Question

Appendix \(\mathrm{B}\) lists the vapor pressure of water at various external pressures. (a) Plot the data in Appendix B,vapor pressure versus temperature \(\left({ }^{\circ} \mathrm{C}\right) .\) From your plot, estimate the vapor pressure of water at body temperature, \(37^{\circ} \mathrm{C}\). (b) Explain the significance of the data point at \(101.3 \mathrm{kPa}, 100^{\circ} \mathrm{C} .(\mathbf{c}) \mathrm{A}\) city at an altitude of \(1525 \mathrm{~m}\) above sea level has a barometric pressure of \(84.3 \mathrm{kPa}\). To what temperature would you have to heat water to boil it in this city? (d) A city at an altitude of \(150 \mathrm{~m}\) below sea level would have a barometric pressure of \(103.14 \mathrm{kPa}\). To what temperature would you have to heat water to boil it in this city?

Short answer

(a) By plotting the data in Appendix B and estimating from the graph, the vapor pressure of water at body temperature (\(37^{\circ} \mathrm{C}\)) is approximately \(6.3 \mathrm{kPa}\). (b) The data point at \(101.3 \mathrm{kPa}, 100^{\circ} \mathrm{C}\) represents the standard boiling point of water at sea level, since the external pressure is equal to the standard atmospheric pressure. (c) In a city at an altitude of \(1525 \mathrm{~m}\) above sea level with a barometric pressure of \(84.3 \mathrm{kPa}\), water would boil at approximately \(95^{\circ} \mathrm{C}\) based on the graph. (d) In a city at an altitude of \(150 \mathrm{~m}\) below sea level with a barometric pressure of \(103.14 \mathrm{kPa}\), water would boil at approximately \(101^{\circ} \mathrm{C}\) based on the graph.

Step-by-step solution

(a) Estimate the vapor pressure of water at body temperature

To do this, follow these steps: 1. Plot the data from Appendix B on graph paper or use software to create the graph. On the x-axis, plot the temperature in °C and on the y-axis, plot the vapor pressure in kPa. 2. Use a smooth curve to connect the points and estimate the vapor pressure of water at \(37^{\circ} \mathrm{C}\). The graph should resemble an increasing curve with a relatively smooth shape.

(b) Significance of the data point at \(101.3 \mathrm{kPa}, 100^{\circ} \mathrm{C}\)

At this data point, the external pressure is equal to the standard atmospheric pressure (\(101.3 \mathrm{kPa}\)). At this pressure, water boils at \(100^{\circ} \mathrm{C}\). This data point represents the standard boiling point of water at sea level.

(c) Boiling temperature of water at \(1525 \mathrm{~m}\) above sea level

To find the boiling temperature of water at this altitude, follow these steps: 1. Use the given barometric pressure, \(84.3 \mathrm{kPa}\), as the external pressure. 2. Locate the external pressure on the y-axis of the previously plotted graph. Find the corresponding temperature on the x-axis. 3. This temperature is the boiling point of water in a city at an altitude of \(1525 \mathrm{~m}\) above sea level.

(d) Boiling temperature of water at \(150 \mathrm{~m}\) below sea level

To find the boiling temperature of water at this altitude, follow these steps: 1. Use the given barometric pressure, \(103.14 \mathrm{kPa}\), as the external pressure. 2. Locate the external pressure on the y-axis of the previously plotted graph. Find the corresponding temperature on the x-axis. 3. This temperature is the boiling point of water in a city at an altitude of \(150 \mathrm{~m}\) below sea level.

Key concepts

Boiling Point

The boiling point of a substance is the temperature at which its vapor pressure equals the external pressure surrounding the liquid. This is the temperature where a liquid changes into vapor, and boiling occurs. Water is a classic example for students learning about the boiling point. At standard atmospheric pressure, water boils at 100°C.
Many factors can affect boiling points. Key among them is atmospheric pressure. For instance, in a city located at sea level, the boiling point of water is typically higher than in a city located at a higher altitude. The vapor pressure reaches the external pressure more swiftly at higher altitudes. This means the boiling occurs at a lower temperature compared to sea level.
Understanding boiling points has practical implications in cooking and chemistry, influencing everything from how quickly food cooks to the efficiency of laboratory and industrial processes.

Standard Atmospheric Pressure

Standard atmospheric pressure is defined as the pressure that supports a column of mercury 760 mm high in a barometer at sea level and at a temperature of 0°C. In more familiar terms, this equates to approximately 101.3 kilopascals (kPa).
This standard pressure is crucial because it serves as a reference point for defining the boiling point of water and other substances. At this stable pressure, water boils at a consistent temperature of 100°C. When the pressure changes, such as in different weather conditions or at different altitudes, the boiling point of water also changes accordingly.
In many scientific and engineering calculations, standard atmospheric pressure is used as a baseline to understand and predict the behavior of gases and liquids. It's important for students to understand this concept, as it links directly to discussions about weather patterns and altitude effects on boiling points.

Altitude and Pressure

Altitude significantly impacts atmospheric pressure. As one ascends to higher altitudes, atmospheric pressure decreases. This is because there are fewer air molecules pushing down from above, which reduces the pressure.
As the atmospheric pressure drops, so does the boiling point of water. For example, in a city at an altitude of 1525 meters above sea level, the atmospheric pressure might drop to 84.3 kPa. Under these conditions, water boils at a lower temperature than the typical 100°C. This concept explains why cooking times and methods differ at various altitudes, particularly in mountainous regions.
Conversely, below sea level, atmospheric pressure increases. Here, the boiling point of water will be higher. In a city 150 meters below sea level, the pressure might be 103.14 kPa, shifting the boiling point upwards. Understanding these adjustments is critical for industries and professions that rely on precise temperature and pressure conditions, such as culinary arts and meteorology.