Problem 121 - General Chemistry

Question

Zinc metal can be purified by distillation (transforming the liquid metal to vapor, then condensing the vapor back to liquid). The metal boils at normal atmospheric pressure at \(1666^{\circ} \mathrm{F}\). What is this temperature in degrees Celsius? in kelvins?

Step-by-Step Solution

Answer

The boiling point of zinc is approximately 907.78°C or 1180.93 K.

Step 1: Convert Fahrenheit to Celsius

To convert degrees Fahrenheit to degrees Celsius, we use the formula: \[ C = \frac{5}{9} (F - 32) \]Substitute the boiling point of zinc, \( F = 1666^{\circ} \mathrm{F} \) into the formula:\[ C = \frac{5}{9} (1666 - 32) \]Calculate the result:\[ C = \frac{5}{9} \times 1634 = 907.78^{\circ} \mathrm{C} \]

Step 2: Convert Celsius to Kelvin

To convert degrees Celsius to kelvins, we use the formula:\[ K = C + 273.15 \]Substitute the calculated Celsius temperature into the formula:\[ K = 907.78 + 273.15 \]Calculate the result:\[ K = 1180.93 \]

Key Concepts

Fahrenheit to Celsius conversion

Converting temperatures from Fahrenheit to Celsius is a valuable skill, especially when dealing with scientific data that predominantly uses the Celsius scale. The conversion formula is:

• \( C = \frac{5}{9} (F - 32) \)

This formula identifies the temperature in Celsius \( C \) by taking the Fahrenheit temperature \( F \), subtracting 32, multiplying by 5, and then dividing by 9. Let's take the boiling point of zinc, for example, which is \( 1666^{\circ} \mathrm{F} \).

By using the formula, subtract 32 from 1666, resulting in 1634. Then multiply 1634 by 5, which equals 8170. Finally, divide by 9 to determine \( 907.78^{\circ} \mathrm{C} \). This calculation shows us how the boiling point of zinc translates into a more universally used unit, making data understandable globally.

Celsius to Kelvin conversion

Moving from Celsius to Kelvin is an essential conversion in the field of thermodynamics and scientific research, as Kelvin is the SI unit for temperature. The formula for this conversion is straightforward:

• \( K = C + 273.15 \)

Here, the calculated Celsius temperature is directly added to 273.15 to switch it to Kelvin. Continuing with our example of zinc: having calculated the boiling point as \( 907.78^{\circ} \mathrm{C} \), the next step is to add 273.15.

This addition results in a temperature of \( 1180.93 \mathrm{K} \), illustrating how we operate within a form of temperature that begins from absolute zero, making it ideal for theoretical computations. Kelvin scale doesn't use degrees but measures absolute thermal energy.

Boiling point of metals

The boiling point of metals is a critical property utilized in material science and engineering. It tells us the temperature at which a metal changes from a liquid to a gas. This is crucial for processes like purification by distillation, where metals like zinc are transformed into vapor and then condensed back to a liquid.

Zinc, for example, boils at \( 1666^{\circ} \mathrm{F} \), demonstrating a high threshold needed to change its state. Understanding boiling points helps in choosing the right process for refining metals. Knowing this also aids in ensuring the right conditions during manufacturing processes to prevent metal loss or contamination. Metal boiling points underscore the necessity for specific tools and settings when dealing with metal work, ensuring efficiency and safety.