Question

The hottest temperature recorded in the United States is 134 " in Greenland Ranch, California. The melting point of phosphorus is 44 . C . At this temperature, would phosphorus be a liquid or a solid?

Short answer

At the hottest temperature recorded in the United States (approximately 56.67°C), phosphorus would be in a liquid state as its melting point (44°C) is below this temperature.

Step-by-step solution

Convert the temperatures to the same unit

To compare the temperatures, both temperatures should be in the same unit. The hottest temperature recorded is given in Fahrenheit, while the melting point of phosphorus is given in Celsius. So, let's convert the 134°F to Celsius using the formula: \(C = (F - 32) \times \frac{5}{9}\)

Calculate the temperature in Celsius

Plug in the value of Fahrenheit temperature (134°F) in the formula: \(C = (134 - 32) \times \frac{5}{9}\)

Simplify the equation

Perform the calculations to get the equivalent Celsius temperature: \(C = (102) \times \frac{5}{9}\) \(C = 56.67^\circ C\) Now, the hottest temperature in the United States is approximately 56.67 degrees Celsius.

Compare the temperatures

Compare the converted temperature (56.67°C) to the melting point of phosphorus (44°C): 56.67°C > 44°C Since the hottest temperature in the United States is greater than the melting point of phosphorus:

Determine the state of phosphorus

At the given temperature, phosphorus would be in a liquid state since its melting point is below the temperature.

Key concepts

States of Matter

Matter can exist in different forms or "states" such as solid, liquid, and gas. These states are determined by the arrangement and energy of the particles that compose the material. In a solid, particles are tightly packed and have a fixed shape. In a liquid, particles are more loosely arranged and can move around, which gives liquids their ability to flow. Gases have widely spaced particles that can move freely, allowing them to expand and fill any container.

When you heat a solid, its particles gain energy and start moving more vigorously. If enough energy is added, the solid can turn into a liquid; this process is called melting. Similarly, when a liquid gains enough energy, it can become gas in a process called vaporization. Understanding these states of matter is crucial when studying physical behavior under various temperature conditions.

Melting Point

The melting point of a substance is the temperature at which it transitions from a solid to a liquid. Every substance has a unique melting point. It's determined by the types of bonds between its molecules and the energy needed to break them. For example, phosphorus has a melting point at 44°C.

The phase change at the melting point occurs because the molecules have enough energy to overcome intermolecular forces holding them in a fixed position. This does not mean that once this temperature is reached, all material instantaneously turns into a liquid. Instead, as energy is applied, the solid begins to melt gradually. For phosphorus, any temperature above 44°C will cause it to be in a liquid form. Therefore, understanding melting points helps us to predict a substance's state at different temperatures.

Fahrenheit to Celsius Conversion

Converting temperatures between Fahrenheit and Celsius is a common necessity, especially in scientific contexts where Celsius is preferred. The formula to convert Fahrenheit (°F) to Celsius (°C) is:

• \[C = (F - 32) \times \frac{5}{9}\]

This formula helps us switch from one temperature unit to the other, facilitating comparisons and calculations. For instance, 134°F is converted to Celsius by substituting into the formula. Subtract 32 from 134, multiply by 5, and then divide by 9, resulting in 56.67°C.

Using this converted temperature, one can accurately determine whether a substance like phosphorus is solid or liquid at any given temperature, aiding in scientific experiments and real-world applications. Understanding these conversions is not only crucial for solving problems but is also helpful for everyday temperature-related tasks.