Introduction to Evaluation in Chemistry

In Chemistry, performing an experiment and getting a result is only half the battle. The most important question a chemist can ask is: "How much can I trust these results?"

Evaluation is the process of looking at your method and your data to decide if they are reliable. In this chapter, we will learn how to spot "weird" results, calculate exactly how much error our equipment introduces, and suggest ways to make our experiments even better. Whether you are aiming for a career in research or just trying to pass your practical exam, mastering uncertainty is key.

1. Accuracy vs. Precision

These two words are often used interchangeably in everyday life, but in Chemistry, they mean very specific things. Understanding the difference is the first step to evaluating any experiment.

Accuracy

Accuracy refers to how close a measurement is to the true value. If the true boiling point of a substance is \(100^{\circ}C\) and you measure \(99.9^{\circ}C\), your measurement is very accurate.

Precision

Precision refers to how close a series of measurements are to each other. If you repeat an experiment three times and get \(75.2\), \(75.1\), and \(75.2\), your results are precise, even if they are nowhere near the "true" answer.

The Dartboard Analogy: Imagine you are throwing darts.
- Accurate and Precise: All your darts hit the bullseye.
- Precise but not Accurate: All your darts are bunched together, but they are in the top-left corner far from the bullseye.
- Accurate but not Precise: Your darts are scattered all over the board, but their "average" position is the center.

Key Takeaway: We always aim for both, but high precision usually suggests that our technique is consistent.

2. Dealing with Anomalies

An anomaly (or outlier) is a piece of data that does not fit the trend of the rest of the results. For example, if you are measuring the volume of gas produced every minute and your results are \(12, 24, 35, 98, 46\), the number \(98\) is clearly an anomaly.

What should you do with an anomaly?
1. Identify it: Look for results that are significantly different from repeats or the general trend.
2. Investigate it: Was there a splash? Did you start the stopwatch late?
3. Exclude it: When calculating an average (mean), you must not include the anomalous result. Including it will "drag" your average away from the true value.

Quick Tip: In titrations, OCR expects you to only use concordant results (results within \(0.10\text{ cm}^{3}\) of each other) to calculate your mean titre.

3. Uncertainties in Apparatus

No piece of lab equipment is perfect. Every time you take a measurement, there is a small "margin of error" called uncertainty. This is usually printed on the side of the apparatus or determined by the scale divisions.

Margins of Error

The margin of error is the \(\pm\) value associated with a tool. For example:

  • A Volumetric Flask might have an uncertainty of \(\pm 0.2\text{ cm}^{3}\).
  • A Pipette (25 \(\text{cm}^{3}\)) might have an uncertainty of \(\pm 0.06\text{ cm}^{3}\).
  • A Balance reading to two decimal places usually has an uncertainty of \(\pm 0.005\text{ g}\) for a single reading.

The "Two-Reading" Rule

Some measurements involve taking two readings to get one value. In these cases, the total uncertainty is doubled. Common examples include:
- Temperature Change (\(\Delta T\)): You measure the start and the end temperature.
- Mass Change: You weigh the container, then the container + substance.
- Burette Volume: You take an initial reading and a final reading.

If a burette has an uncertainty of \(\pm 0.05\text{ cm}^{3}\) per reading, the total uncertainty for the volume delivered is \(2 \times 0.05 = \pm 0.10\text{ cm}^{3}\).

4. Calculating Percentage Error

To compare how significant an error is, we calculate the percentage error. This tells us what proportion of our measurement might be wrong.

The Formula:
\( \text{Percentage Error} = \frac{\text{Uncertainty}}{\text{Measured Value}} \times 100 \)

Example: You measure \(25.0\text{ cm}^{3}\) of a solution using a measuring cylinder that has an uncertainty of \(\pm 0.5\text{ cm}^{3}\).
\( \text{Percentage Error} = \frac{0.5}{25.0} \times 100 = 2.0\% \)

Don't forget if you took two readings!
If you measured a temperature rise of \(10.0^{\circ}C\) using a thermometer with an uncertainty of \(\pm 0.5^{\circ}C\) per reading:
\( \text{Percentage Error} = \frac{2 \times 0.5}{10.0} \times 100 = 10.0\% \)

Key Takeaway: To reduce percentage error, you should either use more precise equipment (smaller uncertainty) or measure a larger quantity (larger measured value).

5. Limitations and Refining Design

In the evaluation section of an exam, you are often asked to suggest why an experiment gave a result different from the textbook value and how to fix it. This is called refining the design.

Common Limitations and Improvements

1. Heat Loss: In enthalpy experiments (\(q = mc\Delta T\)), heat often escapes to the surroundings.
Refinement: Use a polystyrene cup (insulator), add a lid, or use a copper calorimeter with a draft shield.

2. Large Percentage Error: If you measure a very small mass or a very small temperature change, your percentage error will be huge.
Refinement: Use a more accurate balance (e.g., 3 decimal places instead of 2) or use larger amounts of reactants to get a bigger reading.

3. Evaporation: If you are heating a liquid (like in organic synthesis or alcohol combustion), some of it might evaporate before it reacts.
Refinement: Use a lid or a condenser (Reflux) to prevent vapors from escaping.

4. Difficulty in spotting the end-point: In titrations, the color change might be hard to see.
Refinement: Place the flask on a white tile to see the color more clearly, or use a pH probe.

Quick Review:
- Precision = consistency; Accuracy = closeness to the truth.
- Anomalies should be identified and ignored for averages.
- Percentage Error decreases when the measured value increases.
- Refining means suggesting specific kit or procedural changes to reduce error.

Don't worry if these calculations feel a bit "maths-heavy" at first. Just remember: if you used the equipment twice to get a single number, multiply the error by two. The rest is just simple division!