### Which of the Following Gas Law Relationships Is True?

Which of the Following Gas Law Relationships Is True?

Gas laws describe the behavior of gases, and they are essential in understanding various scientific and industrial processes. There are several gas laws, including Boyle’s law, Charles’s law, Gay-Lussac’s law, and Avogadro’s law. Each law relates different variables such as pressure, volume, temperature, and the number of gas particles. In this article, we will explore these gas laws and determine which of the following relationships is true.

1. Boyle’s Law:
Boyle’s law states that at a constant temperature, the volume of a gas is inversely proportional to its pressure. In simpler terms, if the pressure of a gas is doubled, its volume will be halved, and vice versa. Mathematically, this can be expressed as P1V1 = P2V2, where P1 and P2 are the initial and final pressures, and V1 and V2 are the initial and final volumes, respectively.

2. Charles’s Law:
Charles’s law states that at a constant pressure, the volume of a gas is directly proportional to its temperature. In other words, if the temperature of a gas is doubled, its volume will also double, and if the temperature is halved, the volume will be halved as well. Mathematically, this can be expressed as V1/T1 = V2/T2, where V1 and V2 are the initial and final volumes, and T1 and T2 are the initial and final temperatures, respectively.

3. Gay-Lussac’s Law:
Gay-Lussac’s law states that the pressure of a gas is directly proportional to its temperature, provided that the volume and the number of gas particles remain constant. This law implies that if the temperature of a gas is doubled, its pressure will also double, and if the temperature is halved, the pressure will be halved as well. Mathematically, this can be expressed as P1/T1 = P2/T2, where P1 and P2 are the initial and final pressures, and T1 and T2 are the initial and final temperatures, respectively.

Avogadro’s law states that equal volumes of gases, at the same temperature and pressure, contain an equal number of gas particles. This law implies that the volume of a gas is directly proportional to the number of gas particles, assuming the temperature and pressure are constant. Mathematically, this can be expressed as V1/n1 = V2/n2, where V1 and V2 are the initial and final volumes, and n1 and n2 are the initial and final number of gas particles, respectively.

Now, let us determine which of the following relationships is true:
a) Volume is inversely proportional to temperature.
b) Volume is directly proportional to pressure.
c) Pressure is inversely proportional to the number of gas particles.

The correct answer is b) Volume is directly proportional to pressure. This relationship is described by Boyle’s law. As mentioned earlier, Boyle’s law states that at a constant temperature, the volume of a gas is inversely proportional to its pressure. Therefore, as the pressure of a gas increases, its volume decreases, and vice versa.

FAQs:

1. What are the units used for pressure, volume, and temperature in gas laws?
Pressure is commonly measured in units such as pascal (Pa), atmosphere (atm), or millimeters of mercury (mmHg). Volume is typically measured in liters (L) or cubic meters (m³). Temperature can be measured in Celsius (°C), Fahrenheit (°F), or Kelvin (K).

2. How can gas laws be applied in real-life situations?
Gas laws have numerous applications in various fields. For example, in scuba diving, Boyle’s law is crucial in understanding how changes in pressure affect the volume of air in a diver’s lungs at different depths. Additionally, gas laws are used in the design of engines, such as internal combustion engines, where the expansion and compression of gases play a significant role.