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 \(33.695 \mathrm{g}\). She then filled the flask with water and obtained a mass for the full stoppered flask of \(64.356 \mathrm{g}\). From these data, and the fact that at the temperature of the laboratory the density of water was 0.9978 \(\mathrm{g} / \mathrm{cm}^{3},\) 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 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 yolume and that of the flask. Make the necessary calculation. Volume of water = volume of flask = _____________ \(\mathrm{cm}^{3}\)

Step-by-Step Solution

Answer

The volume of the flask is approximately 30.728 cm³.

Step 1: Identify Mass of Water

First, we need to calculate the mass of the water by subtracting the mass of the empty flask from the mass of the filled flask. The mass of the filled flask is 64.356 g, and the mass of the empty flask is 33.695 g. \[\text{Mass of water} = \text{Mass of filled flask} - \text{Mass of empty flask} = 64.356\, \text{g} - 33.695\, \text{g}\]

Step 2: Calculate Mass of Water

Perform the subtraction to find the mass of the water.\[\text{Mass of water} = 64.356\, \text{g} - 33.695\, \text{g} = 30.661\, \text{g}\]

Step 3: Use Density to Find Volume

Now that we know the mass of the water, we can find its volume using the known density. The formula for density is:\[\text{Density} = \frac{\text{mass}}{\text{volume}}\]Rearrange it to find the volume:\[\text{Volume} = \frac{\text{mass}}{\text{density}}\]

Step 4: Calculate Volume of Flask

Substitute the mass of the water and the density into the formula to find the volume:\[\text{Volume} = \frac{30.661\, \text{g}}{0.9978\, \text{g/cm}^3} \]Then calculate:\[\text{Volume} \approx 30.728\, \text{cm}^3 \]

Key Concepts

Measuring by Difference

Measuring by difference is a valuable method used in chemistry to determine the mass of a substance indirectly. It involves weighing the container first when it is empty and again after filling it with the substance of interest. By subtracting the mass of the empty container from the mass of the filled container, one can obtain the mass of the added substance.

This method is practical and widely used because it allows for the accurate measurement of liquid substances without directly measuring them. It also helps avoid issues related to evaporation or absorption that could occur during direct mass measurement. Remember, always ensure the container and the added substance are both at room temperature to prevent inaccuracies due to thermal expansion or contraction.

Advantages of measuring by difference include:

• Minimizing user handling errors.
• Reducing potential loss of substance during handling.
• Providing a straightforward way to measure without complex equipment.

Volume Measurement

Volume measurement in experiments often requires precision and accuracy. For liquids, this is typically done using volumetric flasks, graduated cylinders, or, as in this exercise, by calculating volume via mass and density. When you have the density of a liquid and its mass, you can calculate its volume using the formula:

\(\text{Volume} = \frac{\text{Mass}}{\text{Density}}\)

This formula tells us that dividing the mass of the liquid by its density gives us its volume. It's essential to ensure that the mass and density are in corresponding units (e.g., grams for mass and grams per cubic centimeter for density) for the volume calculation to be correct.

Considerations for volume measurement:

• Check the calibration of volumetric instruments to ensure accuracy.
• Ensure that temperature is constant, as it affects liquid density and subsequently the volume.
• Clean and dry all equipment to ensure no contamination affects the measurement.

Analytical Balance Use

An analytical balance is a highly sensitive laboratory instrument designed to measure small mass values with high precision. It often features a draft shield to protect against environmental factors such as air currents that could influence the stability of the readings.

To use an analytical balance effectively:

• Warm up the balance by allowing it to calibrate or self-test upon startup.
• Always handle samples with clean, dry tools to avoid contamination or moisture affecting the readings.
• Use the tare function to set the balance to zero after placing an empty container, allowing the direct measurement of the sample mass.
• Avoid touching the balance pan as it is sensitive, and even slight pressure can cause erroneous readings.

Maintaining the analytical balance and ensuring it is placed on a stable, vibration-free surface is crucial for obtaining accurate measurements. Regular calibration using standard weights is also necessary to maintain its precision over time.