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 0.997 \(\mathrm{g} / \mathrm{cm}^{3},\) 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 and stoppered flask: Mass of filled stoppered flask = (mass of cmpty stoppered flask) + (mass of water) So mass of water \(=\) (mass of filled flask) - (mass of cmpty flask) Mass of water = ______ \(g\) _____ \(g\) _____ \(=\) _____ \(g\) Many mass and volume measurements in chemistry are made by the method used in \(1(\) a). This method is called measuring by difference, and it 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. Calculate the volume of the flask. Volume of flask \(=\) volume of water \(=\frac{\text { mass of water }}{\text { density of water }}=\) $$\frac{g}{g / c m^{3}}=$$ ______ \(\mathrm{cm}^{3}\)

Step-by-Step Solution

Answer

The volume of the flask is approximately 34.016 cm³.

Step 1: Calculate Mass of Water

Calculate the mass of the water by subtracting the mass of the empty stoppered flask from the mass of the filled stoppered flask. \[\text{Mass of water} = 68.090 \text{ g} - 34.166 \text{ g} = 33.924 \text{ g}\]

Step 2: Use Density to Find Volume

Utilize the formula for density to determine the volume. Since density is mass divided by volume, rearrange the formula to find the volume: \[\text{Volume} = \frac{\text{Mass}}{\text{Density}}\] Insert the known values: \[\text{Volume of flask} = \frac{33.924 \text{ g}}{0.997 \text{ g/cm}^3} \approx 34.016 \text{ cm}^3\]

Key Concepts

Density Calculations

Density is a fundamental concept in chemistry and physics, playing a crucial role in understanding the properties of substances. It is defined as the mass of a substance per unit volume. The formula for calculating density is:\[\text{Density} = \frac{\text{Mass}}{\text{Volume}}\]To find the volume of an object using its mass and the known density, the equation can be rearranged to:\[\text{Volume} = \frac{\text{Mass}}{\text{Density}}\]This relationship helps solve many practical problems. By knowing any two of these values, you can find the third. For example, if you know the mass and want to find the volume, simply divide the mass by the density. This calculation is often utilized in laboratory settings to determine the volume of containers or spaces that contain certain substances.

Analytical Balance

An analytical balance is a precise instrument used in laboratories to measure mass. Unlike regular scales, analytical balances are capable of measuring very small masses in the sub-milligram range, which is critical for experimental accuracy. These balances often have an enclosed chamber to prevent interference from air currents that might affect measurement. Using an analytical balance:

• Ensure the balance is properly calibrated and zeroed before each use.
• Handle objects with care to avoid contaminating the surface.
• Place the object on the balance pan carefully, observing the digital display for a stable reading.

An analytical balance is essential when precise mass measurements can greatly influence the results of an experiment, such as in preparing solutions or determining the density of substances.

Volume Measurement

Volume measurement is a basic yet essential part of many scientific experiments. There are various methods to measure volume, and choosing the right one depends on the context of the experiment and the level of precision required. For liquids, volume is typically measured with tools like graduated cylinders, burettes, or pipettes, but in the case of a substance's volume in a container, the volume can also be inferred if you know the mass and density of the liquid, as explained in the density section. Volumes might also be measured using the displacement method. That is particularly useful for irregularly shaped objects. When a solid object is submerged into a fluid, the volume of the object is equal to the volume of the displaced fluid. In our example, the volume of the flask was determined using the volume of water it contained, calculated from its mass and known density, which is a precise method for volume determination in laboratory settings.

Measuring by Difference

Measuring by difference is an effective technique used in laboratories to ascertain the mass or volume of a substance indirectly. This method involves recording the measurements before and after an event and using the difference to find the desired value.In our exercise, the student's objective was to find the mass of the water in the flask. The calculation used the mass of the flask when empty and when filled with water. By subtracting the mass of the empty flask from the mass of the filled flask, the mass of the water was determined:\[\text{Mass of water} = \text{Mass of filled flask} - \text{Mass of empty flask}\]This technique is particularly useful when measuring the mass of volatile or reactive liquids, where direct measurement would be impractical. It provides an accurate method to eliminate systematic errors that might occur in weighing empty vessels separately.