Percent error is a fundamental concept in chemistry, serving as a tool to evaluate the accuracy of experimental results. It provides a standardized way to compare a measured quantity against a known or theoretical value. Understanding this calculation helps scientists assess the reliability of their experimental procedures and the precision of their measurements.
Understanding Experimental Accuracy
In scientific experiments, obtaining perfectly precise measurements is rarely possible due to inherent limitations in equipment and technique. Accuracy in experimental data refers to how closely a measured value aligns with the true or accepted value. The accepted value represents the true or correct quantity. The experimental value is the specific measurement or result obtained during a particular experiment. Percent error quantifies this accuracy by providing a numerical comparison between these two values.
The Percent Error Calculation
The formula for calculating percent error is straightforward: `Percent Error = (|Experimental Value – Accepted Value| / Accepted Value) 100%`. The “Experimental Value” is the result obtained directly from a laboratory measurement or observation. The “Accepted Value” is the theoretical, true, or known value that is widely recognized and used as a standard for comparison.
The absolute value bars, indicated by `| |`, around the difference between the experimental and accepted values are important; they ensure that the percent error is always a positive number, regardless of whether the experimental value is higher or lower than the accepted value. Finally, multiplying the result by 100 expresses the error as a percentage. This conversion makes the error easier to interpret and compare across different experiments.
Practical Application and Meaning
To illustrate, consider an experiment measuring the density of aluminum. The accepted density of aluminum is 2.70 g/cm³. Suppose an experimental measurement yields a value of 2.68 g/cm³. To calculate the percent error, first find the absolute difference between the experimental and accepted values: `|2.68 g/cm³ – 2.70 g/cm³| = |-0.02 g/cm³| = 0.02 g/cm³`.
Next, divide this absolute difference by the accepted value: `0.02 g/cm³ / 2.70 g/cm³ ≈ 0.0074074`. Multiplying this result by 100% gives the percent error: `0.0074074 100% ≈ 0.74%`. This low percent error indicates a high degree of accuracy in the experimental measurement.
A low percent error, approaching 0%, suggests that the experimental result is very close to the true value, indicating accurate measurements and sound experimental technique. A higher percent error, conversely, indicates a greater deviation from the accepted value, implying less accurate results and potentially pointing to systematic errors in the experimental setup or procedure. Analyzing the magnitude of percent error helps scientists refine their methods and improve the reliability of future experiments.