Gas laws describe the behavior of gases in relation to pressure, volume, and temperature. They are fundamental in various scientific fields and everyday applications. Below are three practical examples of gas law problems along with solutions to illustrate how these principles can be applied in real-world scenarios.
In medical settings, syringes are frequently used to administer injections. The relationship between pressure and volume of air in the syringe can be explained using Boyle’s Law, which states that the pressure of a gas is inversely proportional to its volume at constant temperature.
Consider a situation where a 10 mL syringe is filled with air at a pressure of 1 atm. If the plunger is pushed to reduce the volume to 5 mL, what is the new pressure of the air inside the syringe?
Using Boyle’s Law:
The equation is:
P1 × V1 = P2 × V2
Substituting the values:
1 atm × 10 mL = P2 × 5 mL
Solving for P2:
P2 = (1 atm × 10 mL) / 5 mL = 2 atm
Thus, the pressure of the gas inside the syringe is now 2 atm when the volume is reduced to 5 mL.
Notes: In practical applications, this principle helps in understanding how gas behavior changes with volume adjustments.
The behavior of gases can be described using the Ideal Gas Law, which combines Boyle’s Law, Charles’s Law, and Avogadro’s Law. This law is crucial for various applications, including weather balloons, which expand as they rise in altitude due to decreasing pressure.
Imagine a balloon filled with helium gas at a temperature of 25°C (298 K) and a pressure of 1 atm. If the volume of the balloon is 2.5 L, what would be the volume of the balloon at a temperature of 0°C (273 K) while maintaining the pressure at 1 atm?
Using the Ideal Gas Law: PV = nRT
Since pressure remains constant, we can use Charles’s Law:
the relationship is V1/T1 = V2/T2
Substituting the values:
2.5 L / 298 K = V2 / 273 K
Solving for V2:
V2 = (2.5 L × 273 K) / 298 K = 2.3 L
Therefore, the volume of the balloon at 0°C while maintaining 1 atm pressure is approximately 2.3 L.
Notes: This example highlights how temperature changes can affect gas volume, which is critical for understanding meteorological phenomena.
In industrial applications, understanding the behavior of gases in closed containers is vital for safety and efficiency. When a gas is heated in a rigid container, the pressure increases. This scenario can be analyzed using a combination of Charles’s Law and Boyle’s Law.
Suppose a rigid container holds 20 L of nitrogen gas at 25°C (298 K) and 2 atm of pressure. If the gas is heated to 75°C (348 K), what will be the new pressure inside the container?
Using the Combined Gas Law:
the relationship is P1/T1 = P2/T2
Substituting the values:
2 atm / 298 K = P2 / 348 K
Solving for P2:
P2 = (2 atm × 348 K) / 298 K = 2.33 atm
Thus, the new pressure inside the container after heating to 75°C is approximately 2.33 atm.
Notes: Understanding the changes in pressure due to temperature variations in a closed system is essential for managing chemical processes safely.