Question

Using this graph of \(\mathrm{CS}_{2}\) data, determine (a) the approximate vapor pressure of \(\mathrm{CS}_{2}\) at \(30^{\circ} \mathrm{C}\), (b) the temperature at which the vapor pressure equals 300 torr, (c) the normal boiling point of \(\mathrm{CS}_{2}\). [Section 11.5]

Short answer

(a) The approximate vapor pressure of \(\mathrm{CS}_{2}\) at \(30^{\circ} \mathrm{C}\) can be read from the graph. (b) The temperature at which the vapor pressure equals \(45 \mathrm{kPa}\) can be found by locating the point on the graph where the vapor pressure is \(45 \mathrm{kPa}\) and reading the corresponding temperature on the x-axis. (c) The normal boiling point of \(\mathrm{CS}_{2}\) is the temperature at which the vapor pressure equals the atmospheric pressure (\(101.3 \mathrm{kPa}\)). This can be found by locating the point on the graph where the vapor pressure is equal to \(101.3 \mathrm{kPa}\) and reading the corresponding temperature on the x-axis.

Step-by-step solution

Determine the approximate vapor pressure at \(30^{\circ} \mathrm{C}\).

To find the vapor pressure at \(30^{\circ} \mathrm{C}\), locate the point on the graph where the temperature is \(30^{\circ} \mathrm{C}\). Read the value of the vapor pressure corresponding to this temperature on the y-axis.

Determine the temperature at which the vapor pressure is equal to \(45 \mathrm{kPa}\).

To find the temperature where the vapor pressure is equal to \(45 \mathrm{kPa}\), locate the point on the graph where the vapor pressure is \(45 \mathrm{kPa}\). Read the value of the temperature corresponding to this vapor pressure on the x-axis.

Determine the normal boiling point of \(\mathrm{CS}_{2}\).

The normal boiling point is the temperature at which the vapor pressure of a substance equals the atmospheric pressure. For this problem, we will assume the normal atmospheric pressure to be \(101.3 \mathrm{kPa}\). Locate the point on the graph where the vapor pressure is equal to \(101.3 \mathrm{kPa}\) and read the corresponding temperature on the x-axis. This temperature is the normal boiling point of \(\mathrm{CS}_{2}\).

Key concepts

Graphical Analysis

Graphical analysis is a powerful tool for interpreting data visually. In this context, using a graph to examine the relationship between temperature and vapor pressure helps us extract valuable insights. Graphs provide a quick way to identify trends, patterns, and specific data points. By plotting temperature on the x-axis and vapor pressure on the y-axis, we can see how they relate to each other. This approach is particularly helpful when determining specific values like vapor pressure at a certain temperature, or finding what temperature corresponds to a given vapor pressure. With precise plotting, we can quickly find these points by visually inspecting where lines intersect without complicated calculations.

Carbon Disulfide

Carbon disulfide (CS₂) is a volatile, colorless liquid with a distinct odor. It's often used as an industrial solvent and sometimes in chemical synthesis. One of its key characteristics is its vapor pressure, which signifies how readily it evaporates at a given temperature. Understanding the properties of carbon disulfide is crucial when working with it, especially because of its flammability and potential health effects. When analyzing vapor pressure, it's important to recognize that carbon disulfide has a relatively high vapor pressure at room temperature compared to many other liquids, which contributes to its volatility.

Boiling Point Determination

Determining the boiling point of a liquid involves finding the temperature at which its vapor pressure equals external atmospheric pressure. The normal boiling point refers specifically to the temperature where the vapor pressure is equal to the standard atmospheric pressure of 101.3 kPa. To find the normal boiling point of carbon disulfide from a graph, locate the point where the curve reaches 101.3 kPa on the y-axis. The corresponding temperature on the x-axis gives the normal boiling point. This concept is fundamental in understanding phase transitions and in designing equipment and processes that involve heating substances.

Pressure-Temperature Relationship

The pressure-temperature relationship is governed by the Clausius-Clapeyron equation, which describes how vapor pressure of a substance changes with temperature. For any given substance, as the temperature increases, the vapor pressure increases. This is because higher temperatures provide more energy for molecules to escape the liquid phase into the vapor phase. In practical terms, this relationship helps predict how a substance behaves under different conditions. For carbon disulfide, understanding this relationship aids in safe handling and storage, as well as in utilizing it effectively as a solvent in varying temperature conditions.