Problem 120 - General Chemistry

Question

Mercury metal is liquid at normal temperatures but freezes at \(-38.9^{\circ} \mathrm{C}\). What is this temperature in kelvins? in degrees Fahrenheit?

Step-by-Step Solution

Answer

The temperature is 234.25 K and -38.02°F.

Step 1: Convert Celsius to Kelvin

To convert a temperature from Celsius to Kelvin, use the formula \[ K = C + 273.15 \]where \( C = -38.9^{\circ} \mathrm{C} \). Substituting in the values, we have:\[ K = -38.9 + 273.15 = 234.25 \]Thus, the temperature in kelvins is 234.25 K.

Step 2: Convert Celsius to Fahrenheit

To convert a temperature from Celsius to Fahrenheit, use the formula\[ F = \left( C \times \frac{9}{5} \right) + 32 \]Using \( C = -38.9^{\circ} \mathrm{C} \), we calculate:\[ F = \left( -38.9 \times \frac{9}{5} \right) + 32 = -38.02 \]Therefore, the temperature in degrees Fahrenheit is approximately -38.02°F.

Key Concepts

Kelvin

The Kelvin scale is a measurement for temperature that is particularly important in scientific contexts. Unlike Celsius and Fahrenheit, it starts at absolute zero—the coldest possible temperature where molecular motion ceases.
This makes Kelvin ideal for physics and chemistry calculations. When converting from Celsius to Kelvin, you simply add 273.15 to the Celsius temperature.
For instance, as shown in our original solution for mercury freezing,
if you have a temperature of r> -38.9°C, you add it to 273.15 to get 234.25 K. Kelvin never dips into negative numbers, which is why scientists often prefer it for experiments that involve extreme temperatures.

• Always starts at absolute zero
• Useful for scientific purposes
• No negative values

Celsius

The Celsius scale is a familiar temperature scale for many of us. Named after Swedish astronomer Anders Celsius, it is widely used around the world, especially in daily weather forecasts and environmental science.
The scale sets the freezing point of water at 0°C and the boiling point at 100°C under standard atmospheric conditions.
It's a straightforward scale, and easy to understand: negative values indicate conditions colder than freezing, such as the -38.9°C for the freezing point of mercury.

• Widely used globally
• Based on freezing and boiling points of water
• Negative numbers for very cold conditions

Fahrenheit

The Fahrenheit scale, primarily used in the United States, has its origins in the early 18th century. Created by Daniel Gabriel Fahrenheit, the scale sets the freezing point of water at 32°F and the boiling point at 212°F.
When converting from Celsius to Fahrenheit, the formula used is \[ F = \left( C \times \frac{9}{5} \right) + 32 \]
Taking the Celsius temperature of -38.9°C for mercury, when you plug it into the formula, the result is approximately -38.02°F.
This offers a perspective tailored for a human comfort range, yet requires conversion to fit globally used standards like Kelvin or Celsius.

• Used mainly in the USA
• Freezing point of water is 32°F
• Focused on human experience

Chemical Properties of Mercury

Mercury is a fascinating metal with unique chemical properties. Unlike most metals, it is a liquid at room temperature, which displays a shiny, silvery appearance.
Its atomic number is 80, and it is classified under the d-block elements in the periodic table. Mercury has a high density, allowing it to conduct electricity, making it useful in various scientific instruments such as thermometers and barometers.
However, it has a freezing point of -38.9°C, where it becomes solid. Its unusual liquid state over such a broad range of temperatures makes it particularly useful in measuring tools.
Despite its usefulness, mercury is toxic if mishandled, making it crucial to use cautiously and following safety protocols.

• Liquid at room temperature
• Useful in electrical instruments
• Toxic and requires careful handling