Question

Which evaporates more quickly: \(55 \mathrm{~mL}\) of water in a beaker with a diameter of \(4.5 \mathrm{~cm}\) or \(55 \mathrm{~mL}\) of water in a dish with a diameter of \(12 \mathrm{~cm}\) ? Why?

Short answer

The water in the dish with a diameter of 12 cm will evaporate more quickly because it has a larger surface area, allowing more water molecules to escape into the air.

Step-by-step solution

Understanding Evaporation

Evaporation is a process where liquid turns into vapor. One of the factors that influence the evaporation rate is the surface area in contact with the air. A larger surface area allows more molecules to escape, thereby increasing the rate of evaporation.

Comparing Surface Areas

The water in both containers is the same volume, but the surface areas will be different because they have different diameters. We can compare the evaporation rates by calculating the surface areas of the water in both containers. The surface area of water in a circular container can be calculated using the formula for the area of a circle, which is \( A = \pi r^2 \), where \( r \) is the radius.

Calculating the Surface Area for the Beaker

First, calculate the radius by dividing the diameter by 2. For the beaker with a diameter of \(4.5 \text{cm}\), the radius is \(4.5 \text{cm} / 2 = 2.25 \text{cm}\). Now, plug the value into the area formula: \( A = \pi (2.25 \text{cm})^2 \). Calculate to find the surface area of the water in the beaker.

Calculating the Surface Area for the Dish

Similarly, calculate the radius for the dish, which is \(12 \text{cm} / 2 = 6 \text{cm}\). Then, use the area formula: \( A = \pi (6 \text{cm})^2 \). Calculate to find the surface area of the water in the dish.

Comparing the Calculated Surface Areas

With the calculated surface areas for both the beaker and the dish, compare the two. The dish with the larger surface area will allow more water to evaporate over the same time period.

Conclusion

Since the dish has a larger diameter than the beaker, it will have a larger surface area. This means that the water in the dish will have a higher evaporation rate as it allows more molecules to escape at once. Therefore, the water in the dish will evaporate more quickly than the water in the beaker.

Key concepts

Surface Area and Evaporation

Evaporation is the process by which a liquid turns into a vapor, and understanding this process in the context of chemistry can be fascinating. A key concept when discussing evaporation is surface area. Surface area is essentially the amount of space on the liquid's surface that is exposed to air. The greater this area, the more molecules are at the surface and thus have a higher chance to escape into the air as vapor.

Imagine two pools of water, one spread thin and wide, the other deep and narrow. Even if both contain the same amount of water, the shallow pool will evaporate faster due to its larger surface area. This indicates how crucial the surface area is when determining the evaporation rate of liquids. In fact, increasing surface area is a commonly used strategy in various industries, such as in cooling towers in power plants where water needs to be evaporated efficiently.

Calculating Surface Area

Knowing how to calculate the surface area is essential in predicting the evaporation rate. For curved surfaces, such as the circular surface of water in a beaker or a dish, we use the formula for the area of a circle, which is \( A = \pi r^2 \), where 'r' is the radius of the circle. To get the radius, we divide the diameter of the container by two.

To visualize this, picturing a circle and understanding that the radius is half the length from one edge of the circle to the other can help. By squaring the radius and multiplying it by Pi (approximately 3.14159), we can find the area that will contribute to the evaporation process. Acting as armchair mathematicians, students can calculate the surface areas for both the beaker and the dish, with their given diameters, to understand which will have a greater evaporation rate.

Factors Affecting Evaporation

Several factors play a role in the rate of evaporation beyond surface area. These include temperature, humidity, wind speed, and the nature of the liquid itself. A higher temperature increases the energy of water molecules, prompting faster evaporation. On the other hand, high humidity in the air reduces evaporation since the air already has a significant amount of water vapor.

Temperature Influences

Warmer conditions lead to higher kinetic energy in liquid molecules, which can break free from the surface more readily.

Humidity Impacts

Drier air means less water vapor present, making it easier for evaporation to occur as the air can 'take in' more vapor.

Wind and Air Circulation

Greater wind speeds carry away vapor from the surface, speeding up the evaporation process.
Understanding these factors is vital for solving real-world problems involving evaporation in fields like meteorology or environmental science.

Chemistry Problem Solving

Problem solving in chemistry often involves a practical blend of theory and computation. When faced with a chemistry problem, first clarify the concept at hand—in this case, evaporation rates. After grounding understanding with theory, apply mathematical calculations as needed, ensuring each step is based on sound chemical principles.

A systematic approach is key in chemistry problem solving. Start by identifying what you know and what you need to find out. Here, we knew the volume of water and the diameters of the containers, and we sought to determine which would evaporate quicker. Steps included understanding evaporation, calculating surface areas, and applying the knowledge that a larger surface area leads to increased evaporation rate. By following these steps, one can methodically arrive at a logical conclusion, which is a fundamental skill not just in chemistry, but in any scientific endeavor.