Question

When a 16.74-g rubber stopper is placed in a graduated cylinder containing \(25.46 \mathrm{~mL}\) of water, the water level rises to \(37.42 \mathrm{~mL}\). What is the density of the stopper in grams per milliliter?

Short answer

The density of the rubber stopper is approximately \(1.40~g/mL\).

Step-by-step solution

Determine the volume of the rubber stopper

To find the volume of the rubber stopper, we will subtract the initial volume of water from the final volume of water when the rubber stopper is submerged. The difference will give us the volume of the rubber stopper. Initial volume of water: \(25.46~mL\) Final volume of water (with rubber stopper): \(37.42~mL\) Volume of rubber stopper: \(37.42-25.46~mL\)

Calculate the volume of the rubber stopper

Now, subtract the initial volume of the water from the final volume of the water to get the volume of the rubber stopper. Volume of rubber stopper: \(37.42~mL - 25.46~mL = 11.96~mL\)

Calculate the density of the rubber stopper

To find the density of the rubber stopper, divide the mass of the rubber stopper by its volume. In this case, we have: Mass of rubber stopper: \(16.74~g\) Volume of rubber stopper: \(11.96~mL\) Density of rubber stopper: \(\frac{16.74~g}{11.96~mL}\)

Find the density of the rubber stopper

Finally, divide the mass of the rubber stopper by its volume to determine the density in grams per milliliter: Density of rubber stopper: \(\frac{16.74~g}{11.96~mL} = 1.40~g/mL\) The density of the rubber stopper is approximately \(1.40~g/mL\).

Key concepts

Rubber Stopper

Rubber stoppers are small, tapered plugs made from rubber material. They serve various functions in science labs, frequently used to seal test tubes and flasks.
Their ability to create airtight seals makes them crucial for experiments requiring containment of liquids or gases. When discussing rubber stoppers in the context of density calculations, their primary role is to displace liquid, which is essential in determining volume changes.
Understanding the structure and properties of rubber helps explain why rubber stoppers are impermeable and resistant to water, thus ensuring accuracy when immersed in liquids for volume displacement experiments. Rubber stoppers are not only essential in labs, but their practical design and adaptability make them an indispensable part of scientific toolkits.

Graduated Cylinder

A graduated cylinder is a cylindrical container with markings, or graduations, along its length. These marks indicate volume, typically measured in milliliters (mL).
Graduated cylinders are designed to measure the volume of a liquid precisely. They are more accurate than beakers or flasks due to their narrow structure and incremental graduations.
When a solid object like a rubber stopper is submerged, it displaces the liquid, making the liquid level rise. This increase in water level directly corresponds to the volume of the submerged object.

• Accurate measurement requires observation at eye level to avoid parallax error.
• Using a graduated cylinder ensures precision in experiments, crucial for reliable results.

Graduated cylinders are indispensable in density calculations because they allow for the exact determination of an object's volume by measuring how much liquid it displaces.

Mass and Volume

Mass and volume are fundamental concepts in physics and chemistry. Mass refers to the amount of matter in an object, measured in grams (g).
Volume is the space that an object occupies, typically expressed in milliliters (mL) for liquids and cubic centimeters (cm³) for solids in scientific contexts.
Calculating the density of an object involves these two properties: mass and volume. The formula for density is \[ ext{Density} = rac{ ext{Mass}}{ ext{Volume}} \]

• This formula requires precise measurements of both mass and volume to yield an accurate density.
• A balance is used to measure mass, while volume is often determined using displacement, especially for irregularly shaped objects.

Understanding these concepts allows one to determine how compact or spread out the matter within an object is.

Grams per Milliliter

Grams per milliliter (g/mL) is a unit of density commonly used in chemistry and physics. This unit expresses how much mass is contained in one milliliter of a substance.
Density tells us about a material’s compactness or how tightly matter is packed within a given volume. For example, if a rubber stopper has a density of 1.40 g/mL, it means each milliliter of the stopper’s volume contains 1.40 grams of mass.
Understanding density in units of g/mL helps compare different materials directly.

• A higher density indicates a substance is more compact, while a lower density suggests it is more spread out.
• In practical applications, density can indicate how substances interact, such as whether one material will sink or float in another.

Grams per milliliter is a crucial concept in material science, informing decisions about material selections based on density properties.