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Chapter 11: Problem 54

Explain the following observations: (a) Water evaporates more quickly on a hot, dry day than on a hot, humid day. (b) It takes longer to cook an egg in boiling water at high altitudes than it does at lower altitudes.

Short Answer

Expert verified
On a hot, dry day, water evaporates more quickly because the air has a higher capacity to hold water vapor due to the low humidity, enhancing evaporation. In contrast, a hot, humid day has a slower evaporation rate because the air is already saturated with water vapor. For cooking an egg in boiling water, high altitudes have lower air pressure and thus a lower boiling point for water, which means the temperature may not be high enough to cook the egg efficiently, taking longer to cook compared to lower altitudes where water boils at higher temperatures.

Step by step solution

01

Understanding evaporation and humidity

Evaporation is the conversion of a liquid (like water) into vapor, which then diffuses into the surrounding air. The rate of evaporation is influenced by external factors like temperature and humidity. Higher temperature increases the rate of evaporation, while higher humidity (i.e. more water vapor in the air) decreases the rate of evaporation, as the air is already saturated with water vapor and can't hold much more.
02

Observation (a) explanation: Hot, dry vs. hot, humid day

On a hot, dry day, the air temperature is high and the relative humidity is low. The high temperature provides more energy to the water molecules, which results in increased evaporation. Meanwhile, the low humidity means that the air can hold more water vapor, allowing water to evaporate more quickly. On the other hand, on a hot, humid day, the air temperature is still high, but the relative humidity is also high. The higher humidity means that the air is already saturated with water vapor, which slows down the evaporation process. Therefore, water evaporates more slowly on a hot, humid day compared to a hot, dry day.
03

Understanding boiling point and air pressure

The boiling point of a liquid is the temperature at which its vapor pressure equals the atmospheric pressure. At this point, the liquid turns into a gas. The boiling point of a liquid, such as water, varies with the external pressure. Generally, when the pressure is reduced, the boiling point of water also decreases.
04

Understanding the effect of altitude on air pressure and boiling point

At higher altitudes, the air pressure is lower compared to a lower altitude. This is because there is less air above pushing down on you. As the pressure decreases with altitude, the boiling point of water also decreases. This means that at high altitudes, water will boil at temperatures lower than 100掳C (212掳F).
05

Observation (b) explanation: Cooking an egg at high vs. low altitudes

When cooking an egg in boiling water, the proteins in the egg coagulate. The coagulation temperature for egg proteins is typically around 60-70掳C (140-158掳F). At lower altitudes, water boils at around 100掳C (212掳F), so there is sufficient heat to cook the egg efficiently. However, at higher altitudes, as the boiling point of water decreases because of the lower air pressure, the boiling water temperature is also lower. The temperature may not be high enough to cook the egg as quickly or efficiently as at lower altitudes. As a result, it takes longer to cook an egg in boiling water at high altitudes than at lower altitudes.

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Most popular questions from this chapter

Acetone \(\left[\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CO}\right]\) is widely used as an industrial solvent. (a) Draw the Lewis structure for the acetone molecule and predict the geometry around each carbon atom. (b) Is the acetone molecule polar or nonpolar? (c) What kinds of intermolecular attractive forces exist between acetone molecules? (d) 1-Propanol \(\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH}\right)\) has a molecular weight that is very similar to that of acetone, yet acetone boils at \(56.5^{\circ} \mathrm{C}\) and 1 -propanol boils at \(97.2^{\circ} \mathrm{C}\). Explain the difference.

Name the phase transition in each of the following situations and indicate whether it is exothermic or endothermic: (a) When ice is heated, it turns to water. (b) Wet clothes dry on a warm summer day. (c) Frost appears on a window on a cold winter day. (d) Droplets of water appear on a cold glass of beer.

Ethylene glycol \(\left(\mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{OH}\right)\) is the major component of antifreeze. It is a slightly viscous liquid, not very volatile at room temperature, with a boiling point of \(198^{\circ} \mathrm{C}\). Pentane \(\left(\mathrm{C}_{5} \mathrm{H}_{12}\right)\), which has about the same molecular weight, is a nonviscous liquid that is highly volatile at room temperature and whose boiling point is \(36.1^{\circ} \mathrm{C}\). Explain the differences in the physical properties of the two substances.

Suppose the vapor pressure of a substance is measured at two different temperatures. (a) By using the ClausiusClapeyron equation (Equation 11.1) derive the following relationship between the vapor pressures, \(P_{1}\) and \(P_{2}\), and the absolute temperatures at which they were measured, \(T_{1}\) and \(T_{2}:\) $$ \ln \frac{P_{1}}{P_{2}}=-\frac{\Delta H_{\text {vap }}}{R}\left(\frac{1}{T_{1}}-\frac{1}{T_{2}}\right) $$ (b) Gasoline is a mixture of hydrocarbons, a major component of which is octane \(\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{3}\right)\). Octane has a vapor pressure of \(13.95\) torr at \(25^{\circ} \mathrm{C}\) and a vapor pressure of \(144.78\) torr at \(75^{\circ} \mathrm{C}\). Use these data and the equation in part (a) to calculate the heat of vaporization of octane. (c) By using the equation in part (a) and the data given in part (b), calculate the normal boiling point of octane. Compare your answer to the one you obtained from Exercise 11.80. (d) Calculate the vapor pressure of octane at \(-30^{\circ} \mathrm{C}\).

Benzoic acid, \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}\), melts at \(122^{\circ} \mathrm{C}\). The density in the liquid state at \(130^{\circ} \mathrm{C}\) is \(1.08 \mathrm{~g} / \mathrm{cm}^{3}\). The density of solid benzoic acid at \(15^{\circ} \mathrm{C}\) is \(1.266 \mathrm{~g} / \mathrm{cm}^{3}\). (a) In which of these two states is the average distance between molecules greater? (b) Explain the difference in densities at the two temperatures in terms of the relative kinetic energies of the molecules.
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