Problem 76 - Chemistry The Molecular Nature of Matter

Question

A glass apparatus contains \(26.223 \mathrm{~g}\) of water when filled at \(25^{\circ} \mathrm{C}\). At this temperature, water has a density of \(0.99704 \mathrm{~g} / \mathrm{mL}\). What is the volume, in \(\mathrm{mL}\), of the apparatus?

Step-by-Step Solution

Answer

The volume of the apparatus is 26.313 mL.

Step 1: Understand the Relationship Between Mass, Density, and Volume

To find the volume of the water in the apparatus, we need to use the formula linking mass, density, and volume. The formula is: Volume = Mass / Density. Here, we are given the mass of the water and the density of water at the given temperature.

Key Concepts

Mass and Volume Relationship

To comprehend the intrinsic link between mass and volume, one needs to delve into the concept of density. Density is the measure of mass per unit volume and is a pivotal property in the realm of physical sciences. To calculate the volume when the mass and density are known, we simply rearrange the formula for density, \( \rho = \frac{m}{V} \), which gives us the volume formula, \( V = \frac{m}{\rho} \).

In the context of the exercise, the mass of water is given as \(26.223\, \text{g}\) and the density at \(25^\circ\text{C}\) is \(0.99704\, \text{g/mL}\). To find the volume, we divide the mass by the density using the formula, obtaining the volume of water the apparatus can contain at that specific temperature. This simple relationship allows us to solve many practical chemistry problems involving the quantitative aspects of substances.

Chemistry Problem Solving

Chemistry problems often require a step-by-step approach to untangle the various relationships between physical quantities. Problem solving in chemistry hinges on a clear understanding of fundamental concepts, such as the mass-volume relationship we explored and the ability to apply them to diverse scenarios.

To tackle the exercise effectively, the first step is to identify the known quantities and the quantity you need to find. Next, choose an appropriate formula, plug in the known values, and solve for the unknown. It is crucial to pay attention to units and to convert them if necessary to ensure consistency throughout the calculation. In this case, both mass and density are given in compatible units (grams and grams per milliliter), thus simplifying the computation.

Temperature Effects on Density

Temperature can have a significant impact on the density of a substance. Generally, as temperature increases, substances expand, increasing their volume but not their mass, leading to a decrease in density. Conversely, a drop in temperature usually causes a substance to contract, resulting in a higher density.

In the context of our example, water's density at \(25^\circ\text{C}\) is specified, but it is worth noting that if the temperature were to change, the density would also change, and thus the volume of water that the apparatus could hold would differ. When solving chemistry problems, it's vital to ensure that the density value used corresponds to the substance's temperature at the time of measurement. Changes in density due to temperature fluctuations are a fundamental concept in many real-world applications, such as designing thermal systems or predicting substance behavior under varying environmental conditions.