Chemistry: Charles's Law (Gas Laws) with 2 example problems

TLDR;

This video explains Charles's Law, which demonstrates the direct relationship between the temperature and volume of a gas when pressure is held constant. It details how to use the law for calculations through examples and provides an overview of related gas laws.

• Charles's Law states that the volume of a gas is directly proportional to its temperature.
• Additional gas laws include Boyle’s Law, Gay-Lussac’s Law, Avogadro’s Law, and the Ideal Gas Law, which consider other variables such as pressure and amount of gas.

Definition of Charles's Law [0:00]

Charles's Law states that the volume of a gas is directly proportional to its temperature when the pressure is held constant. As the temperature of a gas increases, its volume also increases, and vice versa. This law can be mathematically expressed as V = kT, with V as volume, T as temperature in Kelvin, and k as a proportionality constant. The relationship can also be expressed as V/T = k, indicating that the ratio of volume to temperature remains constant.

Using Charles's Law to compare two situations (before and after) [1:47]

Charles's Law is often used to compare two conditions of a gas, termed as "before" and "after" states. This can be represented as V1/T1 = V2/T2, where V1 and T1 are the initial volume and temperature, respectively, and V2 and T2 are the final volume and temperature. This format allows for easy calculation of the unknown values when one condition is changed.

Example 1 [2:08]

In the first example, the volume of a hot air balloon is 2,800 m³ at 99 °C. To find the volume when the temperature drops to 80 °C, temperatures must be converted to Kelvin. With T1 at 372.15 K and T2 at 353.15 K, we apply the formula V1/T1 = V2/T2. By substituting the known values and solving for V2, we find that the new volume is 2,657 m³.

Example 2 [3:22]

The second example explores how hot a gas must be in Celsius to expand from 22.4 L at 0 °C to 25.0 L. Initially converting 0 °C to Kelvin gives T1 as 273.15 K. Using the relationship V1/T1 = V2/T2 and substituting the known volumes leads to the calculation of T2 = 304.9 K. Converting back to Celsius results in T2 being approximately 31.7 °C.

Other Gas Laws [4:42]

While Charles’s Law relates temperature to volume, other gas laws address different relationships in gaseous states. Boyle’s Law examines the relationship between pressure and volume, while Gay-Lussac’s Law covers pressure and temperature interactions. The combined gas law integrates these three variables (Temperature, Pressure, and Volume). Avogadro’s Law, meanwhile, focuses on the volume and the amount of gas present (in moles). The Ideal Gas Law fuses all four laws for comprehensive application. When solving gas-related problems, it is important to identify known and unknown variables to apply the appropriate gas law.