Many times errors are expressed in terms of percentage. The percent error is the absolute value of the difference of the true value and the experimental value, divided by the true value, and multiplied by 100 . Percent error \(=\frac{\mid \text { true value }-\text { experimental value } \mid}{\text { true value }} \times 100\) Calculate the percent error for the following measurements. a. The density of an aluminum block determined in an experiment was \(2.64 \mathrm{~g} / \mathrm{cm}^{3}\). (True value \(2.70 \mathrm{~g} / \mathrm{cm}^{3}\).) b. The experimental determination of iron in iron ore was \(16.48 \%\). (True value \(16.12 \% .)\) c. A balance measured the mass of a \(1.000-\mathrm{g}\) standard as \(0.9981 \mathrm{~g}\)

Understanding how to quantify uncertainty in experimental results is a key skill in chemistry. Experimental error calculation is a process that helps chemists evaluate the accuracy of their measurements compared to a known or accepted reference point, often referred to as the 'true value'. Calculating experimental error often involves finding the percent error, which is a ratio of the deviation of the experimental result from the true value relative to the true value itself, expressed as a percentage.

For instance, if a chemist is measuring the density of an aluminum block and determines it experimentally to be 2.64 g/cm³ while the true density is recognized to be 2.70 g/cm³, to calculate the experimental error, one would first calculate the difference between these two values. This difference is then divided by the true value to normalize it, providing a dimensionless figure that is then converted into a percent. This process is central in analyzing the quality and reliability of experimental data.

• Identify true and experimental values.
• Calculate the absolute difference.
• Divide by the true value and multiply by 100 to find percent error.

In scientific experiments, especially in chemistry, distinguishing between true value and experimental value is crucial for interpreting results. The true value is a theoretical value based on accepted literature or standard values; it represents what would be obtained in an ideal scenario, free of error. On the other hand, the experimental value is the value actually measured during an experiment. It's susceptible to various sources of error, such as instrumental imprecision, human error, or environmental influences.

Importance of True and Experimental Values

Understanding the relationship between these two types of values is essential for error analysis. When measuring the iron content in iron ore, if the true value is 16.12% but the experimental determination yields 16.48%, this discrepancy must be addressed and understood. Acknowledging the difference helps in refining experimental techniques, calibrating instruments, and ultimately improves the accuracy of outcomes. It's the gap between the true and experimental values that guides chemists in evaluating their methods and procedures for potential sources of error.

Error analysis in chemistry measurements is a critical process which involves assessing the accuracy and precision of experimental data. Accuracy pertains to how close a measurement is to the true value, while precision refers to the reproducibility of the measurements under unchanged conditions. Error analysis not only helps in documenting the reliability of results but also in improving experimental techniques.

Systematic vs Random Errors

Analyzing errors involves differentiating between systematic errors, which are consistent and repeatable deviations influenced by equipment or methodology, and random errors, which arise from unpredictable and fluctuating factors. For example, if a balance consistently measures a 1.000-g standard as 0.9981 g, there might be a systematic error in calibration to address. Understanding these concepts and learning to calculate the percent error from systematic and random sources are foundational skills for progressing in chemical experimentation and critical analysis.