Question

Draw a picture showing the markings (graduations) on glassware that would allow you to make each of the following volume measurements of water and explain your answers (the numbers given are as precise as possible). a. \(128.7 \mathrm{~mL}\) b. \(18 \mathrm{~mL}\) c. \(23.45 \mathrm{~mL}\) If you made the measurements of three samples of water and then poured all of the water together in one container, what total volume of water should you report? Support your answer.

Short answer

To measure the given water volumes, use glassware with appropriate graduations: for 128.7 mL, use a graduated cylinder or beaker with markings in increments of 0.1 mL; for 18 mL, use one with markings in increments of 1 mL; and for 23.45 mL, use one with markings in increments of at least 0.05 mL. The total volume of water when these samples are combined is \(170.15 \mathrm{~mL}\).

Step-by-step solution

Draw a picture for 128.7 mL measurement

Firstly, we need a glassware that has at least 128.7 mL in its volume. It could be a graduated cylinder or a measuring beaker with volume markings in milliliter (mL). To measure 128.7 mL as accurately as possible, the glassware should have markings in increments of 0.1 mL. To represent the measurement on the glassware, directly locate the marking at 128.7 mL and pour the water until that level.

Draw a picture for 18 mL measurement

For this measurement, we can use a smaller graduated cylinder or a measuring beaker that has at least 18 mL in its volume. To measure 18 mL precisely, the glassware should have markings in increments of at least 1 mL. To represent the measurement on the glassware, directly locate the marking at 18 mL and pour the water until that level.

Draw a picture for 23.45 mL measurement

For measuring 23.45 mL, we need a glassware that has at least a volume of 23.45 mL. This can be a graduated cylinder or a measuring beaker. To measure 23.45 mL as accurately as possible, the glassware should have markings in increments of 0.01 mL or at least 0.05 mL. To represent the measurement on the glassware, directly locate the marking at 23.45 mL and pour the water until that level.

Calculate the total volume of water

To calculate the total volume of the three samples, we will add the volumes of each measurement together: Total Volume = 128.7 mL + 18 mL + 23.45 mL

Reporting the total volume of water

Now, we can report the total volume of water obtained by adding the three measurements. We need to keep the same precision level. In our case, it's to the hundredth place. Total Volume = \(128.7 \mathrm{~mL} + 18 \mathrm{~mL} + 23.45 \mathrm{~mL} = 170.15 \mathrm{~mL}\) The total volume of water when the three samples are combined in a single container is \(170.15 \mathrm{~mL}\).

Key concepts

Graduated Cylinder

A graduated cylinder is a common piece of laboratory glassware that is used to accurately measure the volume of liquids.
These cylinders are tall and narrow, with markings along their sides—known as graduations—that indicate volume. Made from glass or plastic, they come in various sizes with different measurement increments to cater to precise volume readings. For instance, for measuring small volumes, a graduated cylinder with 0.1 mL graduations is appropriate. Conversely, for larger quantities, you might find cylinders marked in 10 mL increments.

Its distinct design features a narrow cylindrical shape that allows for more accurate volume measurements compared to beakers, which are wider and less precise. To read the volume accurately, you must look at the lowest point of the liquid's meniscus at eye level. This procedure helps minimize parallax errors and enhances measurement reliability.

In our textbook exercise, we drew a picture of a graduated cylinder that could measure 128.7 mL, 18 mL, and 23.45 mL, with precise increments for the highest accuracy possible. Notably, the resolution—the smallest volume interval marked on the cylinder—directly affects our ability to get a precise reading.

Volume Measurement in Chemistry

Volume measurement in chemistry is a fundamental skill for conducting experiments and processes accurately. It involves determining the amount of three-dimensional space occupied by a liquid. The units of measurement commonly used in the laboratory are milliliters (mL) and liters (L), with 1,000 mL equating to 1 L.

Various types of glassware are employed for volume measurements, such as beakers, volumetric flasks, burettes, and, as discussed, graduated cylinders. Each piece of glassware is chosen based on the volume of liquid to be measured and the required precision. For example, volumetric flasks are used for precise dilutions and are calibrated to hold a precise volume at a specific temperature.

Understanding the degree of precision needed for an experiment is crucial. This precision is dictated by the required significant figures in a measurement. In the exercise, measurements are to the nearest 0.1 mL, 1 mL, and 0.05 or 0.01 mL for each of the graduated cylinder examples, indicating that precision can be tailored to the specific demands of the measurement.

Precision in Volumetric Measurements

Precision in volumetric measurements is essential to obtain repeatable and accurate results in the laboratory. Precision refers to the degree to which repeated measurements under unchanged conditions show the same results. It is closely related to the concept of 'significant figures,' which reflect the accuracy of a measurement.

In volumetric glassware like graduated cylinders, the precision is determined by the smallest graduation interval and the skill of the user in reading the volume correctly. To achieve high precision, it is critical to prevent systematic errors, which can be caused by factors such as improper calibration of equipment, misreading the meniscus, or environmental conditions.

When reporting the combined volume of different samples, like in our exercise solution, it's important to maintain consistent precision based on the least precise measurement. The volume is reported as 170.15 mL because this value reflects the appropriate level of precision based on the given measurements. Always remember, the final result should not have more precision than the least precise measurement in the sequence of additions or subtractions.