Precision and Accuracy in General Chemistry

In the study of chemistry, particularly in experimental procedures, the concepts of precision and accuracy are foundational. Understanding these concepts not only facilitates better experimental results but also fosters proper interpretation of scientific data.

Definitions

Accuracy refers to how close a measured value is to the actual or true value, which is often considered a standard measure. In contrast, Precision signifies how close multiple measurements are to each other, regardless of their proximity to the true value. This distinction is critical in determining the reliability and validity of experimental data.

Understanding Accuracy and Precision Through Examples

To illustrate these concepts, consider the case where a standard measure of a table's length is 16 cm. A student conducts three measurements: 15.54 cm, 16.01 cm, and 16.05 cm. To assess the accuracy of these measurements, one can calculate the average by summing the values and dividing by the number of measurements:

15.54 + 16.01 + 16.05 = 47.60

rac{47.60}{3} = 15.87

From this calculation, it can be concluded that although the measurements are not on target (hence not perfectly accurate) since the average (15.87 cm) deviates from the true value (16 cm), they are consistently close to one another, indicating a degree of precision.

Significant Figures

Significant figures play a vital role in reporting measurements and calculated results in chemistry. They represent the digits that carry meaningful information about a quantity's precision. Understanding how to determine significant figures is essential for ensuring that results are communicated accurately. The following rules can help identify significant figures:

All nonzero digits (from 1 to 9) are significant, e.g., 749 ml has 3 significant figures.
Leading zeros (zeros to the left of the first nonzero digit) are not significant. For instance, in 0.005869, there are 4 significant figures.
Zeros between nonzero digits are significant, e.g., 4036 has 4 significant figures.
Trailing zeros in a decimal number are significant. For example, 95.70 mm has 4 significant figures.
Trailing zeros in a whole number without a decimal point are not significant; for example, 300 km has 1 significant figure.

Significant Figures in Calculations

When performing mathematical operations, the number of significant figures dictates the precision of the results:

Addition and Subtraction

The result of an addition or subtraction should have the same number of decimal places as the measurement with the least decimal places. For example:

2.051 + 3.56 + 72.1 = 77.711

Due to the least precise measurement (72.1, with 1 decimal place), the answer is rounded to 77.7 mm.

Multiplication and Division

For multiplication and division, the answer should be reported with the same number of significant figures as the factor with the least number of significant figures. For instance:

7.065 imes 12.0 = 84.78

Since 12.0 has the least significant figures (3), the final answer should be 84.8 m².

Exercises on Significant Figures

It is important to practice identifying significant figures. Consider the following measurements:

0.001002 km
20003 m
8000 ml
95764 mg
0.1300 g

By applying the rules of significant figures outlined, one can determine the correct number of significant figures for each measurement, thus practicing and reinforcing the learning of precision and accuracy in scientific contexts.

Understanding Precision and Accuracy in General Chemistry

Understanding Precision and Accuracy in General Chemistry