Problem 2 - Chemistry: Introducing Inorganic, Organic and Physical Chemistry

Question

Oxygen gas liquefies at \(-183.0^{\circ} \mathrm{C}\) and freezes at \(-218.4^{\circ} \mathrm{C}\) Work out its melting point, \(T_{\mathrm{m}},\) and boiling point, \(T_{\mathrm{b}},\) in kelvin. (Section \(1.2)\)

Step-by-Step Solution

Answer

Oxygen has a melting point of 54.75 K and a boiling point of 90.15 K.

Step 1: Understand Temperature Conversion

The conversion formula from Celsius to Kelvin is given by \( K = ^{ackslash circ}C + 273.15 \). This formula will be used to convert both given temperatures into Kelvin.

Step 2: Convert Liquefaction Temperature

The liquefaction temperature of oxygen is given as \(-183.0^{\circ} \text{C}\). Applying the conversion formula: \( T_{b} = -183.0 + 273.15 = 90.15 \text{ K}\).

Step 3: Convert Freezing Temperature

The freezing temperature of oxygen is given as \(-218.4^{\circ} \text{C}\). Applying the conversion formula: \( T_{m} = -218.4 + 273.15 = 54.75 \text{ K}\).

Step 4: Summarize Findings

After conversion, the boiling point \( T_{b} \) of oxygen is \( 90.15 \text{ K} \) and the melting point \( T_{m} \) is \( 54.75 \text{ K} \).

Key Concepts

Celsius to Kelvin conversion

Converting temperatures from Celsius to Kelvin is a straightforward process, thanks to the formula: \( K = ^{\circ}C + 273.15 \). This might just seem like adding a number, but it's grounded in the history of temperature scales.

• Lord Kelvin developed this scale to ensure there were no negative numbers, making it ideal for scientific measurements.
• The Kelvin scale starts at absolute zero, which is \(-273.15^{\circ}\text{C}\), the point where atomic movement ceases.

So when you convert from Celsius to Kelvin, remember you're just adjusting to a scale that eases calculations by having no negatives.

oxygen boiling point

When it comes to understanding the boiling point of oxygen, we're looking at the temperature where oxygen transitions from liquid to gas. In Celsius, this happens at \(-183.0^{\circ}\text{C}\). By converting this to Kelvin, using \( T_b = -183.0 + 273.15 = 90.15 \text{ K} \), we present it in a universal scientific standard.

• The Kelvin temperature unit is crucial as it helps us understand thermal dynamics without the confusion of negative values.
• Oxygen's boiling point at \(90.15 \text{ K}\) is significantly below room temperature, explaining why oxygen is a gas under typical earthly conditions.

oxygen melting point

The melting point of a substance is the temperature where it transitions from solid to liquid. For oxygen, this point is extremely cold, at \(-218.4^{\circ}\text{C}\).
Using the conversion formula, this temperature in Kelvin is \( T_m = -218.4 + 273.15 = 54.75 \text{ K} \). This tells us that oxygen must be extremely chilled to exist as a solid.

• Oxygen solidifies at \( 54.75 \text{ K} \), indicating a state of matter that rarely occurs outside of specialized conditions on Earth.
• Melting point data is essential for industrial applications involving liquid or solid oxygen.

temperature in kelvin

The importance of measuring temperature in Kelvin lies in its absolute nature. Unlike Celsius and Fahrenheit, Kelvin begins at absolute zero, which is why it doesn't have negative temperatures.

• Using Kelvin, scientists and engineers benefit from a scale that aligns with the laws of thermodynamics and energy calculations.
• In disciplines like physics and chemistry, Kelvin provides a more natural context for temperature calculations, easing the conversion to energy and other related computations.

By expressing the boiling and melting points of gases like oxygen in Kelvin, we ensure consistency and precision in scientific discussion and experiments.