Problem 98 - Chemistry

Question

Sodium chloride has a melting point of \(1074 \mathrm{~K}\) and a boiling point of \(1686 \mathrm{~K}\). Convert these temperatures to degrees Celsius and to degrees Fahrenheit.

Step-by-Step Solution

Answer

Melting point: 800.85 °C, 1473.53 °F; Boiling point: 1412.85 °C, 2575.13 °F.

Step 1: Convert Kelvin to Celsius

To convert from Kelvin to Celsius, use the formula: \( T_{\text{C}} = T_{\text{K}} - 273.15 \). - For the melting point: \( 1074 \mathrm{~K} - 273.15 = 800.85 \mathrm{~°C} \).- For the boiling point: \( 1686 \mathrm{~K} - 273.15 = 1412.85 \mathrm{~°C} \).

Step 2: Convert Celsius to Fahrenheit

To convert from Celsius to Fahrenheit, use the formula: \( T_{\text{F}} = (T_{\text{C}} \times \frac{9}{5}) + 32 \).- For the melting point: \( 800.85 \mathrm{~°C} \times \frac{9}{5} + 32 = 1473.53 \mathrm{~°F} \).- For the boiling point: \( 1412.85 \mathrm{~°C} \times \frac{9}{5} + 32 = 2575.13 \mathrm{~°F} \).

Key Concepts

Sodium Chloride

Sodium chloride, commonly known as table salt, is a versatile compound crucial in various applications. Essential in cooking and food preservation, it consists of sodium and chloride ions. Sodium chloride is also used in industrial processes and as a road de-icing agent.

Understanding the melting and boiling points of sodium chloride is vital, especially for industries relying on high-temperature processes. The melting point of sodium chloride is 1074 Kelvin (K), meaning it transforms from solid to liquid at this temperature. It is important for processes that require salt to be in a liquid form, such as certain industrial cleaning techniques. The boiling point is 1686 K, where it transitions from liquid to gas. This knowledge is used in manufacturing and scientific applications where precise temperature control is necessary.

Kelvin to Celsius Conversion

Temperature conversion is essential in science and everyday life. Kelvin to Celsius conversion is straightforward and commonly needed in scientific contexts.

Kelvin (K) is the SI unit of temperature, commonly used in science due to its absolute nature, starting at absolute zero—the lowest temperature possible. Celsius (°C) is more commonly used in everyday life and is part of the metric system.

The equation for converting Kelvin to Celsius is:

• \( T_{\text{C}} = T_{\text{K}} - 273.15 \)

Simply subtract 273.15 from the Kelvin temperature to find the equivalent in Celsius.

For example, the melting point of sodium chloride is 1074 K. Using the conversion equation, we find:

• \( 1074 - 273.15 = 800.85 \ \text{°C} \)

For the boiling point of 1686 K:

• \( 1686 - 273.15 = 1412.85 \ \text{°C} \)

This process illustrates the ease of transitioning between these two temperature scales, which is crucial in experiments and industrial processes.

Celsius to Fahrenheit Conversion

Celsius to Fahrenheit conversion is often necessary, particularly when dealing with international contexts where the imperial system is used, such as in the United States. Understanding this conversion can aid in various applications, from cooking to scientific undertakings.

To convert Celsius to Fahrenheit, use the formula:

• \( T_{\text{F}} = (T_{\text{C}} \times \frac{9}{5}) + 32 \)

This formula accommodates the differences in scale increments between Celsius and Fahrenheit.

Take, for instance, the converted melting point of sodium chloride, 800.85 °C. By applying the formula:

• \( 800.85 \times \frac{9}{5} + 32 = 1473.53 \ \text{°F} \)

Similarly, the boiling point of 1412.85 °C becomes:

• \( 1412.85 \times \frac{9}{5} + 32 = 2575.13 \ \text{°F} \)

Through these calculations, you can see how to convert Celsius temperatures into Fahrenheit, bridging the gap between different measurement systems for effective communication and understanding.