Problem 1 - Chemical Principles in the Laboratory

Question

A student obtained a clean, dry glass-stoppered flask. She weighed the flask and stopper on an analytical balance and found the total mass to be \(34.166 \mathrm{g}\). She then filled the flask with water and obtained a mass for the full stoppered flask of \(68.090 \mathrm{g}\). From these data, and the fact that at the temperature of the laboratory the density of water was 0.9975 g/mL, find the volume of the stoppered flask. a. First we need to obtain the mass of the water in the flask. This is found by recognizing that the mass of a sample is equal to the sum of the masses of its parts. For the filled, stoppered flask: Mass of filled stoppered flask \(=\) mass of empty stoppered flask \(+\) mass of water, so mass of water \(=\) mass of filled flask - mass of empty flask Mass of water \(=\)______ \(g-\) ______ \(g=\) ______ \(g\) Many mass and volume measurements in chemistry are made by the method used in la. This method is called measuring by difference, and is a very useful one. b. The density of a pure substance is equal to its mass divided by its volume: Density \(=\frac{\text { mass }}{\text { volume }}\) or volume \(=\frac{\text { mass }}{\text { density }}\) The volume of the flask is equal to the volume of the water it contains. Since we know the mass and density of the water, we can find its volume and that of the flask. Make the necessary calculation. Volume of water \(=\) volume of flask \(=\) _______ m L

Step-by-Step Solution

Answer

The volume of the flask is 34.009 mL.

Step 1: Calculate the Mass of the Water

To find the mass of the water, use the formula: \[ \text{Mass of water} = \text{mass of filled flask} - \text{mass of empty flask} \] Substitute the given values: \[ \text{Mass of water} = 68.090\, \text{g} - 34.166\, \text{g} = 33.924\, \text{g} \] Thus, the mass of the water is 33.924 g.

Step 2: Calculate the Volume of the Flask

Since the volume of the flask is equal to the volume of water it contains, use the formula for volume: \[ \text{Volume} = \frac{\text{mass}}{\text{density}} \] Substitute the known values: \[ \text{Volume of water} = \frac{33.924\, \text{g}}{0.9975\, \text{g/mL}} = 34.009\, \text{mL} \] Consequently, the volume of the flask is 34.009 mL.

Key Concepts

Density

Density is a fundamental property of matter that relates to how much mass is contained in a given volume. It is expressively significant in analytical chemistry because it allows us to understand how substances behave under different conditions. The formula for density is:

• Density \(=\ \frac{\text{mass}}{\text{volume}}\)

This relationship means that for a substance with a high density, a small volume contains a lot of mass, while a substance with a low density has less mass in the same volume. In the context of laboratory experiments, knowing the density of a liquid like water allows chemists to calculate volumes from masses, as seen in our exercise.
Density varies with temperature and pressure, specifically for gases and liquids. For instance, the density of water is approximately 0.9975 g/mL at room temperature, which is essential information for calculating volumes accurately in experimental procedures. With this in hand, you can calculate the volume of an unknown space by dividing the mass by this density.

Mass Measurement

Mass measurement is a critical component in many chemical experiments. Understanding how to measure mass accurately helps ensure that experimental results are reliable and reproducible. In this exercise, the mass of the container and water was measured using an analytical balance, providing two different readings:

• Mass of empty stoppered flask = 34.166 g
• Mass of full stoppered flask with water = 68.090 g

Mass measurement by difference, as seen in our exercise, involves calculating the mass of the water by subtracting the mass of the empty flask from the mass of the full flask. This is expressed as:

• Mass of water = Mass of full flask - Mass of empty flask

The result was found to be 33.924 g, which then serves as the basis for further calculations, such as determining the volume of the flask.
Precision in mass measurement helps in identifying the correct volume, affecting the outcome of experiments significantly. Any errors in weighing could lead to incorrect volume calculations, illustrating the importance of using precise instruments in the lab.

Volume Calculation

Volume calculation comes into play once the mass and density are known. In scientific contexts, volume can often be derived when these variables are present. For example, from the exercise we derive the volume of water (and thus the flask) using the relationship:

• Volume = \( \frac{\text{mass}}{\text{density}} \)

Substituting our values in, with the mass of water as 33.924 g and the density as 0.9975 g/mL, we calculate:

• Volume of the flask = \( \frac{33.924 \text{ g}}{0.9975 \text{ g/mL}} = 34.009 \text{ mL} \)

This simple relationship allows us to understand the capacity of the flask—essential in experiments where precise volumes matter.
Volume calculations are crucial for preparing solutions, measuring reactants, and assessing products in chemical reactions. Knowing how to calculate volume from mass and density is an indispensable skill for students and professionals in the fields of chemistry and beyond.