Calculating percentage error in chemistry is a fundamental step in evaluating the quality of experimental work. This calculation provides a quantitative measure of accuracy by comparing an experimentally derived result to a standard, known value. Understanding this concept is necessary for assessing the reliability of data collected during quantitative analysis. The resulting figure reveals the magnitude of the deviation, helping to identify potential sources of inaccuracy in the procedure.
The Essential Values Needed for Calculation
To calculate the percentage error, two distinct values must be established from the experimental context. The first is the measured value, also known as the experimental value, which is the number obtained directly from the laboratory procedure. This value is determined by the equipment and technique used, and is susceptible to variations in the measurement process.
The second required input is the accepted value, often called the theoretical or true value. This is the established, known quantity for the substance or property being measured, typically found in scientific literature or authoritative references. This accepted value serves as the benchmark against which the experimental results are judged.
Calculating Absolute and Percentage Error
Determining the percentage error requires a two-step mathematical sequence, beginning with the calculation of the absolute error. The absolute error is the positive difference between the measured value and the accepted value, showing the magnitude of the discrepancy without regard to its direction. This value is calculated using the formula: Absolute Error = |Measured Value – Accepted Value|.
Once the absolute error is found, it is used to calculate the percentage error, which expresses this deviation as a fraction of the accepted value. The complete formula for the percentage error is: Percentage Error = (Absolute Error / Accepted Value) x 100%.
Applying the Calculation with a Practical Example
Consider a common introductory chemistry experiment involving the determination of the density of distilled water. The accepted value for the density of water at 4 degrees C is known to be 1.00 g/mL. During a laboratory session, a student measures the mass and volume of a water sample and calculates an experimental density of 1.04 g/mL.
The first step is to find the absolute error by taking the difference between the measured and accepted values. Subtracting the accepted value from the measured value gives |1.04 g/mL – 1.00 g/mL|, resulting in an absolute error of 0.04 g/mL. This figure represents the raw deviation from the known density.
Next, this absolute error is incorporated into the percentage error formula to express the deviation as a percentage of the accepted value. The calculation becomes (0.04 g/mL / 1.00 g/mL) x 100%. The units cancel out during the division, leaving a pure ratio. This yields a result of 0.04 x 100%, meaning the final percentage error for the student’s density measurement is 4.0%.
Understanding the Significance of the Result
The percentage error figure provides immediate feedback on the accuracy of the experimental procedure. A percentage error value that is close to zero indicates that the measured result is highly accurate, meaning it closely aligns with the established true value. Conversely, a larger percentage error suggests a substantial deviation, prompting the experimenter to review their technique or equipment for flaws.
Acceptable limits for percentage error vary widely depending on the complexity of the experiment and the field of study, but in many undergraduate chemistry labs, a result under 5% is often considered acceptable. A high percentage error can point to a systematic error, such as an improperly calibrated balance or a consistently flawed technique that shifts all measurements in one direction. This metric is distinct from the precision of the measurements, which refers to how close multiple measurements are to each other, not how close they are to the true value.