Question

The measurements of length taken by a student are $15.5\mathrm{cm}$ and $15.6\mathrm{cm}$ whereas the true value is $16\mathrm{cm}$. The measurement taken by the student are (a) precise (b) accurate (c) not precise (d) neither precise not accurate

Short answer

The measurements taken by the student are precise but not accurate, so the correct answer is (c) not accurate.

Step-by-step solution

Determine Precision

Compare the student's measurements to each other. They are 15.5 cm and 15.6 cm, so they are very close to each other. This indicates that these measurements are precise.

Determine Accuracy

Now, we compare the student's measurements to the true value. The true value is 16 cm, but the student's measurements are 15.5 cm and 15.6 cm. They are quite close to the true value but not exactly the same. Thus, these measurements are not completely accurate.

Key concepts

Precision in Measurements

In the world of measurements, precision refers to the consistency of repeated measurements. If you measure the same quantity several times and get results that are very similar to each other, your measurements are considered precise. Precision is important because it indicates how repeatable and reliable your measurements are.

For example, in the exercise given, the student measured lengths of 15.5 cm and 15.6 cm. These measurements are very close to each other, showing that the student's measuring process is precise. If the student were to measure the same item repeatedly and get results like these consistently, it would show a high level of precision regardless of whether the measurements are accurate or not.

Keep in mind that precision doesn't mean you're measuring the true value. It simply means your results are consistent with one another. A measuring tool that is out of calibration can still produce precise results, but they may not be accurate.

Accuracy in Measurements

Accuracy refers to how close a measurement is to the true or accepted value. In our exercise, the true length is 16 cm, while the student reported measurements of 15.5 cm and 15.6 cm. These measurements, although precise (as we discussed), are not completely accurate because they deviate from the true value.

Accuracy is important because it measures the correctness or validity of a measurement. A measurement with high accuracy will be close to the actual or expected value. To achieve high accuracy, it's crucial to use well-calibrated instruments and correct methodologies.

• Accuracy evaluates the correctness of a single measurement.
• It helps in validation of experimental data by comparing with standard or true values.

Understanding accuracy and how it differs from precision is key in all experiments and measurements.

Error Analysis in Physical Chemistry

Error analysis is critical in any scientific measurement process, including physical chemistry, where both the accuracy and precision of measurements can greatly influence results. Errors can stem from various sources such as instrumental failures, human errors, and environmental conditions.

Understanding and analyzing these errors helps scientists improve their methods and outcomes. For instance, systematic errors affect accuracy and are often due to inaccuracies in the measuring device, while random errors affect precision and occur when measurements fluctuate.

• Identify and minimize errors to enhance measurement reliability and accuracy.
• Quantitative error analysis can provide information on both the precision and accuracy of measurements.

In physical chemistry, accurate and precise measurements are essential for reliable experiments, making error analysis a cornerstone of quality data.