Problem 80 - General Chemistry: Principles and Modern Applications

Question

A pycnometer (see Exercise 78 ) weighs 25.60 g empty and \(35.55 \mathrm{g}\) when filled with water at \(20^{\circ} \mathrm{C}\) The density of water at \(20^{\circ} \mathrm{C}\) is \(0.9982 \mathrm{g} / \mathrm{mL}\). When \(10.20 \mathrm{g}\) lead is placed in the pycnometer and the pycnometer is again filled with water at \(20^{\circ} \mathrm{C}\), the total mass is \(44.83 \mathrm{g}\). What is the density of the lead in grams per cubic centimeter?

Step-by-Step Solution

Answer

The density of the lead is \( 1.10 g/mL \) or \( 1.10 g/cm^{3} \)

Step 1: Determine volume of the pycnometer

The volume of the pycnometer can be established by utilising the recorded mass of the water and the known density of water. Given the mass of the water-filled pycnometer less the mass of the empty pycnometer equals to the mass of the filled water, which is \(35.55 g - 25.60 g = 9.95 g\). Now, use the mass and density of the water to find the volume. The volume will be \( \frac{mass_{water}}{density_{water}} = \frac{9.95 g}{0.9982 g/mL} = 9.97 mL \)

Step 2: Determine volume of the lead

Subtract the mass of the pycnometer containing water and lead by the mass of the empty pycnometer and the mass of water. That gives the mass of the lead \(44.83 g - 25.60 g - 9.95 g = 9.28 g \). The difference between the total volume of water and pycnometer and the volume of the water will give the volume of lead. Therefore the volume of the lead is \(44.83 g - 35.55 g = 9.28 g \)

Step 3: Calculate density of the lead

The density can be calculated by taking the mass of the lead divided by its volume. Therefore the density of the lead will be \( \frac{mass_{lead}}{volume_{lead}} = \frac{10.20 g}{9.28 mL} = 1.10 g/mL \)

Key Concepts

Pycnometer

A pycnometer is a laboratory instrument used to measure the density of liquids and solids. It is often used because of its ability to provide precise volume measurements through a simple design.
Its primary feature is a tightly fitting stopper, which helps in preventing any loss of liquid. This ensures consistency and accuracy in measurements.

• Pycnometers are typically made from glass.
• They come in various sizes, but their function remains the same - to provide a known, fixed volume.
• Understanding how to use a pycnometer is essential when experimenting with density calculations.

The way it works is straightforward: You first weigh the empty pycnometer, then fill it with a liquid, and weigh it again. Finally, using known densities, you calculate the volume, which can then be used in a variety of calculations, like finding the density of a solid when combined in the pycnometer with a liquid.

Volume of a substance

The volume of a substance is a measure of the space it occupies. This is a crucial quantity in many scientific fields, and understanding it helps in determining other important characteristics like density.
When using a pycnometer to measure the volume, here's what typically happens:

• Fill the pycnometer with a known liquid (usually water) whose density is also known.
• Weigh the filled pycnometer and subtract the weight of the empty pycnometer to find the mass of the liquid.
• Calculate the volume using the formula: \( \, ext{Volume} = \frac{\text{Mass}}{\text{Density}} \, \)

In the given exercise, the water used to fill the pycnometer provided a mass, which allowed us to accurately determine the volume it could hold. Creating precise volume measurements is vital, especially in density calculations, as minor errors in volume can lead to significant discrepancies in results.

Mass measurement

Mass measurement is a fundamental concept in chemistry and physics. It helps us to understand how much matter is in a given object.
The use of a balance is crucial here, as it allows us to determine the mass of various items with precision. In the context of our exercise:

• We initially weigh the empty pycnometer.
• Then, after filling it with water, the total mass is recorded.
• Finally, once the pycnometer is combined with lead and refilled, the new total mass is noted.

This step-by-step measurement provides the necessary data to calculate the density of different substances. Accurate mass measurements allow for the precise calculation of volume and, subsequently, density. It provides the foundation for resolving various experimental and real-world problems.

Density of water

The density of water is a well-known and standardized value, often used in scientific calculations. At room temperature, or around 20°C, the density of water is approximately 0.9982 g/mL.
This value serves as a benchmark for other density determinations, allowing us to calculate the volume and density of other substances accurately using it as a reference.

• It's used to calculate the volume of water in the pycnometer.
• Helps determine how much of another substance is present when added to the pycnometer.
• Provides a comparison baseline for calculating the density of other materials, such as lead in the exercise.

Understanding the density of water is fundamental, as it often serves as a stepping stone to more complex calculations in both laboratory and industrial settings. Its consistent nature ensures reliability when used to gauge other densities.