Question

Molecular motion is minimized at \(-273^{\circ} \mathrm{C}\). Oxygen goes from liquid to solid at \(-218^{\circ} \mathrm{C}\). After oxygen turns from liquid to solid, how much colder does it need to get for its molecular motion to be minimized?

Short answer

Answer: 55°C colder.

Step-by-step solution

Identify the given temperatures

We have the following given temperatures: - Molecular motion is minimized at -273°C - Oxygen goes from liquid to solid at -218°C

Calculate the difference in temperatures

To find how much colder oxygen needs to get after it turns from liquid to solid, we subtract the temperature when oxygen goes from liquid to solid from the temperature when molecular motion is minimized: \((-273°C) - (-218°C)\)

Perform the subtraction

Now, subtract -218 from -273: \((-273°C) - (-218°C) = -273°C + 218°C = -55°C\) So, after oxygen turns from liquid to solid, it needs to get 55°C colder for its molecular motion to be minimized.

Key concepts

States of Matter

Understanding the states of matter is fundamental when analyzing the properties of any substance, including oxygen. Matter exists in three primary states: solid, liquid, and gas. What distinguishes these states is the behavior of their molecules. In solids, molecules are tightly packed together, vibrating in place but not moving around, which gives solids a definite shape and volume. Liquids have molecules that are less tightly packed, allowing them to flow and take the shape of their container, yet they still have a fixed volume. Gases, on the other hand, have molecules that are far apart and move rapidly in all directions, filling any space available to them.

When a substance transitions from one state to another, we say it undergoes a phase change. This happens at specific temperatures and pressures. For instance, the exercise mentions that oxygen transitions from a liquid to a solid at -218^{circ} C. Such transformations are accompanied by changes in the molecular motion, as seen when solidification minimizes the extent of this motion due to the close packing of molecules.

Temperature Conversion

Temperature conversion is a crucial skill in many scientific fields, as different countries and disciplines use different temperature scales. The Celsius scale, denoted as °C, is widely used internationally and is the one mentioned in the exercise. However, the Kelvin scale is often used in scientific experiments to measure thermodynamic temperature. One key aspect of the Kelvin scale is that it starts at absolute zero, which is -273.15^{circ} C in Celsius and represents the theoretical point where molecular motion ceases.

To convert temperatures between scales, you need the appropriate conversion formulas. To convert Celsius to Kelvin, you add 273.15; thus, 0^{circ} C is 273.15 K. In conducting scientific temperature analysis, such conversions are indispensable, especially when they concern absolute temperature measurements, molecular motion, or reactions happening at extreme temperatures.

Properties of Oxygen

Oxygen is a diatomic molecule (O_2) and is a key element for life on Earth. It is typically found as a colorless, odorless gas at room temperature. However, under conditions of reduced temperature or increased pressure, oxygen can condense into a blue liquid and eventually solidify. As mentioned in the problem, oxygen becomes a solid at around -218^{circ} C. This property, like many others, is influenced by the temperature as it affects the kinetic energy and interaction of oxygen molecules.

The ability of oxygen to exist in different states is particularly important in industrial applications such as the storage and transportation of liquid oxygen. Understanding the properties and behavior of oxygen under various temperatures is crucial for safety and efficiency in its use, making exercises such as the one presented valuable for students exploring physical science and engineering topics.