Problem 104 - General Chemistry: Principles and Modern Applications

Question

Which of the following quantities has the greatest mass? (a) \(752 \mathrm{mL}\) of water at \(20^{\circ} \mathrm{C}\) (b) 1.05 L of ethanol at \(20^{\circ} \mathrm{C}(d=0.789 \mathrm{g} / \mathrm{mL})\) (c) \(750 \mathrm{g}\) of chloroform at \(20^{\circ} \mathrm{C}(d=1.483 \mathrm{g} / \mathrm{mL})\) (d) a cube of balsa wood \(\left(d=0.11 \mathrm{g} / \mathrm{cm}^{3}\right)\) that is \(19.20 \mathrm{cm}\) on edge

Step-by-Step Solution

Answer

The ethanol has the greatest mass.

Step 1: Calculate the mass of water

We know the density of water at \(20^{\circ} \mathrm{C}\) is approximately \(1 \mathrm{g/mL}\), so, the mass is: Mass = volume * density = \(752 \mathrm{mL} * 1 \mathrm{g/mL} = 752 \mathrm{g}\)

Step 2: Calculate the mass of ethanol

The volume is given in L, we need to convert it to mL since the density is in \(g/mL\). \[1.05 \mathrm{L} = 1050 \mathrm{mL}\]. Now we can calculate the mass: Mass = volume * density = \(1050 \mathrm{mL} * 0.789 \mathrm{g/mL} = 827.95 \mathrm{g}\)

Step 3: Compare the mass of chloroform

The mass of chloroform is given directly as \(750 \mathrm{g}\)

Step 4: Calculate the mass of the cube of balsa wood

First, calculate the volume of the cube using the formula \(V=a^3\), where 'a' is the edge of the cube: Volume = \(19.2 \mathrm{cm} * 19.2 \mathrm{cm} *19.2 \mathrm{cm} = 7078.56 \mathrm{cm^3}\). Since 1 \(\mathrm{mL}=1\mathrm{cm^3}\), substitute \(\mathrm{cm^3}\) with \(\mathrm{mL}\). Then, calculate the mass = volume * density = \(7078.56 \mathrm{mL} * 0.11 \mathrm{g/mL} = 778.64 \mathrm{g}\)

Step 5: Compare the masses

The calculated masses are water = 752 g, ethanol = 827.95 g, chloroform = 750 g, balsa wood = 778.64 g. Thus, the one with the greatest mass is ethanol.

Key Concepts

Density

Density is a key concept in physics and chemistry, referring to the mass of a substance per unit volume. It is often represented by the symbol \( \rho \) and is calculated using the formula \( \rho = \frac{m}{V} \), where \( m \) is mass and \( V \) is volume. For example, if you have a material with a mass of 10 grams and a volume of 2 cubic centimeters, the density would be \( \frac{10}{2} = 5 \mathrm{g/cm^3} \).
Understanding density is crucial when determining how much "stuff" is packed into a given space. Different substances have different densities, which explains why some things float while others sink. This diversity in densities also makes it possible to calculate mass if volume and density are known, as demonstrated in the exercise.
Density helps identify substances and predict how they interact in a mixture or solution. Hence, it is a fundamental property to consider in scientific experiments and real-world applications.

Volume Conversion

When dealing with different substances and their respective measurements, volume conversion becomes essential. In the metric system, common units for volume include milliliters (mL), liters (L), and cubic centimeters (cm³). The key equivalence to remember is that \( 1 \mathrm{mL} = 1 \mathrm{cm}^{3} \). This equality is particularly handy when dealing with liquid volumes and densities expressed in \( \mathrm{g/mL} \).
In practice, you often need to convert units to match the density measurement, as seen when converting 1.05 liters of ethanol into 1050 milliliters in the given exercise. Such conversions ensure accuracy in calculations and easy comparisons between different metric system units. To convert between liters and milliliters, remember that \( 1 \mathrm{L} = 1000 \mathrm{mL} \).
Easy conversions between these units help simplify complex problems and ensure precise results, allowing comparisons across potentially different measurement systems or presentation formats.

Material Properties

Material properties are characteristics that define how a substance behaves under various conditions. One essential property when calculating mass from volume is density, but there are many other properties too, such as hardness, elasticity, and thermal conductivity.
When considering the material properties of a substance, you'd often examine how it interacts with physical forces or other materials, its durability, and its resistance to temperature changes or chemical reactions. In the exercise example, the density of balsa wood is used to calculate its mass, illustrating how density serves as a vital property for understanding mass relationships.
Knowing a material's properties can aid in selecting it for specific applications, predicting its behavior in different environments, and understanding its compatibility with other substances. In scientific and engineering contexts, these properties are crucial for building functional, efficient, and safe structures or systems.

Chemical Substances

Chemical substances are elements or compounds with a definite composition and consist of molecules or atoms. These substances exhibit unique properties, including density, boiling point, and reactivity, which are critical for understanding how they behave individually and in mixtures.
In calculations, such as the exercise provided, knowing the density of a chemical substance like ethanol or chloroform helps us determine its mass when given its volume. Different chemical substances can have widely varying densities, affecting how they interact, whether in solutions or when layered. Ethanol, for instance, is less dense than water, which explains why when mixed, ethanol rises to the top.
Examining the specific chemical properties and variations among substances can help predict outcomes in chemical reactions and mixtures. This knowledge serves as the backbone for chemistry-related fields, where anticipating and controlling interactions between chemicals is paramount.