A sample of nitrogen gas in a 1.75-L container exerts a pressure of 1.35 atm at 25 C. What is the pressure if the volume of the container is maintained constant and the temperature is raised to 355 C?

Gas laws are a set of scientific principles that define the behavior of gases. They describe the relationships between volume, temperature, and pressure of a gas under certain conditions. One of the fundamental gas laws is Charles's Law, which focuses on the relationship between temperature and volume, holding pressure constant. An extension to this can be applied when volume is constant to show a direct relationship between temperature and pressure, which is exactly what we explored in the exercise with nitrogen gas.

When studying gas laws, it's important to remember that these relationships assume ideal gases, which is an idealization for educational purposes. Real gases follow these laws closely under a range of conditions but can deviate at high pressures or low temperatures.

Temperature plays a vital role in the behavior of gases, and in gas law problems, we always use Kelvin as the unit for temperature. The Kelvin scale is known as the absolute temperature scale because it starts at absolute zero, the lowest possible temperature where particles theoretically stop moving.

To convert Celsius to Kelvin, which is crucial in problems involving Charles's Law, you use the formula: \
\( Kelvin = Celsius + 273.15 \). This ensures that all temperature values are in the same unit and reflect the true proportionality that the gas laws describe. Remember, forgetting to convert temperatures into the correct scale can lead to incorrect results in your calculations.

In scenarios where we keep the volume of a gas constant but change its temperature, there is a direct relationship between pressure and temperature. This is a special case of Charles's Law, reflected in the following mathematical expression:

\
\( P1/T1 = P2/T2 \)

Here, P1 and T1 are the initial pressure and temperature, while P2 and T2 are the final values after the change. When the temperature increases, and the volume doesn't change, the pressure also increases because the gas particles move faster and hit the walls of the container with greater force. Conversely, if the temperature drops, the pressure does as well, assuming constant volume. It's a simple yet powerful concept crucial for understanding how gases will behave under controlled conditions.