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# Estimating Errors in Chemistry There are two types of error which occur in measurements

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Introduction

Estimating Errors in Chemistry There are two types of error which occur in measurements: 1. Random Errors Random errors or uncertainties cause repeat measurements to vary and be scattered around a mean value. Averaging a number of readings helps to reduce random uncertainties. Precision Precise measurements have a small random uncertainty. Measurements are more precise if the scale used has smaller intervals. e.g. a 50 cm3 measuring cylinder is more precise than a 50 cm3 beaker. A 50 cm3 burette is even more precise. It is possible for a measurement to have great precision but be inaccurate. 2. Systematic Errors Systematic errors affect all the measurements in the same way making them all inaccurate, so they are all lower or higher than the true value. They do not average out so repeating results does not help to eliminate systematic errors. ...read more.

Middle

Absolute uncertainty = Measurement � Uncertainty Absolute Uncertainty Percentage uncertainty = ______________________ x 100 Measurement Mass 1. Consider weighing 1.00g of solid. If you use a two decimal place balance, the mass recorded will be to the nearest 0.01g. The absolute uncertainty is 1.00g � 0.01g 0.01 The percentage error is _____ x 100 = 1% 1.00 2. Consider weighing the same mass of solid on a three decimal place balance. The mass recorded will be to the nearest 0.001g. The absolute uncertainty is 1.00g � 0.001g 0.001 The percentage error is _____ x 100 = 0.1% 1.000 3. Consider weighing 10g of solid on a three decimal place balance. The absolute uncertainty is 10.000g � 0.001 g 0.001 The percentage error is _______ x 100 = 0.01% 10.000 Volume 4. ...read more.

Conclusion

A burette is more accurate still, and you can obtain readings to the nearest 0.05cm3. However there are two uncertainties in the measurement because an initial and a final reading are taken. If 25cm3 is measured, the % error would be: 0.05 _______ x 2 x 100 = 0.4% 25.00 Used well, the burette is very accurate. However the uncertainty increases dramatically for smaller volumes. Time 10. Finally, consider a reaction time of 100s measured on a digital stopwatch. These often show times to the nearest 0.01s. The % error would be: The absolute uncertainty is 100.00 s � 0.01s 0.01 The percentage error is _____ x 100 = 0.01% 100.0 This is wonderful, but how quickly can you stop and start it? The error is really more like 0.2%, and operator incompetence becomes important. Propagating Uncertainty in Equations The overall percentage uncertainty is the sum of all the percentage uncertainties obtained for the different measurements. ...read more.

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