Problem 16 - Chemistry: Principles and Reactions

Question

Gallium is one of the few metals that can melt at room temperature. Its melting point is \(29.76^{\circ} \mathrm{C}\). If you leave solid gallium in your car on an early summer morning when the temperature is \(75^{\circ} \mathrm{F}\), in what physical state is the gallium when you return to your car and the interior car temperature is \(85.0^{\circ} \mathrm{F} ?\)

Step-by-Step Solution

Answer

Answer: The physical state of Gallium will be solid when you return to your car.

Step 1: Convert the initial car temperature to Celsius

We can covert Fahrenheit to Celsius using the formula: \(C = \frac{5}{9}(F - 32)\) Substitute the initial car temperature (\(75^{\circ}\mathrm{F}\)) into the formula: \(C = \frac{5}{9}(75 - 32)\) \(C \approx 23.89^{\circ}\mathrm{C}\)

Step 2: Convert the final car temperature to Celsius

Substitute the final car temperature (\(85.0^{\circ}\mathrm{F}\)) into the formula: \(C = \frac{5}{9}(85 - 32)\) \(C \approx 29.44^{\circ}\mathrm{C}\)

Step 3: Compare the final car temperature with the melting point of Gallium

The melting point of Gallium is \(29.76^{\circ}\mathrm{C}\), and the final car temperature is \(29.44^{\circ}\mathrm{C}\). Since the final car temperature is lower than Gallium's melting point: \(29.44^{\circ}\mathrm{C} < 29.76^{\circ}\mathrm{C}\)

Step 4: Determine the physical state of Gallium

Since the final car temperature is less than the melting point of Gallium, the Gallium will remain in a solid state when you return to your car.

Key Concepts

Gallium

Gallium is a fascinating metal known for its unique properties. It is one of the few metals that can melt at or near room temperature, making it particularly interesting in scientific studies and applications.
Gallium's melting point is approximately 29.76°C (about 85.57°F). What's remarkable about gallium is how it behaves at temperatures that humans commonly experience in everyday environments. If you hold a piece of gallium in your hand, it can start to melt due to your body heat, as human skin temperature can be higher than its melting point.
Scientists appreciate gallium for its thermal properties and use it in various applications. These include electronics, where it's used in semiconductors and thermometers, and in creating mirrors due to its reflective properties when melted and re-solidified.

Melting Point

The melting point of a substance is the temperature at which it transitions from a solid to a liquid.
This fundamental physical property is key in determining the state of matter under different temperature conditions. When a substance reaches its melting point, its molecules have enough energy to overcome their organized structure in a solid and move freely to form a liquid.
Different substances have different melting points. Gallium, for instance, has a relatively low melting point of 29.76°C, which is unusual compared to many other metals that melt at much higher temperatures, such as iron or aluminum.

• A lower melting point means a substance can change its state in everyday ambient conditions, making it useful for specific practical applications. For gallium, this means switching easily between solid and liquid states, influencing its use in electronic devices.
• Understanding melting points is critical for applications where temperature control is vital, such as in manufacturing and material science.

Temperature Conversion

Temperature conversion is crucial when working with scientific calculations and everyday tasks like monitoring the weather.
Different systems measure temperature, with Celsius (°C) and Fahrenheit (°F) being two of the most commonly used ones. To convert temperatures from Fahrenheit to Celsius, a standard formula is used:

• The formula is: \( C = \frac{5}{9}(F - 32) \), where \( C \) is the temperature in Celsius, and \( F \) is the temperature in Fahrenheit.

This formula is crucial when considering phase changes for materials such as gallium. For example, if you're trying to determine whether gallium will be solid or liquid at a given room temperature expressed in Fahrenheit, converting to Celsius will allow you to compare it directly to gallium's melting point of 29.76°C.
When converting, each calculation must be precise, as even small errors in temperature conversion can lead to incorrect conclusions about the state of the matter you're working with. Therefore, knowing how and when to make these conversions ensures the integrity of scientific and everyday temperature-related decisions.