Welcome to Evaluation, Errors, and Uncertainties!

In your OCR Chemistry B (Salters) course, practical work isn't just about following a recipe and getting a result. It’s about being a "scientific detective." This chapter focuses on how we look at our results and ask: "How much do I trust this data?" and "How could I make it better?"

Don't worry if the math or the terminology feels a bit heavy at first. Once you master a few simple formulas and definitions, you'll be able to evaluate any experiment like a pro!

1. Accuracy vs. Precision: What’s the Difference?

These two words are often used interchangeably in everyday life, but in the chemistry lab, they mean very different things.

Accuracy is how close your experimental value is to the "true" or accepted value. If the textbook says the enthalpy change is \(-57 \text{ kJ mol}^{-1}\) and you got \(-56.8 \text{ kJ mol}^{-1}\), your result is very accurate.

Precision is how close your repeated measurements are to each other. If you did a titration three times and got \(25.10 \text{ cm}^3\), \(25.15 \text{ cm}^3\), and \(25.10 \text{ cm}^3\), your results are very precise because they are consistent.

Analogy: Think of a dartboard.
- High Accuracy, High Precision: All darts hit the bullseye.
- Low Accuracy, High Precision: All darts hit the same spot, but it’s in the corner of the board, not the bullseye.
- Low Accuracy, Low Precision: The darts are scattered all over the board.

Key Takeaway

Precision is about consistency; Accuracy is about correctness.

2. Understanding Errors

No measurement is ever "perfect." Errors are the reason our results might not be 100% accurate or precise.

Anomalies

An anomaly is a result that doesn't fit the pattern of the rest of your data.
- What to do: If you spot one during an experiment, repeat that part.
- Important: Never include an obvious anomaly in your calculation for a mean (average)!

Random Errors

These cause measurements to be spread around the true value. They are unpredictable.
Example: Your eye being at a slightly different angle when reading a burette (parallax error), or slight fluctuations in room temperature.

Systematic Errors

These occur when your measurements are consistently shifted in one direction (always too high or always too low).
Example: A balance that hasn't been "zeroed" properly, or a gas syringe that leaks.

3. Calculating Uncertainties

Every piece of equipment has a margin of error (also called uncertainty). This is usually half of the smallest scale division.

Absolute Uncertainty

This is the fixed margin of error for a specific piece of kit.
- A balance reading to \(2\) decimal places usually has an uncertainty of \(\pm 0.005 \text{ g}\).
- A \(25.0 \text{ cm}^3\) volumetric pipette usually has an uncertainty of \(\pm 0.06 \text{ cm}^3\).

Percentage Error

This is the most common calculation you will need to do in your exams. It tells us how significant the error is compared to the measurement itself.

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

Important Tip: The "Two-Reading" Rule
If you have to take two readings to get one measurement, you must double the uncertainty.
- Burette: You read the start and the end volume. If each reading is \(\pm 0.05 \text{ cm}^3\), the total uncertainty for the titre is \(0.10 \text{ cm}^3\).
- Thermometer: You read the initial and final temperature. The uncertainty is doubled for the temperature change (\(\Delta T\)).
- Mass: If you weigh a container, then the container + solid, and subtract them, you have two readings!

Step-by-Step Example:

You measure a temperature rise of \(10.5 \text{ } ^\circ\text{C}\) using a thermometer with an uncertainty of \(\pm 0.5 \text{ } ^\circ\text{C}\) per reading.
1. Because you measured two temperatures (start and end), the total uncertainty is \(0.5 \times 2 = 1.0 \text{ } ^\circ\text{C}\).
2. \(\text{Percentage Error} = \frac{1.0}{10.5} \times 100 = 9.52\%\).

4. Evaluating and Refining Procedures

In Component 03 (Practical Skills), you are often asked how to improve an experiment. This is called refining the design.

Common Limitations and Fixes:

  • Problem: Heat loss to the surroundings (common in enthalpy experiments).
    Refinement: Use a polystyrene cup with a lid (insulation) or a vacuum flask.
  • Problem: The percentage error in a titration is too high because the titre volume is too small.
    Refinement: Decrease the concentration of the solution in the burette or increase the amount of substance in the flask to get a larger titre.
  • Problem: Difficulty in seeing a colour change at the end-point.
    Refinement: Use a pH meter or place a white tile under the flask.
  • Problem: Mass of a very small amount of solid is inaccurate.
    Refinement: Use a balance with more decimal places (e.g., a 3-place balance instead of a 2-place balance).

5. Summary Checklist

When you are evaluating an experiment in your exam, ask yourself these three questions:

1. Is the data valid? (Did we measure what we intended to measure? Were variables controlled?)

2. Is the data accurate and precise? (Check the percentage errors and the consistency of repeats.)

3. What were the procedural limitations? (Identify where the "leaks" in the method were—heat loss, evaporation, incomplete reactions—and suggest specific equipment to fix them.)

Quick Review:
  • Accuracy: Closeness to true value.
  • Precision: Closeness of repeats.
  • Anomalies: Results to be ignored in averages.
  • Doubling Error: Do this for burettes, thermometers, and balances (when calculating a difference).

Pro-tip for Salters Students: Always look at the Significant Figures of your answer! Your final answer should generally be given to the same number of significant figures as the measurement with the fewest significant figures used in the calculation. (See the "Analysis, graphs and significant figures" chapter for more on this!)