Uncertainty in Measurements Lecture Notes

A laboratory experiment requires you to measure 10 mL of a solution as accurately as possible. You have access to a beaker (precision: +/- 10% of maximum volume), a graduated cylinder (precision: +/- 1 mL), and a volumetric pipette (precision: +/- 0.04 mL). Which device should you choose and why, considering the uncertainty in measurements?

• Beaker, because it is the easiest to use and has the lowest uncertainty.

• Graduated cylinder, because its uncertainty is always less than that of a volumetric pipette.

• Volumetric pipette, because it has the smallest uncertainty and will provide the most accurate measurement.

• Any device, because the uncertainty does not matter for this measurement.

You are given a measuring device with divisions marked on it. Explain how the presence of these divisions affects your ability to accurately read and record measurements, and why this is important in scientific experiments.

• The divisions make it harder to read measurements, increasing uncertainty.

• The divisions allow for more precise readings, reducing uncertainty and improving accuracy.

• The divisions are only for decoration and do not affect measurement accuracy.

• The divisions are used to calibrate the device, but do not impact reading accuracy.

A beaker is labeled to measure volumes with an uncertainty of +/- 25% of its maximum volume. If you need to measure 100 mL of liquid as accurately as possible, what is the potential error in your measurement, and how does this compare to using a graduated cylinder with an uncertainty of +/- 1 mL?

• The beaker could be off by up to 25 mL, which is much greater than the 1 mL uncertainty of the graduated cylinder.

• The beaker could be off by up to 1 mL, which is the same as the graduated cylinder.

• The beaker could be off by up to 0.04 mL, which is less than the graduated cylinder.

• The beaker and graduated cylinder have the same uncertainty for 100 mL.

A student needs to prepare a solution that requires delivering exactly 25.00 mL of liquid with the highest possible accuracy. Which instrument should the student choose, and why?

• Graduated cylinder, because it can measure a wide range of volumes.

• Volumetric pipette, because it delivers one specific, very accurate volume.

• Burette, because it can deliver a range of volumes with high accuracy.

• Volumetric flask, because it holds large, precise volumes.

You are tasked with titrating an acid with a base and need to deliver varying amounts of the base with very high accuracy. Which instrument is most appropriate for this task, and what feature makes it suitable?

• Graduated cylinder, because it is easy to use for any volume.

• Volumetric pipette, because it is very accurate for one specific volume.

• Burette, because it can deliver a range of possible volumes with very accurate volume.

• Volumetric flask, because it holds a large, precise volume.

A laboratory procedure requires you to prepare a solution with a total volume of 250 mL, and the final volume must be extremely precise. Which instrument should you use, and what is its precision?

• Graduated cylinder; precision of +/- 0.1 mL to +/- 10 mL.

• Volumetric pipette; precision of +/- 0.05 mL.

• Burette; precision of +/- 0.02%.

• Volumetric flask; precision of 0.04 mL.

Compare the accuracy and use cases of a graduated cylinder and a burette. In which scenario would you choose a burette over a graduated cylinder, and why?

• When measuring a large, imprecise volume, because burettes are less accurate.

• When delivering a range of possible volumes with very high accuracy, because burettes have a precision of +/- 0.02%.

• When holding a solution for storage, because burettes are designed for storage.

• When delivering one specific volume, because burettes are more accurate for single measurements.

A 100 mL graduated cylinder is used to measure the volume of a liquid. The smallest division on the cylinder is 1 mL. If the bottom of the meniscus falls between two marks, how should you reason about the precision of your measurement and what steps should you take to record the most accurate volume?

• Estimate the volume to the nearest 0.1 mL and record it, acknowledging the uncertainty is still +/- 1 mL.

• Only record the volume at the lower mark, ignoring the meniscus position.

• Record the volume at the higher mark, assuming the meniscus will rise to that level.

• Average the values of the two marks and record that as the volume.

A student is measuring the volume of a liquid in a graduated cylinder. The liquid forms a curved surface at the top. Explain why it is important to read the volume from the bottom of the meniscus rather than from the top, and describe the potential error that could occur if the reading is taken from the top.

• Reading from the bottom of the meniscus ensures that only the liquid volume is measured, preventing the inclusion of air above the liquid.

• Reading from the top of the meniscus gives a more accurate measurement because it is easier to see.

• Reading from the bottom of the meniscus is only necessary for colored liquids.

• Reading from the top of the meniscus is standard practice in chemistry.

When recording the volume from graduated glassware, why is it recommended to estimate one decimal place beyond the smallest graduation mark, and how does this practice affect the precision of the measurement?

• Estimating one decimal place beyond the smallest graduation mark increases the precision of the measurement by providing a more accurate value.

• Estimating one decimal place is unnecessary and decreases the accuracy of the measurement.

• Only whole numbers should be recorded to avoid estimation errors.

• Leaving the decimal place blank is more precise than making an estimate.