Problem 54 - Chemistry: The Central Science in SI Units, Global Edition

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 \(101.3 \mathrm{kPa}\), 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 \(101.3 \mathrm{kPa}\), so the boiling point of water is much higher than at sea level.

Step-by-Step Solution

Answer

The best explanation for the water not being hot enough to make tea high up in the mountains is (c) because at high altitudes, the air pressure is significantly less than \(101.3 \mathrm{kPa}\), resulting in a lower boiling point for water than at sea level.

Step 1: Eliminate explanations related to evaporation

First, let's examine explanations (a) and (b). Both explanations involve the rapid evaporation of water from the cup, which cools the water. While it is true that dry and/or windy conditions could cause water to evaporate, neither of these factors would affect the boiling point of the water or the actual temperature of the tea. So, we can eliminate explanations (a) and (b).

Step 2: Understand the relationship between air pressure and the boiling point of water

Now let's focus on explanations (c) and (d), which both involve changes in air pressure and their effect on the boiling point of water. From science principles, we know that the boiling point of water decreases as air pressure decreases. The boiling point of water at normal atmospheric pressure (\(101.3 \mathrm{kPa}\)) is \(100 ^{\circ}\mathrm{C}\). At higher altitudes, air pressure decreases, so the boiling point of water is expected to be lower.

Step 3: Choose the correct explanation

With our understanding of how air pressure and the boiling point of water are related, we can now evaluate explanations (c) and (d). - (c) High in the mountains, the air pressure is significantly less than \(101.3 \mathrm{kPa}\), 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 \(101.3 \mathrm{kPa}\), so the boiling point of water is much higher than at sea level. Since we know that the boiling point of water decreases as air pressure decreases, the best explanation for the unusual behavior of boiling water at high altitudes is explanation (c).

Key Concepts

Air Pressure

Air pressure is the force exerted by the weight of air molecules pressing down on Earth's surface. This pressure can vary depending on the location and weather conditions. At sea level, the average air pressure is commonly known as atmospheric pressure, which is approximately \(101.3 \text{kPa}\). Fortunately, air pressure is easily measurable, and it plays a vital role in determining the boiling point of liquids, especially water.

When you heat water, it begins to turn into vapor, and this process is called boiling. The boiling point is the temperature at which the water vapor pressure equals the surrounding air pressure. If the air pressure is high, the boiling point will also be higher, as it takes more heat energy for the water to turn into vapor and equal the atmospheric pressure. Conversely, if the air pressure is lower, such as at higher elevations, less heat energy is required, hence the water boils at a lower temperature. Understanding how air pressure affects the boiling point of water helps explain some everyday phenomena, especially in varied atmospheric conditions.

Altitude Effects

Altitude is the height above sea level, and it has a significant effect on air pressure. As altitude increases, the air becomes less dense and thinner, which means there are fewer air molecules pushing down. As a result, the atmospheric pressure decreases.

This decrease in atmospheric pressure affects various physical processes, one of the most noticeable being the boiling point of water. At sea level, water boils at \(100^{\circ} \text{C}\), but at higher altitudes, due to lower air pressure, water boils at a lower temperature. This is why when you're high up in the mountains and try to make tea, your water may boil at around \(90^{\circ} \text{C}\) instead of the usual \(100^{\circ} \text{C}\).

While this effect might seem negligible, it fundamentally changes cooking times and methods at high altitudes. Foods may take longer to cook or may not reach the desired internal temperature if solely relying on boiling water. Understanding altitude's effect on boiling point helps in planning cooking and heating activities in high mountain areas.

Water Evaporation

Water evaporation is a process in which liquid water turns into vapor and mixes into the air. While evaporation can cool a cup of hot liquid quickly, it is not usually significant enough to affect the boiling point of water by itself.

However, factors like wind and low humidity, which are often present in high mountain areas, can speed up this evaporation process. Wind blows away the water vapor as it forms, allowing more liquid to evaporate. Similarly, low humidity means there is less water vapor in the air, so the water in your cup can evaporate more freely and quickly.

While rapid evaporation might cool down the boiled water quickly, it’s important to note that it doesn't lower the boiling temperature. Therefore, regardless of how windy or dry it might be, these factors don’t directly change the boiling point like air pressure does. Understanding water evaporation helps in managing how quickly liquids cool but not in assessing boiling temperatures.