Introduction to Measurement in Chemistry
Welcome! In Chemistry, especially in your Unit 3: Practical Skills exam, it isn't enough to just get a result. You need to know how reliable that result is. Whether you are measuring the volume of a gas or the temperature change in a reaction, every measurement has some level of "doubt." In this chapter, we will learn how to describe that doubt using the concepts of accuracy, precision, and uncertainty.
Don't worry if these terms sound similar at first—by the end of these notes, you'll be able to distinguish them easily and calculate errors like a pro!
1. Accuracy vs. Precision
In everyday life, we use these words interchangeably, but in the Chemistry lab, they mean very different things. A great way to remember the difference is to think of a dartboard.
Accuracy
Accuracy is how close a measurement is to the true value or the "accepted" value. If you are aiming for the bullseye, an accurate throw hits the center. In a lab, if the true concentration of an acid is \(0.100 \text{ mol dm}^{-3}\) and you calculate \(0.099 \text{ mol dm}^{-3}\), your result is very accurate.
Precision
Precision is how close a series of measurements are to each other. It is about consistency. If you throw three darts and they all land in the same small spot in the "double 5" section, you are very precise, even if you are not accurate (because you missed the bullseye!).
Key Takeaway: You can be precise without being accurate! This usually happens when there is a problem with your equipment.
2. Understanding Errors
In science, an "error" isn't necessarily a "mistake" (like spilling your solution). It refers to the difference between your measured value and the true value. There are two main types you need to know for your exam:
Random Errors
These cause measurements to be scattered around the true value. They affect precision. Example: Reading a burette from a slightly different angle each time (parallax error) or slight fluctuations in room temperature. How to reduce them: Repeat the experiment and calculate a mean (average).
Systematic Errors
These cause the measurement to be "off" by the same amount every single time. They affect accuracy. Example: A balance that hasn't been "zeroed" correctly, so it always adds \(0.05 \text{ g}\) to every mass. How to reduce them: Recalibrate your equipment or change your experimental technique.
3. Measurement Uncertainty
Every piece of lab equipment has a limit to how "fine" it can measure. This is called its resolution. The uncertainty is the range in which the true value is expected to lie.
For most manual equipment (like a thermometer or a ruler), the uncertainty is usually taken as plus or minus (\( \pm \)) half of the smallest scale division. However, for digital equipment, it is usually the smallest scale division itself.
Quick Tip: For a burette, the smallest division is \(0.1 \text{ cm}^3\). We usually say the uncertainty of a single reading is \( \pm 0.05 \text{ cm}^3 \).
The "Two-Reading" Rule
Some measurements involve taking two readings to find a difference. In these cases, the uncertainty is doubled. Common examples include:
1. Burette Titrations: You take an initial reading and a final reading.
2. Temperature Changes (\( \Delta T \)): You measure \( T_{\text{initial}} \) and \( T_{\text{final}} \).
3. Mass Changes: You weigh a container, then the container + substance.
Example: If a thermometer has an uncertainty of \( \pm 0.5 \text{ °C} \), the uncertainty of a temperature change is \( 0.5 \times 2 = \pm 1.0 \text{ °C} \).
4. Calculating Percentage Uncertainty
This is a very common calculation in the Unit 3 exam. It tells us how significant the error is compared to the size of the measurement itself.
The formula is:
\( \text{Percentage Uncertainty} = \frac{\text{Uncertainty}}{\text{Measured Value}} \times 100 \)
Example Calculation:
You use a balance with an uncertainty of \( \pm 0.01 \text{ g} \) to weigh \( 2.50 \text{ g} \) of a solid.
\( \text{Percentage Uncertainty} = \frac{0.01}{2.50} \times 100 = 0.4\% \)
Did you know?
To reduce percentage uncertainty, you should try to measure larger quantities. For example, using a larger mass of solid or a larger volume of liquid makes the equipment's fixed uncertainty a smaller "percentage" of the total.
5. Significant Figures (Sig Figs)
When processing data, your final answer should not have more "certainty" than your measurements. In the exam, a good rule of thumb is to give your answer to the same number of significant figures as the measurement with the fewest sig figs used in the calculation (usually 3 sig figs is a safe bet if you are unsure).
Common Mistake to Avoid: Do not round your numbers in the middle of a multi-step calculation! Keep the full number in your calculator and only round the final answer at the very end.
Summary Checklist
1. Accuracy: How close you are to the bullseye (true value).
2. Precision: How close your repeated results are to each other.
3. Random Error: Affects precision; fix it by repeating and averaging.
4. Systematic Error: Affects accuracy; fix it by checking equipment.
5. Percentage Uncertainty: \( \frac{\text{Error}}{\text{Reading}} \times 100 \). Remember to double the error if you took two readings (like in a titration)!
For more details on how these apply to specific experiments, see the chapters on Titrations and Thermochemical Experiments.