Question

The following procedure was used to determine the volume of a flask. The flask was weighed dry and then filled with water. If the masses of the empty flask and filled flask were \(56.12 \mathrm{~g}\) and \(87.39 \mathrm{~g}\), respectively, and the density of water is \(0.9976 \mathrm{~g} / \mathrm{cm}^{3},\) calculate the volume of the flask in cubic centimeters.

Short answer

The volume of the flask is approximately 31.34 cm³.

Step-by-step solution

Calculate the Mass of the Water

First, determine the mass of the water by subtracting the mass of the empty flask from the mass of the filled flask. This is done using the formula: \[ \text{Mass of Water} = \text{Mass of Filled Flask} - \text{Mass of Empty Flask} = 87.39 \text{ g} - 56.12 \text{ g} = 31.27 \text{ g} \]

Use the Density Formula to Calculate Volume

With the mass of the water known, use the density formula to find the volume. The formula is \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \). Rearrange this to solve for volume: \( \text{Volume} = \frac{\text{Mass}}{\text{Density}} \).

Substitute Known Values and Solve

Substitute the mass of the water and the density of water into the rearranged density equation: \[ \text{Volume} = \frac{31.27 \text{ g}}{0.9976 \text{ g/cm}^3} = 31.34 \text{ cm}^3 \]

Key concepts

Density

Density is a physical property that measures how much mass is contained in a given volume. It is generally expressed in units of grams per cubic centimeter (g/cm³) or kilograms per cubic meter (kg/m³). Understanding density is essential for calculating the volume of objects, as it provides the link between mass and volume.
Diverse materials have different densities, which means the same volume of different substances will have different masses. For example, metals typically have high densities compared to gases.

• Formula: \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \)
• Units: Typically g/cm³ or kg/m³.

By knowing the density of a material, you can determine its mass if you know its volume, or vice versa. This formula is particularly useful in laboratory settings where determining one of these quantities is necessary for experiments.

Mass

Mass is a measure of the amount of matter in an object. Unlike weight, which depends on gravity, mass remains constant regardless of location. It's usually measured in grams (g) or kilograms (kg).
In the context of volume calculations like in this exercise, knowing the mass of an object is crucial when density is known because it allows you to compute the volume.

• Units: Commonly grams or kilograms.
• Relation to volume: With a known density, volume can be deduced from mass.

In the exercise provided, two masses are significant: the mass of the empty flask and the mass of the flask filled with water. Subtracting these gives the mass of the water alone, enabling the subsequent calculation of the flask's volume.

Water Displacement

Water displacement is an ancient technique used to determine the volume of an irregularly shaped object. However, in this exercise, it can also be understood through the direct measurement of water mass to calculate volume, owing to the known density of water.
Instead of directly measuring the volume of the flask by displacement, the concept of water displacement is one of understanding how a known mass of water – and knowing its density – can be used to determine volume.

• Alternative to direct measurement.
• Utilizes the principle of known density.

With a fixed density like water’s, the mass measurement approach effectively substitutes for physical displacement, offering a precise way to calculate volume in a laboratory.

Laboratory Techniques

Laboratory techniques for measuring volume often rely on precise and repeatable methods. In this exercise, the use of a balance to weigh the flask is a fundamental technique in any laboratory.
This approach emphasizes accuracy and consistency in measurements. Utilizing balances can help measure differences as small as tenths of grams, allowing for accurate determination of mass – which is essential in calculating volume based on density.
For liquids, as demonstrated, filling a container to measure the volume is effective when paired with calculations based on mass and known densities.

• Precision in measurement is crucial.
• Instruments like balances play a key role.

These techniques ensure that the student's approach and calculations mimic those used in professional scientific environments, reinforcing their understanding and proficiency in practical applications.