Question

The hottest temperature recorded in the United States is \(134^{\circ} \mathrm{F}\) in Greenland Ranch, CA. The melting point of phosphorus is \(44^{\circ} \mathrm{C}\). At this temperature, would phosphorus be a liquid or a solid?

Short answer

At the hottest temperature recorded in the United States, which is approximately \(56.67^{\circ}\mathrm{C}\), phosphorus would be in a liquid state, as it exceeds its melting point of \(44^{\circ}\mathrm{C}\).

Step-by-step solution

Convert the temperature from Fahrenheit to Celsius

To convert the temperature from Fahrenheit to Celsius, we use the formula: \[ \mathrm{C} = \frac{5}{9}(\mathrm{F} - 32) \] Where (C) is the temperature in Celsius, and (F) is the temperature in Fahrenheit. In this case, F = \(134^{\circ}\mathrm{F}\). So, \[ \mathrm{C} = \frac{5}{9}(134 - 32) \]

Calculate the Celsius temperature

We need to perform the operations inside the parentheses first and then multiply the result by \(\frac{5}{9}\): \[ \mathrm{C} = \frac{5}{9}(102) \] Now, multiply by \(\frac{5}{9}\): \[ \mathrm{C} \approx 56.67 ^{\circ}\mathrm{C} \] So, the hottest temperature recorded in the United States is approximately \(56.67^{\circ}\mathrm{C}\).

Compare the temperature with the melting point of phosphorus

The melting point of phosphorus is \(44^{\circ}\mathrm{C}\). Since the hottest temperature recorded in the United States (\(56.67^{\circ}\mathrm{C}\)) is higher than the melting point of phosphorus (\(44^{\circ}\mathrm{C}\)), phosphorus would be a liquid at this temperature.

Key concepts

Melting Point

The concept of melting point is crucial in understanding the phase transition of substances from solid to liquid. It is defined as the specific temperature at which a solid becomes a liquid.
At this temperature, the solid's orderly structure becomes loose enough for it to slide and flow as a liquid.
Key points:

• Melting point is a physical property that remains constant under specific conditions.
• Pressure can affect the melting point of a substance, although it has a significant impact mostly at high pressures.
• Knowing the melting point helps identify substances and predict their behavior under various temperatures.

For example, if you have a block of ice, it will start melting exactly at 0°C. Similarly, phosphorus will start melting at 44°C.

Phosphorus

Phosphorus is a fascinating chemical element with remarkable versatility. It is represented by the symbol P and has an atomic number of 15.
In nature, phosphorus is never found as a free element due to its high reactivity; instead, it exists in various phosphate minerals.

• There are different allotropes of phosphorus, including white, red, and black phosphorus, each having distinct physical properties.
• White phosphorus is highly reactive and toxic, often stored underwater or in inert gases to prevent it from reacting with oxygen.
• Phosphorus is essential for life, forming a component of DNA, RNA, and ATP, the molecule responsible for energy transfer in cells.

At 44°C, which is its melting point, phosphorus transitions from a solid to a liquid form, making it crucial to store it properly to avoid handling challenges.

Celsius to Fahrenheit Conversion

Converting temperatures from Celsius to Fahrenheit (and vice versa) is a necessary skill in various scientific calculations and daily life scenarios.
The conversion formula is derived from the linear relationship between the two temperature scales.
Here's a step-by-step guide:

• The formula to convert Fahrenheit to Celsius is given by:\[ C = \frac{5}{9}(F - 32) \]where \(C\) is the Celsius temperature and \(F\) is the Fahrenheit temperature.
• First, subtract 32 from the Fahrenheit temperature, as this accounts for the offset between the two scales.
• Next, multiply the result by \(\frac{5}{9}\), which adjusts for the different size of the degree units between Fahrenheit and Celsius.

For instance, to convert the record temperature of 134°F, you'd perform:\[ C = \frac{5}{9}(134 - 32) \approx 56.67 ^{\circ}C \]This way, you can accurately convert and understand temperatures in contexts like weather reports or scientific experiments.