A cylinder with a moveable piston contains \(218 \mathrm{~mL}\) of nitrogen gas at a pressure of \(1.32\) atm and a temperature of \(298 \mathrm{~K}\). What must the final volume be for the pressure of the gas to be \(1.55 \mathrm{~atm}\) at a temperature of \(335 \mathrm{~K}\) ?

The ideal gas law is a fundamental equation in chemistry and physics that describes the relationship between the pressure, volume, temperature, and amount of an ideal gas. Ideal gases are hypothetical substances that perfectly follow the gas laws under all conditions of temperature and pressure. The law is often expressed as the formula: \[ PV = nRT \] where

• \( P \) is the pressure of the gas,
• \( V \) is the volume,
• \( n \) is the number of moles,
• \( R \) is the ideal gas constant (equal to 0.0821 L·atm/mol·K), and
• \( T \) is the temperature in Kelvin.

Gas pressure is defined as the force that the gas exerts on the walls of its container per unit area. It results from the collisions of gas particles with the container's walls. The unit of pressure in the International System of Units (SI) is the Pascal (Pa), but other units like atmospheres (atm), millimeters of mercury (mmHg), and torr are also commonly used. Pressure can be influenced by several factors, including the amount of gas (\( n \) moles), the temperature (\( T \) in Kelvin), and the volume (\( V \) in liters) of the container according to the ideal gas law. For instance, increasing the temperature or the number of gas particles while keeping the volume constant will increase the pressure.

Gas volume is the three-dimensional space occupied by a gas. It is commonly measured in liters (L), milliliters (mL), or cubic meters (m^3). According to the ideal gas law, the volume of a gas is directly proportional to the number of moles and temperature, and inversely proportional to the pressure. This relationship indicates that if a gas expands, its pressure will decrease if the temperature and number of moles remain constant. Conversely, compressing a gas by reducing its volume will increase its pressure.

Gas temperature is a measure of the average kinetic energy of the particles in a gas. Temperature is typically measured in degrees Celsius (°C) or Kelvin (K). One of the important principles to understand is that temperature must always be in Kelvin when working with the ideal gas law and its related concepts, as this is an absolute temperature scale. An increase in temperature will cause the gas particles to move more rapidly which commonly leads to an increase in pressure if the gas is in a closed system, or an increase in volume if the gas can expand.

To convert Celsius to Kelvin, add 273.15 to the Celsius temperature. Therefore, understanding how temperature affects gas behavior is vital for predicting and manipulating the changes that occur within a gaseous system.