Question

The table below lists the density of \(\mathrm{O}_{2}\) at various temperatures and at \(1 \mathrm{~atm}\). Graph the data and predict the substance's normal boiling point.

Short answer

The given data represents the densities of \(\mathrm{O}_{2}\) at various temperatures under 1 atm pressure. To predict the normal boiling point, we can create a graph with the temperature on the x-axis and density on the y-axis. Plot the given data points on the graph and connect them with a smooth curve. Analyze the curve and find the temperature at which there is a significant change in the graph, where the density of liquid \(\mathrm{O}_{2}\) approaches the density of \(\mathrm{O}_{2}\) gas. This temperature can be estimated as the normal boiling point of the substance.

Step-by-step solution

Analyzing the given data

Observe the data of densities of O2 at various temperatures and pressures. It is important to understand the relationship between temperature and density under constant pressure (1 atm).

Creating a graph using the provided data

Using the given data of temperatures and densities, plot the points on a graph. To create a graph, choose the temperature as the x-axis and density as the y-axis. Then, plot the given data points on the graph and connect these points with a smooth curve.

Interpreting the graph to predict the normal boiling point

Now that you have drawn the graph, carefully analyze the curve. Remember, the normal boiling point of a substance is the temperature at which its vapor pressure equals atmospheric pressure (1 atm). Since this problem assumes constant pressure (1 atm), the boiling point may be inferred from temperature. Observe where the curve begins to level off or where there is a significant change in the linear behavior of the graph. The corresponding temperature at that point should give you an estimate of the normal boiling point of the substance, as it implies that the density of liquid O2 approaches the density of O2 gas under 1 atm at this temperature.

Key concepts

Density to Temperature Relationship

Understanding the relationship between the density of a substance and its temperature is crucial when predicting its boiling point. Density, essentially the mass per unit volume of a substance, typically decreases as the temperature increases due to the expansion of matter. This is a direct result of the increase in kinetic energy which causes particles to move more rapidly and spread apart. However, at a substance's boiling point, a unique scenario occurs: the density of the liquid phase and the gas phase reach equilibrium.

For most substances, this relationship can be graphically represented by a curve on a Density vs. Temperature graph. As temperature rises, you would generally see a smooth decrease in density up until the boiling point. At this point, there's often a more pronounced change in the slope of the curve. This happens because the phase change from liquid to gas involves a large increase in volume, which translates to a sudden decrease in density. By examining the curve, it's possible to predict where the substance would enter the gaseous state, which would correspond to its boiling point under a given pressure.

Graphical Data Analysis

Graphical data analysis is a powerful tool for interpreting complex data sets and extracting valuable insights. By plotting the relationship between two variables, like density and temperature, one can visually assess how they interact. After plotting the data points on a graph with temperature on the x-axis and density on the y-axis, we can study the plot's trend.

The importance of creating a smooth curve through the points cannot be overstated—it captures the gradual changes as well as any abrupt shifts in the relationship between temperature and density. Such shifts are indicative of phase changes, like boiling. In an educational setting, graphical analysis aids in developing a student's ability to predict and understand transitions between states of matter, such as when a substance will boil.

States of Matter

When considering the states of matter, it's essential to explore the fundamental differences between solids, liquids, and gases—chiefly in terms of density and arrangement of particles. In solids, particles are tightly packed in a structured formation, resulting in a relatively high density. On moving to the liquid state, a substance's particles are less tightly packed due to increased energy, leading to a moderate density. Finally, in the gaseous state, particles are far apart and have much more energy – this corresponds with the lowest density of the three states.

This transition between states is typically a continuous process as temperature changes, depicted graphically with a density-temperature plot. As educators, it's crucial to convey these concepts with clarity, as understanding them is fundamental to many fields within science, from chemistry to materials science.

Vapor Pressure

Vapor pressure is the pressure exerted by vapor that is in equilibrium with its liquid or solid form at a given temperature. It's an essential concept when it comes to understanding boiling points because a substance's normal boiling point occurs when its vapor pressure equals the surrounding atmospheric pressure. In this case, the atmospheric pressure is 1 atm.

In the classroom, it's vital to teach that as the temperature of a liquid increases, so does its vapor pressure, due to particles gaining enough energy to escape into the gas phase. The moment the vapor pressure reaches the atmospheric pressure, the liquid will begin to boil. This key concept aids in interpreting temperature-density graphs and connecting them to changes in vapor pressure as one approaches the boiling point of a substance.