A sample of \(\mathrm{CO}_{2}\) gas occupies a volume of \(125 \mathrm{~mL}\) at \(21^{\circ} \mathrm{C}\). If pressure remains constant, what will be the new volume if temperature changes to: (a) \(-5^{\circ} \mathrm{C}\) (b) \(95^{\circ} \mathrm{F}\) (c) \(1095 \mathrm{~K}\)

Understanding gas laws is crucial for grasping various phenomena in chemistry and physics. When dealing with gases, their behavior under different conditions of temperature, volume, and pressure needs to be predictable. One of the fundamental laws that describe the behavior of gases is Charles's Law. It is part of a broader category called gas laws, which also includes Boyle's Law, Gay-Lussac's Law, and the Combined Gas Law, among others. These laws are simplified models for gas behavior under various conditions.

Charles's Law specifically addresses how the volume of a given mass of gas changes in direct proportion to its temperature as long as the pressure remains constant. In other words, if you increase the temperature, the volume will increase, provided the pressure doesn't change. Conversely, a decrease in temperature leads to a decrease in volume. Understanding Charles's Law helps explain how hot air balloons rise and why car tires can become overinflated during hot days. The mathematical relationship Charles's Law provides is foundational for further explorations into thermodynamics and kinetic molecular theory.

The Kelvin scale is pivotal in the sciences because it is the absolute temperature scale used to measure thermodynamic temperature. Unlike Celsius or Fahrenheit, Kelvin starts at absolute zero—the point where particles have minimal thermal motion. Converting from Celsius to Kelvin is straightforward: simply add 273.15 to the Celsius temperature. For converting Fahrenheit to Kelvin, a two-step process is required: first, adjust Fahrenheit to the Celsius scale and then convert to Kelvin.

The process of converting Fahrenheit to Celsius involves subtracting 32 from the Fahrenheit figure, multiplying by 5/9, and then adding 273.15 to convert to Kelvin. Knowing how to perform these conversions correctly is essential when applying gas laws, as they require temperatures to be in the Kelvin scale. The need for the Kelvin scale arises because gas laws are based on proportional relationships between quantities like temperature and volume, which only make sense when a temperature of zero accurately represents zero kinetic energy of particles.

Charles's Law dictates a specific volume-temperature relationship for gases: the volume of a gas is directly proportional to its absolute temperature when pressure is held constant. This concept is best visualized on a graph, with the temperature in Kelvin on the x-axis and volume on the y-axis; the resulting line is a straight path signifying direct proportionality. This relationship is crucial in understanding how gases will behave under varying temperatures.

To put this into a mathematical context, Charles's Law is represented as \(\frac{V_1}{T_1} = \frac{V_2}{T_2}\), where \(V_1\) and \(T_1\) represent the initial volume and temperature, and \(V_2\) and \(T_2\) represent the final volume and temperature. When a problem involves changing temperatures and requires you to find a new volume or vice versa, this formula becomes your key to solving it. To use it effectively, remember to convert all temperatures to Kelvin and understand that as the temperature goes up, so does the volume, displaying the kinship between these two variables.