Understanding Error in Chemical Measurements: Random and Systematic Errors

Error in Chemical Measurements

Types of Error

When performing calculations in chemistry, it is important to recognize that errors can occur. These errors are generally classified into two main categories: random errors and systematic errors.

• Random errors: These are unpredictable variations that can cause results to be either too high or too low. They arise from uncontrollable factors and are difficult to eliminate completely.

• Systematic errors: These errors are more predictable and consistent, causing results to be always too high or always too low. They often arise from flaws in equipment, experimental design, or consistent procedural mistakes.

Additional info: Random errors can often be minimized by repeating measurements and averaging results, while systematic errors require identification and correction of the source.

Acceptable Error and Percent Error Calculation

In most chemical experiments, a percent error of less than 10% is considered acceptable. Percent error is a useful metric for evaluating the accuracy of your calculations.

• Experimental value: The value obtained from your measurements or calculations.

• Theoretical value: The value that is accepted as true or known, often from literature or established standards.

The formula for percent error is:

$\text{\% error} = \left| \frac{\text{Experimental value} - \text{Theoretical value}}{\text{Theoretical value}} \right| \times 100$

Example: If your experimental value is 24.8 and the theoretical value is 25.0, the percent error is:

$\text{\% error} = \left| \frac{24.8 - 25.0}{25.0} \right| \times 100 = 0.8\%$

Identifying Random and Systematic Errors

Understanding the difference between random and systematic errors is crucial for improving the accuracy and reliability of chemical measurements.

• Random error examples:

  • Doing numerous measurements and taking the average to minimize errors.

  • Results of an experiment are consistently greater than expected or less than expected.

  • Refining parameters of the experiment to help eliminate errors.

  • The exact source of error is hard to determine.

• Systematic error examples:

  • Weighing the object before all water has evaporated.

  • The scale has not been properly calibrated.

  • Airflow near the balance causes the precise mass to vary.

  • Writing down the incorrect mass of the anhydrous object.

Comparison of Random and Systematic Errors

Error Type	Definition	Examples	How to Minimize
Random Error	Unpredictable fluctuations in measurements	Variation in repeated measurements	Repeat measurements and average results
Systematic Error	Consistent deviation in one direction	Uncalibrated instrument, procedural mistake	Identify and correct the source of error

Key Terms

• Precision: The degree to which repeated measurements under unchanged conditions show the same results.

• Accuracy: The closeness of a measured value to a standard or known value.

• Experimental value: The value obtained from your experiment.

• Theoretical value: The accepted or true value.