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Helium gas is a colorless, odorless, and tasteless noble gas that is incredibly light and non-reactive. It is the second lightest element in the universe, right after hydrogen. Helium's non-reactive nature makes it an ideal gas for various practical applications like balloons, airships, and cooling systems for nuclear reactors.
Helium is used in this exercise as it is one of the stable inert gases, making the calculations primarily dependent on its compressibility and expansion characteristics according to gas laws. Understanding the behavior of helium gas can aid in solving similar problems by applying the principles of gas laws effectively.

Temperature conversion is essential for many scientific calculations, especially when dealing with gas laws. Most gas law equations require temperature to be expressed in Kelvin, as this absolute scale allows for calculations without negative numbers, which Celsius and Fahrenheit scales might involve.
To convert Celsius to Kelvin, we use the formula:

• \( T(K) = T(°C) + 273.15 \)

In the exercise, the initial temperature is given as \(25^{\circ} \mathrm{C}\). Converting it into Kelvin gives \(298 \mathrm{~K}\). This step is crucial, as failing to convert temperatures to Kelvin can lead to incorrect results in gas law calculations. Always remember to add 273.15 to Celsius temperatures for accuracy.
Understanding temperature conversion ensures that all measurements are in the correct unit before proceeding with any calculations.

Boyle's Law is an important principle of gas behavior that examines the relationship between pressure and volume, holding the temperature constant. It states that the pressure of a gas is inversely proportional to its volume, given the temperature remains unchanged. This relationship can be expressed as:

• \( P_1V_1 = P_2V_2 \)

This means if the volume decreases, the pressure increases, and vice versa, provided the amount of gas and temperature remain constant. While Boyle's Law isn't directly applied in the context of the given exercise since the pressure remains constant while the temperature changes, it lays the groundwork for understanding how changes in physical conditions like volume and pressure influence gas behavior.
By mastering Boyle's Law, you can accurately predict how a gas will behave if its container size or pressure is altered while maintaining a certain temperature.

The pressure and volume relationship in gases is a cornerstone of understanding their behavior under different conditions, prominently illustrated by Boyle's Law and other gas laws. In the scenario given, while employing Boyle's Law directly isn't required due to the constant pressure condition, grasping the general relationship aids in conceptualizing how gases respond to changes in volume.
Usually, in a closed system, if the volume reduces, the pressure should increase, and vice versa. However, in this exercise, we observe that the volume reduces due to the entry of ethanol into the vessel while maintaining a constant pressure. This implies an adjustment in temperature instead of pressure, illustrating the interplay between multiple variables (volume, temperature, and pressure) in gas behaviors.
Understanding this intricate balance helps in solving real-world problems efficiently, where factors such as temperature shifts and pressure changes yield accurate predictions of gas behavior.