Textbook Question
(a) Two pans of water are on different burners of a stove. One pan of water is boiling vigorously, while the other is boiling gently. What can be said about the temperature of the water in the two pans?
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Ch.11 - Liquids and Intermolecular Forces
Chapter 11, Problem 56
Appendix B lists the vapor pressure of water at various external pressures. (a) Plot the data in Appendix B, vapor pressure (torr) versus temperature (°C). From your plot, estimate the vapor pressure of water at body temperature, 37 °C. (b) Explain the significance of the data point at 760.0 torr, 100 °C. (c) A city at an altitude of 500 ft below sea level would have a barometric pressure of 774 torr. To what temperature would you have to heat water to boil it in this city?
Verified step by step guidance1
To address part (a), first gather the data from Appendix B, which lists the vapor pressure of water at various temperatures. Plot this data with temperature on the x-axis and vapor pressure on the y-axis. Use a smooth curve to connect the data points. Once the plot is complete, locate 37 °C on the x-axis and draw a vertical line up to the curve. From this intersection, draw a horizontal line to the y-axis to estimate the vapor pressure at 37 °C.
For part (b), understand that the data point at 760.0 torr and 100 °C is significant because it represents the normal boiling point of water at sea level. At this temperature and pressure, the vapor pressure of water equals the atmospheric pressure, allowing water to transition from liquid to gas.
In part (c), to find the temperature at which water boils at a barometric pressure of 774 torr, use the plot from part (a). Locate 774 torr on the y-axis and draw a horizontal line to intersect the curve. From this intersection, draw a vertical line down to the x-axis to determine the corresponding temperature.
If the plot is not precise enough, consider using the Clausius-Clapeyron equation to calculate the boiling point more accurately. The equation is: \( \ln \left( \frac{P_2}{P_1} \right) = \frac{\Delta H_{vap}}{R} \left( \frac{1}{T_1} - \frac{1}{T_2} \right) \), where \( P_1 \) and \( P_2 \) are the initial and final pressures, \( T_1 \) and \( T_2 \) are the initial and final temperatures in Kelvin, \( \Delta H_{vap} \) is the enthalpy of vaporization, and \( R \) is the gas constant.
Convert the temperature obtained from the plot or calculation to Celsius if necessary, as the problem asks for the boiling temperature in this city in degrees Celsius.
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Vapor Pressure
Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid or solid form at a given temperature. It indicates how readily a substance will evaporate; higher vapor pressure means a substance evaporates more easily. The vapor pressure of water increases with temperature, which is crucial for understanding boiling points and phase changes.
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02:40
Raoult's Law and Vapor Pressure
Boiling Point
The boiling point of a liquid is the temperature at which its vapor pressure equals the external pressure surrounding the liquid. For water, this is typically 100 °C at 1 atm (760 torr). However, at lower external pressures, such as those found at higher altitudes or in specific environments, the boiling point decreases, affecting cooking and other processes.
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03:05Boiling Point Elevation
Altitude and Atmospheric Pressure
Altitude affects atmospheric pressure, which in turn influences the boiling point of liquids. As altitude increases, atmospheric pressure decreases, leading to a lower boiling point for water. Conversely, below sea level, atmospheric pressure is higher, requiring a higher temperature to reach the boiling point of water, which is essential for understanding how environmental conditions affect physical properties.
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02:09Total Pressure Example
Related Practice
Textbook Question
You are high up in the mountains and boil water to make some tea. However, when you drink your tea, it is not as hot as it should be. You try again and again, but the water is just not hot enough to make a hot cup of tea. Which is the best explanation for this result? (a) High in the mountains, it is probably very dry, and so the water is rapidly evaporating from your cup and cooling it. (b) High in the mountains, it is probably very windy, and so the water is rapidly evaporating from your cup and cooling it. (c) High in the mountains, the air pressure is significantly less than 1 atm, so the boiling point of water is much lower than at sea level. (d) High in the mountains, the air pressure is significantly less than 1 atm, so the boiling point of water is much higher than at sea level.
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Textbook Question
Using the vapor-pressure curves in Figure 11.25, (d) estimate the external pressure at which diethyl ether will boil at 40 °C.
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Textbook Question
Appendix B lists the vapor pressure of water at various external pressures. (c) A city at an altitude of 5000 ft above sea level has a barometric pressure of 633 torr. To what temperature would you have to heat water to boil it in this city?
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Textbook Question
(b) Could you measure the triple point of water by measuring the temperature in a vessel in which water vapor, liquid water, and ice are in equilibrium under 1 atm of air? Explain.
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