compound and do not have a reference value on hand. The uncertainty is usually within ±0.05 pH units if your electrode is well-maintained and your titrant concentration is accurate.

One counter-intuitive detail that is worth knowing: the sharper the equivalence point on a titration curve, the stronger the acid or base you are dealing with. A weak acid with a pKa above 9 produces an equivalence point so gradual that identifying it precisely becomes unreliable. Below pKa 9, the curve still shows a detectable inflection, but the vertical region is much shorter. If you are working with a very weak acid, switching to a potentiometric method with a Gran plot or using an indicator with a transition range matching your equivalence point pH gives better results than relying on the visual shape of the curve alone. Another detail that causes problems in practice is the effect of concentration. Lowering the concentration of both the analyte and the titrant by a factor of ten reduces the pH jump at the equivalence point by roughly one full pH unit. A 0.01 M strong acid strong base titration shows an equivalence jump of about four pH units instead of six. At 0.001 M, the jump is barely visible. This is why analytical chemistry protocols specify minimum concentrations for volumetric titrations. You cannot simply dilute a sample to fit your burette and expect the same precision. When you are analyzing a weak base titrated with a strong acid, the curve looks like a mirror image of the weak acid titration. The starting pH is above 7, the buffer region appears early, and the equivalence point falls below 7. The same half-equivalence principle applies. At the midpoint, pH equals the pKa of the conjugate acid. If you are measuring a weak base, remember that tables list pKb values for the base itself, not pKa for its conjugate. Convert using pKa plus pKb equals 14 at 25 degrees Celsius before you try to match your curve to literature values. Skipping that conversion is a common source of error.

Polyprotic acids introduce a different set of complications. Phosphoric acid has three dissociable protons with pKa values around 2.1, 7.2, and 12.3. The first two equivalence points are clearly visible in a titration curve. The third is not, because the pKa is so high that hydroxide from the strong base titrant competes with the deprotonation step. The curve just continues rising without a distinct inflection. Carbonic acid is worse. Its second pKa is so close to the pH of atmospheric CO2 absorption that your curve will drift over time unless you work under an inert atmosphere. I have seen students report erratic second equivalence points on carbonic acid titrations and spend hours recalibrating electrodes before discovering the real issue was simply the solution being exposed to lab air. For mixing strong acid with weak base or weak acid with strong base, the indicator choice matters more than the curve shape suggests. Bromothymol blue transitions between pH 6.0 and 7.6, which works for strong acid strong base where the equivalence point is at 7.0. Phenolphthalein, transitioning between 8.2 and 10.0, is appropriate for weak acid strong base. Methyl orange, with a range of 3.1 to 4.4, fits weak base strong acid. Matching the indicator range to the equivalence point pH instead of picking something visually appealing prevents endpoint errors that can be as large as 0.5 mL of titrant near the lower concentration limits. There is also a practical issue with temperature. The pH of neutral water shifts with temperature. At 50 degrees Celsius, neutral pH is about 6.63, not 7.0. If you run your titrations at a different temperature than the calibration buffers, your electrode calibration introduces a systematic shift. Most modern electrodes compensate automatically, but older units do not. If your lab maintains a controlled environment at 25 degrees Celsius, this is rarely a problem. If you are working in an unconditioned space during summer, check your calibration buffers at room temperature before you begin.

The biggest limitation of manual titration curves is human reaction time when adding dropwise near the equivalence point. Even a skilled operator introduces about 0.02 to 0.05 milliliters of overshoot per addition when approaching the steep region. Automated titrators eliminate that variability and can add increments as small as 0.005 milliliters. For routine work at 0.1 M concentrations, manual titration gives relative uncertainties around 0.5 percent. For dilute samples or weak acids near the detection limit, automated systems reduce that to below 0.1 percent. The improvement is measurable but not dramatic for concentrated samples. It becomes essential when you are working below 0.01 M or when the pKa difference between successive protons is less than 3 units. If your goal is simply to determine concentration, the titration curve method is reliable and well-understood. If you need to resolve overlapping equivalence points from a mixture of weak acids with similar pKa values, the curve becomes ambiguous and you should switch to a derivative method or use spectrophotometric titration instead. The derivative of the pH curve with respect to volume, d(pH)/dV, highlights inflection points as peaks. A mixture of acetic acid and formic acid, for example, shows two distinct peaks in the derivative plot even when the raw curve makes the two equivalence regions look like a single broad slope. This technique adds about ten minutes to the analysis but resolves ambiguity that would otherwise require independent separation methods.