Question

An experiment was performed in which an empty \(100-\mathrm{mL}\) graduated cylinder was weighed. It was weighed once again after it had been filled to the \(10.0-\mathrm{mL}\) mark with dry sand. A \(10-\mathrm{mL}\) pipet was used to transfer \(10.00 \mathrm{~mL}\) of methanol to the cylinder. The sand- methanol mixture was stirred until bubbles no longer emerged from the mixture and the sand looked uniformly wet. The cylinder was then weighed again. Use the data obtained from this experiment (and displayed at the end of this problem) to find the density of the dry sand, the density of methanol, and the density of sand particles. Does the bubbling that occurs when the methanol is added to the dry sand indicate that the sand and methanol are reacting? Mass of cylinder plus wet sand \(\quad 45.2613 \mathrm{~g}\) Mass of cylinder plus dry sand \(\quad 37.3488 \mathrm{~g}\) Mass of empty cylinder \(22.8317 \mathrm{~g}\) Volume of dry sand \(10.0 \mathrm{~mL}\) Volume of sand plus methanol \(\quad 17.6 \mathrm{~mL}\) Volume of methanol \(\quad 10.00 \mathrm{~mL}\)

Short answer

The density of dry sand is \(1.4517 \frac{g}{mL}\), the density of methanol is \(0.7913 \frac{g}{mL}\), and the density of sand particles is \(1.9101 \frac{g}{mL}\). The bubbling observed when methanol is added to the dry sand is likely due to the release of trapped air between sand particles rather than a reaction between sand and methanol.

Step-by-step solution

Calculate the mass of dry sand

First, we need to determine the mass of the dry sand by subtracting the mass of the empty graduated cylinder from the mass of the cylinder plus dry sand. Mass of dry sand = Mass of cylinder plus dry sand - Mass of empty cylinder Mass of dry sand = \(37.3488g - 22.8317g = 14.5171g\)

Calculate the mass of methanol

Next, we need to determine the mass of methanol by subtracting the mass of the cylinder plus wet sand from the mass of the cylinder plus dry sand. Mass of methanol = Mass of cylinder plus wet sand - Mass of cylinder plus dry sand Mass of methanol = \(45.2613g - 37.3488g = 7.9125g\)

Calculate the volume of sand particles

Since we know the volume of dry sand and the volume of methanol, we can find the volume of sand particles using the volume of sand plus methanol. Volume of sand particles = Volume of sand plus methanol - Volume of methanol Volume of sand particles = \(17.6mL - 10.00mL = 7.6mL\)

Calculate the density of dry sand

Now, using the formula for density, we can calculate the density of dry sand. Density of dry sand = \(\frac{Mass}{Volume} = \frac{14.5171g}{10.0mL} = 1.4517 \frac{g}{mL}\)

Calculate the density of methanol

Similarly, we can calculate the density of methanol. Density of methanol = \(\frac{Mass}{Volume} = \frac{7.9125g}{10.00mL} = 0.7913 \frac{g}{mL}\)

Calculate the density of sand particles

Finally, we can calculate the density of sand particles. Density of sand particles = \(\frac{Mass}{Volume} = \frac{14.5171g}{7.6mL} = 1.9101 \frac{g}{mL}\)

Determine if sand and methanol are reacting

Since there is no information provided about changes in mass or volume (apart from the displacement of sand particles by the methanol), it is likely that the bubbling observed is due to trapped air between the sand particles being released when the methanol is added and not due to a chemical reaction. In conclusion, the density of dry sand is \(1.4517 \frac{g}{mL}\), the density of methanol is \(0.7913 \frac{g}{mL}\), and the density of sand particles is \(1.9101 \frac{g}{mL}\). The bubbling that occurs when methanol is added to the dry sand is likely not indicating a reaction between sand and methanol, but rather the release of trapped air in the sand.

Key concepts

Density Calculation

Understanding the concept of density is fundamental in scientific studies, particularly in chemistry. Density is the measure of the amount of mass contained within a unit volume of a substance. It can be mathematically expressed by the formula:
\textbf{Density} = \(\frac{Mass}{Volume}\).
Because the values for mass and volume must be in compatible units (e.g., grams for mass and milliliters for volume when dealing with liquids or small solid samples), properly converting measurements becomes a crucial first step in density calculation. In a classroom laboratory setting, precise measurements of mass and volume are taken using balances and volumetric glassware. The accuracy of these measurements impacts the reliability of the density value computed.In a typical density determination experiment, understanding and performing the steps carefully ensures accurate results. For example, when calculating the density of dry sand, as seen in this exercise, the mass of the dry sand is found by subtracting the mass of the empty graduated cylinder from the mass of the cylinder with sand. This subtraction yields the net mass of the sand, which is divided by its volume to determine its density.

Mass-Volume Relationship

The mass-volume relationship is a crucial concept in understanding physical properties such as density. When a substance is described, its mass and volume are two of its most fundamental characteristics. Mass refers to the amount of matter in an object and is usually measured in grams or kilograms, while volume is the space that a substance occupies, measured in milliliters or liters for liquids, and cubic centimeters or meters for solids.Example of Mass-Volume RelationshipIn the context of the exercise, both mass and volume are recorded for the dry sand and methanol before calculating density. If one were to double the volume of methanol while keeping its mass constant, its density would halve, illustrating the inverse relationship between volume and density, given a constant mass. This relationship is central to solving problems in chemistry that deal with density and the composition of mixtures, such as the one involving the determination of methanol and sand densities. It's through understanding the mass and volume data acquired in the experiment we can further explore concepts such as buoyancy, purity of samples, and concentration of solutions.

Chemistry Lab Techniques

Mastering basic laboratory techniques is essential for successful experimentation in chemistry. Accurate measurements, meticulous observation, and proper handling of materials and equipment are all part of the fundamental skills required for any chemist. Important Lab Techniques Used in Density Determination:

• Weighing: Using a balance to find the accurate mass of the empty cylinder, cylinder with dry sand, and after addition of methanol. It is important to calibrate the balance and ensure it's level for precise readings.
• Volume Measurement: Utilizing a graduated cylinder and a pipet to measure liquid volumes. The meniscus, or the curve seen at the top of a liquid in response to its container's sides, should be read at eye level to avoid parallax errors.
• Mixing: Thorough stirring is needed after the addition of methanol to the sand to ensure uniform saturation and release of trapped air. This technique prevents air bubbles from affecting the volume readings.

Stirring until no more bubbles appear, as mentioned in the exercise, suggests that air present in the dry sand is expelled by the methanol. The absence of any other observable chemical reactions, such as heat production or color change, along with no significant change in mass, supports the conclusion that methanol is simply displacing the air. This observation enhances our understanding of the physical changes substances can undergo in a mixture without reacting chemically.